./ncan C. Wyllie/"ai, Golder Associates, Consulting Engineers, Vancouver, Canada

Foreword by Richard E. Goodmanessor of Geological Engineering, University of California, Berkeley,,~,._..

Hall _

London' New York Tokyo' Melbourne' Madras

';2!.j15y,

./s(1-- tIL - r

AUpgf

.

Contents.

>IntroductionForeword

'NotationNote

1 Characteristics of rock foundations1.1 Types of rock foundation f"

1. J.l Spread footiIigs1.1.2 Socketed piers1.1.3 Tension foundations

1.2 Performance of foundations on rock1.2.1 Settlement and bearing capacity failures1.2.2 Creep.1.2.3 Block failure1.2.4 Failure of socketed piers and tension anchors1.2.5 Influence of geological structure1.2.6 Excavation methods1.2',7 Reinforcement

1.3 Structural loads1.3,1 Buildings1.3.2 Bridges1.3.3 Qag:ts1.3.4 Tension foundationsAllowable~ettlement1.4,} Buildings1.4..2 Bridges .

1.4.3 Dams1.5 Influence of ground water on foundation performance

1.5.1 Dams1.5.2 . Tensioned anchors

1.6 Factor of safety and reliability analysis1.6.1 Factor of safety analysis1.6,2 Limit states design1.6,3 Sensitivity analysis /1.6.4 CoefficienT of reliability

1.7 References

xixiiixiv

xviii

1124444557777899

101010101112121414141516161721

vi Contents -i2 Structural geology

23

2.1 Fracture characteristics23

2.1.1 Types of fracture23

2.1.2 Fracture orientation and dimensions25

2.2 Orientation of fractures26

2.3 Stereographic projection27

2.3.1 Pole plots29

2.3.2 Pole density30

2.3.3 Great circles32

2.4 Types of foundation failure33

2.5 Kinematic analysis35

2.5.1 Planar failure37

2.5.2 Wedge faitures37

2.5.3 Toppling failures'37

2.5.4 Friction cone37

2.6 Probabilistic analysis of structural geology39

2.6.1 Fracture orientation39

2.6.2 Fracture length and spacing40

2.7 References41

3 Rock strength and deforrnability42

3.1 Range of rock strength conditions42

3.2 Deformation modulus44

3.2.1 Intact rock modulus,45

3.2.2 Stress-strain behaviour of fractured rock47

3.2.3 Size effects on deformation modulus48

3.2.4 Fracture spacing and modulus50

3.2.5 Modulus of anisotropic rock51

3.2.6 Modulus/rock mass quality relationships52

3.3 Compressive strength53

3.3.1 Compressive strength of intact rock54

3.3.2 Compressive strength of fractured rock56

3.4 Shear strength58

3.4.1 Mohr-Coulomb materials59

3.4.2 Shear strength of fractures59

3.4.3 Shear strength testing63

3.4.4 Shear strength of fractured rock64

3.5 Tensile strength~8

3.6 Time-dependent properties69

3.6.1 Weathering69

3.6.2 Swelling "70

3.6.3 Creep71

3.7 References73

4 Investigation and in situtestillg Uiethods77

4.1 Site selection . ' '.77

4.1.1 Aerial and terrestial photography78

23232325262729303233353737373739394041

42424445474850515253545658595963

rs6969707173

777778

4.1.2 GeophysicsGeological mapping4.2.1 Standard geology descriptions

.4.2.2 Fracture mappingDrilling4.3.1 Diamond drilling4.3.2 Percussion drilling4.3.3 Calyx drillingGround water measurements4.4.1 Water pressure measurements4.4.2 Permeability measurements

. In situ modulus and shear strength testing4.5.1 Modulus testing4.5.2 Direct shear testsReferences

Bearing capacity, settlement and stress distributionIntroductionBearing capacity "\5.2.1 Building codes5.2.2 Bearing capacity of fractured rock5.2.3 Recessed footings5.2.4 Bearing capacity factors5.2.5 Foundations on sloping ground5.2.6 Bearing capacity of shallow dipping bedded formations5.2.7 Bearing capacity of layered formations5.2.8 Bearing capacity of karstic formationsSettlement5.3.1 Elastic rock5.3.2 Transversely isotropic rock5.3.3 Inelastic rockStress distributions in foundations5.4.1 Isotropic rock5.4.2 Layered formations5.4.3 Transversely isotropic rock5.4.4 Eccentrically loaded footingsReferences

Stability of foundations.6,1 Introduction:k.7 Stability of sliding blocks..;3 Stability of wedge blocks;t~f Three-dimensional stability analysis-.:'ig~ Stability of toppling blocks /

.~6:6 . Stability of fractured rock fuasses'j6fl . Seismic design'"Q,8 . References

Contents vii

8081838790909394949598

101101110111

114114116116117120120120122124126128129134136137138142142143145

147147147153155156160162164

viii Contents

7 Foundations of gravity and embankment dams7.1 Introduction

7.1.1 Dam performance statistics7.1.2 Foundation design for gravity and embankment dams7.1.3 Loads on dams7.1.4 Loading combinations

7.2 Sliding stability7.2.1 Geological conditions causing sliding7.2.2 Shear strength7.2.3 Water pressure distributions7.2.4 Stability analysis7.2.5 Factor of safety7.2.6 Examples of stabilization

7.3 Overturning and stress distributions in foundations7.3.1 Overtuming7.3.2 Stress distributions in foundations

7.4 Earthquake response of dams7.4.1 Introduction7.4.2 Sliding stability and overturning' under seismic loadS7.4.3 Finite eleme'nt analysis7.4.4 Displacement analysis

75 Preparation of rock surfaces7.5.1 Shaping

.fP' 7.5.2 Cleaning and sealing...' 75.3 Rebound

7.5.4 Solution cavities7.6 Grouting and drainage

7.6.1 Grouting functions7.6.2 Grout types7.6.3 Mechanism of grouting7.6.4 Drilling method7.65 Hole patterns7.6.6 Grout mixes7.6.7 Grout strength7.6.8 Grout pressures7.6.9 Grouting procedures7.6.10 Penneability criteria for grouted rock7.6.11 Monitoring grouting operations7.6.12 'Leaching7.6.13 Drainage

7.7 References'

r 8 Rock-socketed piersi 8.1 Introduction . ,,/i\ 8.1.IJ"ypesbf deep fou~1ations

8.1.2 Investigationsforsoeketedpiers" 8.2 Load capacitYQfsoclcete~pief~>i~9(5mpression

165165166167168169169170170170172175175177178178181181182184185187187188189189190.190191191193193195195196196197199199200201

205205205205207

../.

I

165165166167168169169 '170170170172175175177178178181181182184185187187188189189190190191191193193195195196196197

,199199200201

205,205205205207

Mechanism of load transferShear behaviour of rock socketsFactors affecting the load capacity of socketed piers

;2';4 Socketed piers in karstic formations'~sign values: Side-wall resistance and end bearingh.l Side-wall shear resistance'3.2 End-bearing capacity

"'i~1 deformation'j Settlement mechanism of socketed piers;2 Settlement of side-wall resistance sockets'

'':3 Settlement of end-loaded piers';4 Settlement of socketed, end-bearing piers:5 Socketed piers with pre-load applied at base

plift;;;.1 Uplift resistance in side-wall shear';5.2 Uplift resistance of belled piers:literally loaded socketed piers;:(';.1 Computing lateral deflection with p-y curves;6.2 Socket stability under lateral load'eferences

l;rision foundations'Iltroduction"nchor materials and anchorage methods/9.2.1 Allowable working loads and safety factors'9.2.2 Steel relaxation).2.3 Strength properties of steel bar and strand,,9.2.4 Applications of rigid bar anchors;\ 9.2.5 Applications of strand anchors,;'9.2.6 Cement grout anchorage

9.2.7 Resin grout anchorage""9.2.8 Mechanical anchorage

Design procedure for tensioned anchors9.3:1 Mechanics of load transfer between anchor, grout and rock9.3.2 Allowable bond stresses and anchor design~c~9;3.3 Prestressed and passive anchors

9.3.4 Uplift capacity of rock anchors'9.3.5 Group action

, .. 9.3.6 Cyclic loading of anchors9.3.7 Time-dependent behaviour and creep9.3.8 Effect of blasting on anchorage

:*-;;9.3:9: Anchors in permafrost"'Corrosion protection~:c9.4.l Mechanism ofcorrosion

," 9.4:2 Types of corrosion ./904.3 Corrosive conditions9.4.4 Corrosion-protection methods

Contents ix

207209210217217218218219219221222223226227228228228229234236

238238240241241243243247247251253254254256260261268268268269270271271273274274

,.. -;'. '"~

319323326329

276277277280281

283283283284286289289291297-'295295

'297299299303

"305-305307307307307309309310310310310311312313317

Stereonets for hand plotting of structural geology dataFieldmapping data sheetsConversion factors

AppendixlAppendixn 'AppendixUlIndex ,-

10 Construction methods10.1 Introduction10.2 Drilling

10.2.1 Diamond drilling10.2.2 Percussion drilling10.2.3 Rotary drills10.204 Overburden drilling10.2.5 Large-diameter drilling10.2.6 Directional drilling

10.3 ,Blasting and non-explosive rock excavationiO.3.1 Rock fracture by explosives10.3.2 Controlled blasting10.3.3 Blasting horizontal surfaces10.304 Ground vibration control10.3.5 ' Vibration in uncured concrete10.3.6 Non-explosive excavation

lOA Bearing surface improvement and rock reinforcement1004.1 Trim blasting1004.2 Surface preparation1004.3 Dental concrete100404 Shotcrete1004.5 Pins1004.6 Rock bolts1004.7 Tensioned rock anchors1004.8 Concrete buttress1004.9 Drain holes

10.5 Contracts and specifications10.5.1 Components of contract documents10.5.2 Types of contract10.5.3 Rock excavation and reinforcement specifications

10.6 'References

9.5 Installation and testing9.5. I Water testing9.5.2 Load testing9.5.3 Acceptance criteria

9.6 References

Contents

LOI

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'troduction

"dations on Rock has been written to fill an apparen t gap in the geotechnical engineer'iterature. Although there is wide experience and expertise in the design and con-'\ion of rock foundations; this has not, to date, been collected in one volume, ',A'ble reason for the absence of a book on rock foundations is that the design andtruction of soil foundations is usually more challenging than that of rock foundations.

'sequentially, there is a vast collection of literature on soil foundations, and a tendencyssume that any structure founded on 'bedrock' will be totally safe against settleme)lt and*bility. Unfortunately, rock has a habit of containing nasty surprises in the form oflogical features such as solution cavities, variable depths of weathering, and clay-filled

'Its. All of these features, and many others, can result in catastrophic failure of'jl

"i!)ir:

xii Introduction

There are many people who have made specific contributions to this book and theirassistance is greatly appreciated. Sections of the book were reviewed by Herb Hawson,Graham Rawlings, Hugh Armitage, Vic Milligan, Dennis Moore, Larry Cornish, NormNorrish and Upu! Atukorala. In addition a number of people contributed photographs andcomputer plots and they are acknowledged in the text. Important contributions were alsomade by Ron Dick who produced all the drawings, and Glenys Sykes who diligentlysearched out innumerable references. Finally, I appreciate the support of my family whotolerated, barely, the endless early-morning and late-night sessions that were involved inpreparing this book.

D.C. Wyllie

I

book and theirHerb Hawson,Cornish, Normhotographs andtions were alsowho diligentlymy family whoere involved in

D.C. Wyllie 310 Wyllie has given us a complete, useful textbook on rock foundations. It is complete;eoverage of all parts of this important subject and in providing reference material forW-up study. It is eminently useful in being well organized, clearly presented, andaI.

6Ck would seem to be the ultimate excellent reaction for engineering loads, and often it'ut the term 'rock' includes a variety of types and conditions of material, some of which'~Ilrely not 'excellent' and some that are potentially dangerous. Examples of frequentlyrdous rock masses are ,those that contain d~solved limestones, undermined coal-

iing sediments, decomposed granites, swelling shal~s and hIghly jointed or faulted~t~' or slates. Moreover, the experience record of construction in rocks includeserous examples of economic difficulties revolving around mistaken or apparentlyvolent behaviour of rock foundations. Such cases have involved excavation overbreak,rioration of prepared surfaces, floodin 0 kin b roundwater see a e, accumulationoulders from excavation, gullyin or i in - f erodible banks,. and misclassification or

'identification of materials in the weathered zone. Another class of difficult problems:"olve the forensic ide of siting in evaluating potentialities for rock slides, fault move-ents, or long-term behaviour. '

,'Problems of investigating andcharacterizing rock foundations are intellectually chal-~nging; and it may require imagination to tailor the design of a foundation to the particularorphological, structural and material properties of a given rock site. Thus the field ofngineering activity encompassed in this book is interesting and demanding. The subject is

.,Worthy of a book on this subject and of your time in studying it.Richard E. Goodman

Berkeley,California

.. ~

Ij

I

The following symbols are used in this book.a Earthquake acceleration (fraction of gravity acceleration), correction

factor in settlement calculation.Area of sliding plane, cross-sectional area of drill hole casing (m2 , ft2,in2).Moment arm (m, ft).Surface area of cone (m2, ft2).Cross-seciional area of drill hole (mm2, in2).width (m, ft) ..Footing width, pier diameter (m, ft).Burden distance in blast hole layout (m, ft).Cohesion (MPa, p.s.i.).Factor in settlement calculation.Constant in plate load test analysisDispersion coefficient, factor in settlement calculation.Factor in calculation of hydrodynamic force on damCorrection factors for foundation shapeSeismic coefficient.Diameter (m, ft).Depth of socketed pier, pipe, rock anchor (m, ft).Anchor diameter (m, ft).Explosive diameter (m, ft).Drill hole diameter (m, ft).Equivalent core diameter.Eccentricity in stress distribution along foundation.Deformation modulus of concrete (GPa, p.s.i.).Deformation modulus of rock mass in base of pier (GPa, p.s.i.).Deformation modulus of rock mass in shaft of pier (GPa, p.s.i.).Deformation modulus of rock mass (GPa, p.s.i.).

.Deformation modulus of intact rock (GPa, p.s.i.).Factor of safety.Driving force (N, Ibf).Resisting force (N,Jef).Resistence factors.Load factors.

A

c'

Notation

CC.CeCn, C'2

. Cs

dDd.d,dbDee

EeEm(blEm(s)EmE,FI.I,1$. Ielu,/oL./LL

.tion), correction

Pa, p.s.i.).Pa, p.s.i.).

pXc'K'. T

. '1(,ILI.I,m

M1t!enNNc,Ny, Nq, NuNo, N~p, PultPPo

Notation xv

Distribution function.Shape factor in permeability measurement.Factor in calculation of stress distribution in anisotropic rock, gravityacceleration (mls2 , ftlsec2).Shear deformation modulus of intact rock (OPa, p.s.i.).Shear deformation modulus of rock mass (OPa, p.s.i.).Factor in calculation of shear strength of fractured rock, and stressdistribution in anisotropic rock.Height, thickness of slab (m, ft).Head of water, height of water on dam face (m, ft).Constant water head in permeabiliiy test (m, ft).Inclination of asperities, roughness angle (degrees).Influence factor.Hydraulic gradientPoint load index.Empirical factor in analysis of socketed piers.Permeability (mlsec).Bulk modulus (OPa, p.s.i.).Rock stiffness of rock in base, shaft of socketed pier (OPalm, p.s.Uin).Hydrodynamic pressure coefficient, constant in blast vibrationcalculations.Normal stiffness (OPalm, p.s.i.lin).Shear stiffness (OPalm, p.s.i.lin).Rankine earth pressure coefficient.Critical horizontal acceleration (mls-Z, ftls- Z).Factor in seismic (geophysical) investigations.Factor for construction type in seismic design.Direction cosine.Length of unbonded socket, drill hole, outcrop, footing (m, ft).Bond length (m, ft).Free stressing length (m, ft).Rock mass strength parameter, direction cosine.Moment (Nm, Ibf tt).Moment due to earthquake force (Nm, ft lbi).Direction cosine.Number of analyses, poles, fractures.Bearing capacity factors.Stability numbers.Resistence of soil for laterally loaded pier (Nlm, Ibflft).Probability of occurance, proportional ratio.Force on side of block (n) in toppling failure (N, lbi).Bearing pressure (Pa, p.s.i.).Foundation load (N, Ibi).Allowable bearing pressure (Pa, p.s.i.).Horizontal hydrodynamic force due to earthquake (N, lbf).Inertial force due to earthquake (N, lbf).Seepage volume per unitiime (rnOlsec, gallmin);

xvi Notation

QurRReSSITIeUUvVWeWWeW~WeXyZZa

p2"t."twIiALias.Axte

"V1\pa(Ju(r)(J'u(m)auea.aval

Net upward bearing capacity (N, Ibf).Radius (m, ft).Radial distance (m, ft), modulus ratio.Radial distance from blast (m, ft).Rock mass strength parameter.Fracture spacing (m, ft).Time (s).Basic time lag in permeability tests, factor in seimic testing (s).Earthquake period (s).Uplift pressure (Pa, p.s.i.), relative velocity (mis, ftlsec).Uplift force (N, Ibf).Velocity (m/sec, ftlsec).Water force (N, lbf).Mass of explosive per unit length of blast hole (kg/m, Ibm/ft).Weight of dam, sliding, toppling block (N, Ibf).Weight of rock cone (N, lbf).Weight of truncated rock cone (N, Ibf).Mass of explosive per delay (kg, Ibm).Distance along rock bolt, sliding plane, socketed pier (m, ft).Velocity, deformation, distance down pier.Factor for seismic design.Radial distance (m, ft).Dip direction of plane, trend of line, angle between face and strike offracture (degrees).Factor in blast vibration design.Angle between fracture and stress direction, base angle in toppling failure(degrees).Settlement calculation factor.Density of rock (N/m" Ibf/ft3).Densi.y of water (N/m3 , Ibf/ft3).Settlement, closure (mm, in).Displacement in radial jacking test (mm, in).Relaxation stress loss (Pa, p.s.i.).Width of toppling block (m, ft).Strain.Angle, apex angle of cone (degrees).Micro.Poisson's ratio.Viscosity (Nsm-2 , lbf sec in-2).Pump constant.Normal stress (Pa, p.s.i.).Unconfined compressive strength, intact rock (Pa, p.s.i.).Unconfined compressive strength, rock mass (Pa, p.s.i.).Unconfined compressive strength, concrete (Pa, p.s.i.).Radial stress (Pi, p.scf.).Overburden pressure (Pa, p.s.i.).Major principal stress. (Pa, p.s.i.).

I

.ng (s).

m/ft).

I, ft).

:e and strike of

toppling failure

Notation xvii

Minor principal stress (Pa, p.s.i.).Tensile stress, strength (Pa, p.s.i.).Shear stress (Pa, p.s.i.).Friction angle (degrees).Dip angle of plane (below horizontal), plunge of line (degrees).Optimal dip of tensioned anchors (degrees).Settlement inclination angle (degrees) .Factor in rock bolt anchor stress distribution.

Note

The recommendations and procedures contained herein are intended as a general guide andprior to their use in connection with any design, report or specification they should bereviewed with regard to the full circumstances of such use. Accordingly, although everycare has been taken in the preparation of this book, no liability for negligence or otherwisecan be accepted by the author or the publisher.

-

eneral guide andI they should be, although every,nce or otherwise

;ypes of rock foundationf'are two distin&.uishing features of founda-n roc~FffSl,lhe ability of the rock to wIth-

')lIuch higher loads than sol!, and second,efects in the rock which. result in

n th of the rock mass beiJ.lg considerablyan that of the intact rock. The compressiveh of rock may range from less tfiaii""51ViPa.s.i.) to moretnan' a 30000 .s.i.),here the roc IS stron substantial I ads can

orted on small s read foot' . However,I{~e low-strength fracture oriented in a parti-

"(directIon may cause sliding failure of the. oun at .,/:r- .ability of rock to sustain significant shear

'nsile loads means that there are many types'~ctures that can be constructed mOre readily.ck than they can be on soil. Examples ofstructures are dams and arch bridges which.ce inclined 19ads in the foundation, theorages for. suspension bridges and other tie-

anchors which develop uplift forces, and"!socketed piers which. support substantialsjn both compression and uplift. Some ofe loading conditions are illustrated in Fig. 1.1

~shows the abutment of an arch bridge. The"jjg-for the arch has an inclined load, while the

'~and the abutment have vertical loads; the.~l'acity of these footings depends primarily.e:'coinpressive and shear strength..oHhe rock,The wall supporting the cut below the

'W-ellt is anchored with tensioned and grouted

1Characteristics ofrock foundations

rock bolts; the load capacity of these bolts dependsupon the shear strength developed at rock-groutinterface in the anchorage zone.

If the material forming the foundations of thebridge shown in Fig. 1.1 was strong, massive,homogeneous rock with properties sImilar to con-crete, design and construction of the footingswould be a trivial matter, because .the loadsapplied by a structure are generally much lessthan the rock strength. However, rock almostalways contains fractures that can range fromjoints with rough surfaces and cohesive infillingsthat have a relatively high shear strength, tomassive faulted zones containing expansive, lowstrength clay's. Figure 1.1 shows how the geo-logical structure can affect the stability of thefoundations. First, there is the possibility of over-all failure of the abutment along a failure plane(aa) passing through both the fault;" and intactrock at the toe of the slope. Second, local failure(b) of the foundation of the vertical column couldoccur on joints dipping out of the slope face.Third, settlement of the arch foundation mayoccur as a result of compression of weak materialsin the fault zone (c). Fourth, weak and fracturedrock in the bolt anchor zone could result infailure of the bolts (d) and loss of support of theabutment.

Foundations on rock can be classified into three"An example of the influence of structural

geology on stability is shown in Fig. 1.3- where a

ock bolts.

on very strong graniteos dipping at about 40';h the bearing capacityr this loading coIidition,-ts and failure of a block:..the wall. Fortunately,onditionallowed reme-'It. This work comprised'rced concrete wall to':-k, -and the installation'

Vd bolts to prevent further movementts.

hre of socketed piers and tension

of socketed piers is usually limited,., table movement which may occur'of loss of bond at the rock/concreten the side walls, or compression of'a! at the base of the pier. A frequentvement is poor Cleaning of the sides

'gf tbe hole. In the case of tensioned:ss of bond at the rock/grout interface

:Wls of the hole may result in gradual"por! and eventually excessive move-ernatively, sudden failure may occur. of corrosion failure of the steel. The'reliability of tensioned anchors de-It large degree on the. details of fabri-

. installation procellflies as discussed9.

hence of geological structure'rations of foundation conditions shown'.1 and 1.3" and the analysis of foun-'lures, show that geological structure

y a significant feature influencing theand construction of rock foundations.

knowledge of fracture characteristics -)on, spacing, length, surface features)ling properties - are all essential infor-,tequired for design. The examination ofctural geology of a site usually requires~-dimensional analysis which can mostiently be carried out -using stereographiclpns as described in Chapter 2. This tech-

: an be used to identify the orientation and'of blocks in the foundation that may failjp,g.ortoppling...also necessary to determine the shear

;offractures along which failure ,could1,~.This involves direct shear tests, whiche:carried out in the laboratory on-Pieces ofE}(lsitu on undisturbed samples. Methods-

.;dJesting are described in Chapter 4.

Stability of foundations on rock 7

1.2.6 Excavation methodsBlasting is often required to excavate rock foun-dations and it is essential that controlled blastingmethods be used that minimize the damage torock that will support the planned structure.Damage caused by excessively heavy blastingcan range from fracturing of the rock with aresultant loss of bearing capacity, to failure ofthe slopes either above or below the foundation.There are sometimes circumstances, when, forexample, existing structures are in close pro-ximity or when excavation limits are precise,in which blasting is not possible. In these situa-tions, non-explosive rock excavation methods,which inClude hydraulic splitting, hydraulichammers and expansive cement, may be justifieddespite their relative expense and slow rate ofexcavation.

The effect of geologica!' conditions on foun-dation excavations is shown iIi Fig. 1.4 wherethe design called for a notch to be cut in stronggranite to form a shear key to resist horizontalforces generated in the backfill. However, thebearing surface formed along pre-existing jointsand it was impractical to cut the required notch.Consequently, dowels were installed to anchorthe wall. Only in very weak rock is it possibleto 'sculpt' the rock to fit the structure, and eventhis _may be both expensive and ineffective.

Methods of rock excavation are discussed indetail in Chapter 10.

1.2.7 ReinforcementThe reinforcement of rock to stabilize slopesabove and below foundations, or to improvebearing capacity, has wide application in rockengineering. Where the intact rock is strongbut contains fractures which form potentially un-stable blocks, the foundation can be reinforcedby installing rigid bolts or cables across the fail-ure plane. The function of such reinforcementis to apply a normal stress across the slidingsur-face which increases the frictional resistallce onthe surface; the shear strength of the steel barprovides little-support in comparison to the fric-

lUIth,19ba,selnifbestyft3;Th,ablpro

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Aseislstrwsno\tane

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nt}ineJfaa&10ofco

(9~:.

tion component of the rock strength. Anotherfunction of the reinforcement is to preventloosening of the rock mass because reductionin the interlock between blocks results in a sig-nificant reduction in rock mass strength.- Where the rock is closely fractured, pumpingof cement grout into holes drilled into the foun-dation can be used to increase the bearing ca-pacity and modulus. The effect of the grout isto limit both interblock movement and closureof fractures under load. Protection of closelyfractured or faulted rock from weathering anddegradation that may reduce bearing capacityor undermine a foundation can be provided byapplying shotcrete - pneumatically applied, fineaggregate concrete.

Methods of construction and rock reinforce-ment are discussed in Chapter 10.

1.3 Structural loadsThe following is a summary of typical loading .'conditions produced by diffet~lJt+ypes of struc-tures based on United State~6iiildlngcodes anddesign practices (Merritt, 1916). The designinformation required oni.leading conditions con-sists of the magnitude' of both the dead and liveloads, as well as the direction and point of appli-cation of these loads. This information is thenused to calculate the bearing pressure and anyoverturning moments acting on the foundation.

An important aspect in foundation design iscommunication between the structural and foun-dation engineers on the factors of safety that;are incorporated in each part of the design. If.the structural engineer calculates the dead and .live loads acting on the foundation and multiplies, 'this by a factor of safety, it is important that the.foundation engineers do not apply their own:factors of safety. Such mUltiplication of factorS"of safety can result in overdesigned and expen;'.sive foundations. Conversely,-failure toincor%;porate adequate factors of safety can result inlunsafe foundations. A description of methods oK_.calculating loads imposed by structures on the]foundation (this is usually the responsibility of .~the structural engineers) is beyond the' scope

Design: wallnotched intorock

Asbuilt" wallanchored to slopingrock surface

",' .

.. ' .....

:..... ': ..... ,' .. .. "&

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. .: ""... ".: ..

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. : ' ... '.,:- ...' .. ' '. '..::' . : .' . '., ' ..

... , . . . ..

... .' ..

Traffic~ load

. :: ... ":.'.:'"

8 Characteristics of rock foundations

(a)

(b)............, .. '....... '-.-,. '-'-C'-,"

Figure 1.4 'Construction of rOcldoundatiojE(a) attempted 'sculpting' of rock fourtdation to form'shear key, and (b) 'as-built' condition.: .

,ck strength. Anotherement is to prevent'ass because reduction:blocks results in a sig.'mass strength.:ly fractured, pumping,s drilled into the fauncrease the bearing ca'effect of the grout is

novement and closureProtection of closely,from weathering and

duce bearing capacity,m can be provided by.matically applied, fine

on and rock.pter 10.

lary of typical loading"lifferent types of struc-ates building codes ant, 1976). The designloading conditions' can'both the dead and live

etion and point of appli 'ilis information is then'aring pressure and anylng on the foundation.'.n foundation design i~the structural and foun '

factors of safety tha~I part of the design. Icalculates the dead and,undation and multiplies:it is important that the'

l not apply their ownnultiplication of factorS'verdesigned and expen",rsely, failure to incor7;,of safety can result in',

:scription of methods of,:d by structures on the;Ily the responsibility oC) is beyon

10 Characteristics of rock foundations

In thethat theindicator

(b). Ii

~FIgure t.!buildings(b) settlelat i; Pmax idisplacemapart lij; .1maximumtwo refererotation;

is the angtthe appro:

(a)

tural meoften th,

, 'angularcritical irresultedgular disbuildings1956; ani

P> 1P>1

\I

P< 1c

forces generated by submerged tanks and thetension in suspension bridge cables and trans-mission lines. Alternatively, the .foundation maybe designed to resist uplift forces generated by ,overturning moments acting on the structure re-sulting from horizontal loads such as wind, ice,traffic and earthquake forces.

1.4 Allowable settlementUndoubtedly the most famous case of founda-tion settlement is that of the Leaning Tower ofPisa which has successfully withstood a differ-ential settlement of 2 m and is leaning at an angleof 5 11' (Mitchell, Vivatrat and Lambe, 1977).However, this situation would not be tolerated inmost structures, except as tourist attractions! Thefollowing is a review of allowable settlementvalues for different types of structures.

ing as the span length increases. Methods of cal-culating impact loads vary with the span length,method of construction and the traffic type.Other forces that may affect the foundations arecentrifugal forces resulting from traffic motion,wind, seismic, stream flow, earth and ice forces,and elastic and thermal deformations. The mag-nitude of these forces is evaluated for the par-ticular conditions at each site.

1.3.3 DamsLoads on dam foundations are frequently ofmuch greater magnitude than those on bridgeand building foundations because of the size ofthe structures themselves and the forces exertedby the water impounded behind the dam. Thewater forces are usually taken as the peak maxi-mum flood (PMI'), with an allowance for aq::umu-lations of silt behind the dam, as appropriate.Any earthquake loadings can be simulated mostsimply as a psuedostatic force proportional tothe weight of the dam. The resultant of theseforces 'acts in' a downstream direction, and thedam must be designed to resist' both slidingand overturn1ngunder this loading condition.There' may also be concentrated compressivestresses at the toe of the dam and it is necessaryto check that these stresses do not cause excessivedeformation.

,A significant difference between dams andmost other structures is the water uplift press-ures.,that are generated within the foundations.In most cases there are high pressure gradientsbeneath the lieel'of the dam where drain holesand grout curtains are installed to relieve waterpressures' and' control seepage. The combina-tion of these load conditions, together with thehigh degreeofSafet{required fdr imy dam, re-quires that the investigation, design and con-struction of the foundation be both thoroughalid comprehensive,

1.4.1 BuildingsSettlement of building foundations that is in-sufficient to cause structural damage, may stillbe unacceptable if it causes significant crackingof architectural elements. Some ".o{'the factorsthat can affect settlement are the size and typeof structure, the properties of the structuralmaterials and the subsurface soil and rock, andthe rate and uniformity of settlement., Becauseof these complexities, the settlement that will.'j.cause significant cracking of structural members"or architectural elements, or both, cannot readilybe calculated. Instead, almost all criterea fortolerable settlement have been established em-pirically 'on the basis of, observations of settle-ment and damage in existing bUildings (Wahls,1981).

Damage due to settlement is usually the result "of differential settlement, i.e. variations in ver- ,tical displacement at different locations in the ~building, rather than the absolute ~settlement.:,

, Means of defining both differential and absolute';.1.3.4 Tension foun"da,tions ,settlement are illustrated in Fig. 1.5, together

- with'the terms defining the various components ';Typical loads on tens[onfd\.lltd#ions'consistof of settlement.the dead load of the stntettrr :sucll.asbuoyancy Study of cracking of walls, floors and stmc-

\

Allowable settlement 11

direct and diagonal tension developed in thewall as a result of bending (Burland and Wroth,1974). The proposed limiting values of AILfor design purposes are in the range of 0.0005to 0.0015.

L

-------8

efinition of settlement terminology forahls, 1981): (a) settlement without tilt;

'itt with tilt. Pris the vertical displacemente maximum displacement; clfj is the

t between tWo points i and j with distance:the relative deflection which is theisplacement from astraight line connecting

points; ro is the tilt, or rigid body

i)-rolar distortion; AIL is the deflection ratio, Or

, "mate curvature of the settlement curve.

1.4.2 BridgesExtensive surveys of horizontal and verticalmovement of highway bridges have been carriedout to assess allowable settlement values(Bozuzuk, 1978; Grover, 1978; Walkingshaw,1978). It is concluded that settlement can bedivided into three categories depending on itseffect on the structure:1. tolerable movements;2. intolerable movements resulting only in poor

riding characteristics; ,3. intolerable movements resulting'in structural

damage'.It is not feasible to specify limiting settl~ment

values for each of these three categories becauseof.the wide variety of bridge designs and sub-surface conditions. For example, Walkinshawreports tolerable vertical movements that rangedfrom 13 to 450mm (0.5 to 17.7in), although the'average value was about 85 mm (3.3 in). Intoler-able vertical movements causing only poor ridingquality averaged about 200mm (7.9in), while

mbers shows that damage was most vertical movements causing structural damageeresult of distortional deformation, so varied from 13 to 600mm (0.5 to 23.6in) with'distortion' P has been selected as the an average value of about 250mm (lOin). As a

:,index of 'settlement. These studies have comparison to these results, Fig. 1.6 shows theii, in the following limiting values of an- results of the survey carried out by Bozuzuk of'distortion being recommended for frame bridge abutments and piers on spread footingsgs (Peck, 1976; Skempton and McDonald, , . with lines giving the limits of tolerable, harmful

-'ndPolshin and Tokar, 1957): but tolerable, and intolerable movements.{I/150 - structural damage probable; The conclusions that can be drawn from these::-J1300 - cracking of load-bearing or panel studies are that tolerable movements can be as--:walls likely; great as 50 to 100mm (2 to 4 in), and thatstruc-,,:U500 - safe level of distortion at which ' tural 'damage may not occur, until movements

.i":';':racking will not occur. are in excess of 200mm (8in). Also, differentialand horizontal movements are more likely to'~fhe,case of load bearing walls;,it-is-iound cause damage than vertical movements alone.

_"the deflection ratio AIL is a more reliable One possibly reason is that vertical settlement"'-ator of damage because it is related to the of simply supported spans can readily be cor-

)merged tanks and thridge cables and trans'ely, the foundation rna.[ift forces generated bling on the structure reloads such as wind, ice'Ifees.

~entfamous case of found&.f the Leaning Tower 0'ully withstood a diffe'md is leaning at an angratrat and Lambe, 1977)"'ould not be tolerated ,"''s tourist attractions! Thof allowable settlemes of structures.

foundations that is ;"otural damage, may slUses significant crackin,ts. Some of the facto:nt are' the size and t,erties of the structurIrface soil and rock, any of settlement. Becauthe settlement that

19 of structural membe:s, or both, cannot readiJ, almost all criterea Clve been established e)f observations of setd,xisting buildings (Wahls

f walls,

,ment is usually the resulnt,. Le. variations in 'venlifferent locations in the,the absolute settlementdifferential and absolu '

:ed in Fig. 1.5, togeth~1 the various component.

Note: lmm=O,OO3ft

contimflow an

Figure 1.6 Engineering performance ofbridge abutments and piers on spreadfootings (Bozozuk, 1978).

1000

500

250EE

100 >-'Zw

50 ~~

25 w00~f! .r10"w>

3

10.0

1.5 Influence ofground wateron,foundation performance ~

"The effect of ground water on the perf~rmance~of foundations should be considered in design,.i.'and particularly in the case of dams and bridges.1\These effects include movement and instability"resulting from uplift pressures, weathering, scour'"of seams of weak rock,.and solution (Fig. 1.7). In,almost all cases, geological structure influences'ground water conditions because. most intactrock is effectively impermeable and water flo",-through rock masses is concentrated in the frac;tures. Flow quantities and pressure distribution .are related to the aperture, spacing and continu:aus length af the fractures: tight, discontinuou.fractllres will tend to produce low seepage quan'titiesand high pressure gradients. Furthermore:the direction of flow wili tend to be parallel

'thelIiain fracture orientation..'Instability caused by water uplift forces ool';~"'"

,

,

,

..-_-.-11

,

"0,

-;---4-lI .. NOT TOLERABlE

0 I

"0 , I,

,

0,,

LERABLE ,,0

"" ,

TOLERABLE NOT tOlERABLE

I PIER 0 JABUTMENT

TO

0.01 0,1 1.0

o

HORIZONTAL l:lISPl.ACEMENT. It

rected by lifting and shimming at the bearingpoints (Grover, 1978). In comparison, horizontalmovements are more difficult to correct, with oneof the most important effects being the lockingof expansion joints.

3 10 25 50 100 250 soo 100010.0 ,,---,----r--.,---r--r-,--,-,--r-.-.---.,

12 Characteristics orrock foundations

1.4.3 Dams

HORIZONTAL DISPLACEMENT mm

Allowable deformation of dams is directly re-lated to the type of dam: concrete dams are muchless tolerant of movement and deformation thanare embankment dams. There are no generalguidelines on allowable settlements for damsbecause the "foundation conditions for eachstructure should be examined individually. How-ever, in. all. Cases, particular attention shouldbe paid to the preseD.ceofr9ck .types with dif-fering moduli, or seallls ofweathered and faultedrock that are more,compr~s~ibiethan thead-jacent rock..Eitherof th.ese ca!i"ditions.maY result-in differential deforlIiati()r!()Uhe stf!ct~I'':' ' ..

10

>-'zw>w

~

E 0.100

~

~w>,

0,01

flIIIil:1tI:iilll

"""'--Flowline

Equipotentialline

Sheet'pilewall

Overflow weir..

(b)

Ground water tablelowered bypumping

Ground water and foundation performance 13

..

.

Upliftpressurehead

. .

.

...

..

. .

upliftpressur~distribution

Water surface

(c)

(a)

Sloughingon walls ofdrill hole

Impervi()us1;7 Typical effects of ground water flow on rock foundations. (a) Uplift presSure developed along(ins fracture surface. (b) Water flow into hole drilled for socketed pier. (c) Typical flow net depicting wateriEiIplift pressure distribution in dam foundation (after Cedergren, 1989)."

-~". . "

Engineering performance:ments and piers on spread:'ozozuk, 1978).

~nd water onIDee'ater on the performan.be considered in desig,ase of dams and bridg "novement arid instabilf

~ssures, weathering, seo:and solution (Fig. 1.7);-gical structure influenillS because. most inta"rmeable and water floconcentrated in the fra

IUd pressure distributio_ure, spacing and cantinures: tight, discontinuo':oduce low seepage qua_, gr,adients. Furthermor:Iill tend to be paralleltation.water uplift forces acti'\'

-14 Characteristics of rock foundations

differeltures. Iwidelyfor a ~accepteensuresto appAdapt3elude tmethodvariabilfactor (reliabilimeterssentingthe parsis is \\that it (parame'ability (ever, d(analysisenginee

.1.6.1 F

Fact,

Design,. tain aminput pgeologypressuresideredsuch asof themethodlmadeb:The faciforce -inforcenslope C(foundati

The ranas prop'

fault may form a barrier to seepage. The studyof seepage paths and quantities, and calculationof water pressure distributions in the foundationare carried out by means of flow nets (Cedergren,1989). A flow net comprises two sets of lines -equipotential lines and flow lines - that are drawnto form a series of curvilinear squares as shownin Fig. 1.7(c). The equipotential lines can also'be used to determine the uplift pressure undera foundation, which is also shown in Fig. 1.7(c).

1.5.2 Tensioned anchorsWhere tensioned anchors are located below thewater table it is necessary to use the buoyantweight of the rock in calculating upliftresistance.Furthermore, an important factbr iIi design isprovision for protection of the steel against cor-rosion. Corrosion occurs most rapidly in low-pHand salt-water environments. Protective measuresfor 'permanent' installations consist of plasticsheaths grouted on to the anchors and PJll-grout '.encapsulation which produces a crackHresistant, ;.high-pH environment around the steel (seeChapter 9).

on potential sliding planes in the foundation isillustrated in Fig. 1.7(a). The uplift force U act-ing on the sliding plane reduces the effectivenormal force on this surface, which producesa corresponding reduction the shear strength(see Chapter 3). For the condition shown in Fig.1.7(a), the greatest potential for instability iswhen a rapid draw down in the water level occurs(V = 0), and there is insufficient time for theuplift pressure to dissipate.

The flow of water through and around a foun-dation can have a number effects on stabilityapart from reducing the shear strength. First,rapid flow can wash out low-strength infillingsand develop open fractures that undermine thefoundation (Fig. 1.7(a. Second, percolation ofwater through soluble rocks such as limestonecan cause substantial cavities to develop. Third,rocks such as shale may weather and deterio-rative with time resulting in loss of bearing ca-pacity. Such weathering may occur so rapidlythat it is necessary to 'protect surfaces as soonas they are excavated, or it may only occur a,considerable time after construction. Fourth,flow of water into an excavation can make clean-ing and inspection of bearing surfaces difficultand generally lead to increased constructioncosts (Fig. 1.7(b. 1.6 Factor of safety and reliability

analysis

1 5 1 D Structural and geotechnical designs are usually" ams based on the following two main ,equifemenls..In the case of dam foundations it is necessary First, the structure and its components must,.to control both uplift to ensure stability, and during the intended service life, haye an alj!!_ateseepage to limit water loss (Fig. 1.7(c. Control marginof saft:~gainstcollapseund"-Lth"'_IDJlXi-measures consist of grout curtains and drains mumloads" and forces that ,.mighLr~asg!!ablyto control seepage and reduce wate;: pres~ure, occur, and second th"Lstrn.clt!l~ and its sgm-as described in Chapter 7. The rock property "oneilts must serve the designed functions with-that determines seepage quantities and pressure oilt excessive deformations and deterioration.distribution is permeability, which relates the Co~of the structure and foundation failt!r,Lquantity of water flow thr

Table 1.1 Values of minimum total safety factors

Factor of safety and reliability analysis 15

the Canadian Foundation Engineering Manual(1987) are given in Table 1.1., The upper values of the total factors of safety

apply to normal loads and service conditions,while the lower values apply to maximum loadsand the worst environmental conditions. Thelower values have been used in conjunctionwith performance observations, large field tests,analysis of similar structures at the end of theservice life and for temporary works.

The factors' of safety quoted in Table 1.1 areemployed in engineering practice, and can beused as a reliable guideline.in the determinationof appropriate values for particular structuresand conditions. However, the design processstill requires a considerable amount of judge-ment because of the variety of factors that mustbe considered. Examples of conditions thatwould generally require the use of factors ofsafety at the high end of the ranges quoted inTable 1.1 include:1. A limited drilling programme that ,does not

adequately sample conditions at the site, ordrill core in which there is extensive mechan-ical breakage orcore loss;

2. Absence of rock outcrops so that detailedmapping of geological structure is notpossible;

3. Inability to obtain undisturbed samples forstrength testing, or difficulty in extrapolatinglaboratory test results to 'in situ conditions;

4. Absence of informatiop on ground watercOll-,clitions; and seasblla!'fl\ictuations in groundwater levels;

5. Uncertainty in failure mechanisms of thefoundation and the reliability of the analysis

~ ..

2-3~

1.3-1.51.5-2.0

Safety factorCategoryEarthworksEarth retaining

structures,excavations

Foundations

Failure type

Shearing

~~tor of safety analysis, geotechnical structures involves a cer-lint of uncertainty in the value of theta.meters which include the structural"material strengths and ground water'.' Additional uncertainties to be con-ndesign are extreme loading conditions"'floods and -seismic events, reliabilitynail'tical procedure, and construction

: Allowance for these uncertainties isinduding a factor of safety in design.

or of safety is the ratio of the resistance(the rock strength and any installed re-ent), to the displacing, force (down-

.lllp,ments of the applied loads and theEio weight).... :. f' f Resisting forces ()~r.zsa ety = Displacing forces ", 1.2i'_,T-';''''~'--''- .- .. _ .. - ~

t design methods for geotechnical struc-acto: of sa!~!)' analysis is by far the most:~ed 'tecl1iligue and factor of safety values

fie of structures are now generallyi'in the engineering community} Thisthat each type of structure is designed',ximately equivalent levels of safety.'()fiS to the factor of safety analysis in-e limit states and sensitivity analysis{both of which examine the effect of

, in design parameters on the calculated{safety. An additional design method,;'analysis, expresses all the design para-,~~ probability density functions repre-Jhe range and degree of variability of

a sliding, overturninJdseepa'ge:"The'onse.t'l- and of" deterioIa1i.ort~1and differentia' move~_Ition. These two service,: and servicability limit'rhof, 1984).:ussion on a number

-frirpI'. .

' ..

cture orientation and dimensionsimportant properties of fractures that:the shape and size of blocks are:

"sketches in Fig. 2.2 illustrate how;.properties influence the stability of aiI.ln both cases there are two sets of'set A dips out of the face at an angle'of

?l~fl.u,ence of fra'ctore length and orientationon the stability ofa foundation: (a) continuous fractures'p-(~-stable foundation; (b) continuous fractures dip out of the slope - unstable foundation:

'gn purposes on the properties of a fracture,"ly for foundations where particulars of

racteristics as the infilling thickness can'[gnificant influence on settlement. Forbn, geological descriptions are useful inriding the general conditions at a site, butpecific geotechnical studies are almost'quired before proceeding to final design.

ion of houses along crest of;

'~, planes are no(controlle;Jaral1el orientation,

1 schist or other coarseck due to the parallII grains of the platey 6mica.

racture categories are weing practice and the like.be anticipated from the

Ie, faults are major struinfillings such as crushe

,hereas joints have le~gt'ler than faults and JOland cohesive, or entire

andard geological nam,icient detailed informatiO

-\r

150'

4.0 !Q'~ 01;'$

(a) ISO Ct,IO~.

N

Strike:\)

/N60E

(b)Dip direction:150'

N'

The strike is at right angles to the. dip and dipdirection of the inclinedplilne.Tile relationship.between the strike and the dip direction is iI .

Filustrated in Fig. 2.3(b) where the plane has a.strike of N60E and a dip of 30SE. In terms of dip" m

Figure 2.3 Terminology defining fracture_orientation.(dip and dip direction):' Ca) isometric view; and (b) planview.

26 Structural geology

2.2 Orientation offractures

1. Dip is the maximum inclination of a fracture tothe horizontill (angle 1jI).

2. Dip direction or dip azimuthis the directionof the horizontal trace of the line of dip,measured clockwise from north (angle a).

to be of concern and settlement will be dependenton the deformation modulus of the intact rock.However, in the case of highly fractured rock,settlement may occur as a result of fractureclosure, and settlement would be determinedfrom the rock mass deformation modulus. Asregards the overall stability of the foundation,the closely fractured rock may be sufficientlyinterlocked to prevent movement of the entirefoundation in a block type failure as shown inFig. 2.2(b). However, ravelling of small frag-ments may occur as a result of frost action orriver scour, and this may eventually underminethe footing (Fig. 2.2(a)).

As will be demonstrated in Section 2.3, the dipldip direction system facilitates field mapping andthe plottifig of stereonets,and the analysis offracture orientation data.

Strike, which is an alternative means of defin-ing the orientation of a plane, is the tra~e oUheintersection of an inclined pIane with a horizontalreference plane.

The first step in the investigation of fractures in afoundation is to analyse their orientation andidentify sets of. fractures, or single fractures,that .could form potentially unstable blocks ofrock... Information on fracture orientation maybe obtained 'from such sources as surface andunderground mapping, diamond drill core and

., geophysics, and it is necessary to combine thisdata into a system that is readily amenableto analysis. This. is facilitated by the use of asimple and unambiguous method of expressingthe orientation of a fracture. The recommendedterminology fOr orientation is the dip and dipdirection which are defined as follows and areshown schematically in Fig. 2.3.'

iplSE

Dip direction:,1500

defining fracture.orientatio ~,,) isometric view; and (b) pi

,t angles to the dip and",ed plane. The relations,nd the dip direction is''b) where the plane ha"dip of 30SE. In terms of

'rection, the orientation of the plane"hich is considered to be a simpler

e. By always writing the dip as twohe dip direction as three digits, e.g.there can be no confusion as to which

of figures refers to which measure-and dip measurements can readily

,into dip and dip direction measure-'\mapping system is preferred., jhe orientation of a line, the terms,end are used. The plunge is the diplth a positive plunge being below thed a negative plunge being above

tal. The trend is the direction of thetojection of the line measured clock-orth, and it corresponds to the dip

i,a plane.inapping is carried out with a geologi-J.of which there are several different'j,Clinton compass is widely available,i$advantage in that measurement of the'-direction require separate operations.-designed to measure strike rather than~~j1; this requires that a conversion be

~h can be a possible source of error.,'Xa number of compasses specifically

.jSi structural mapping which allow dip'''''etion to be measured simultaneously;

,:~XP.hotograph of a structural compassg.dipanddip direction of fracture surfaces.

Stereographic projection 27

these compasses are manufactured by theBreihthaupt Company in Germany and the ShowaSokki company in Japan. A particular feature ofthese structural compasses is the ability to mapaccurately a fracture when only a small portion ofa plane is exposed. In these circumstances it canbe difficult to determine the true dip, as opposedto the apparent dip which is always a flatter angle.The true dip can be visualized by rolling. a balldown the plane; the ball will roll down the lineof maximum inclination which corresponds tothe true dip of the plane. The horizontal direc-tion in which the ball rolls is the dip direction.Figure 2.4 shows the operation of a structuralcompass; the lid is placed on the fracture surfaceand the body of the compass is levelled beforereading the dip direction on the compass scale,and the dip on a scale on the hinge.

2.3 Stereographic projectionThe analysis of structural geology orientationmeasurements requires a convenient method ofhandling three-dimensional data. Fortunatelythe stereographic projection, which is used ex-tensiveIy in the fields of cartography, navigationand crystallography, is ideally suited to geologicalapplications. The stereographic projection is a'procedure for mapping data located on the surfaceof a sphere on to a horizontal plane, and can beused for the analysis of the orientation of planes,lines and forces (Donn and Shimer, 1958; Phillips,1972; Goodman, 1976; Hoek and Bray, 1981).

There are several different types of stereo-graphic projections, but the one most suitablefor geological applications is the equal area net,or Lambert projection. This is also used bygeographers to represent the spherical shape ofthe earth on a flat surface. In structural geology,a point or line on the surface of the sphere re-presenting the dip and dip direction of a fracturecan be projected in a similar manner on to ahorizontal surface. In this way.an analysis ofthree-dimensional data can be carried out in twodimensions. An important property of the equal-area projection is that any solid angle on thesurface of the reference sphere is projected as an

II

Great circle

Figure 2.5 Stereographic representation of theorientation ofa plane. (a) Plane surface located inlower hemisphere of the reference sphere showinggreat circle and pole to plane. (b) Vertical sectionthrough reference sphere showing lower hemisphere,equal-area projections of great circle and pole. (c) Plan 1view of reference plane showing projections of great)circle and pole. 1

representation of the orientation of the plane.IThe upper and lower halves of the sphere give ridentical inl'ormation and in engineering appli.cations the usual procedure is to use the lower Ihalf of the sphere only. The projection is known, therefore, as a lower hemisphere projection. Note'that this projection technique only examines thelorientation of planes and there is no information!.on their position in space. That. is, it is assumed.; .that all the planes pass through the centre of the1 reference sphere. If the stereographic projection'"identifies a plane on which thefo-ufiaation-coulslide, its location on the geological map woulJ

(b)

PoleProjection

Projection of of Great cirClepole __-====i:::::::o_.l-"",,::::::::-'__.k:::::"'_

Plane

N

N

(a)

Great circle-------

Pole

28 Structural geology

equal area on to a horizontal surface. One of theapplications of this property is in the contouringof pole populations to find the orientation of setsof fractures as described in Section 2.3.2.

The principle of the projection method is il-lustrated in Fig. 2.5. The basic element of theprojection is a reference sphere which is orientedin space, usually with respecttotruenorth.Whena plane (fracture). is'centredinthe referencesphere,' the intersectionlletween'th.,plane.andthe surface of the sphereis a circle which iscommonly known as a great circhi (Figo..2;5(a)).The orientation of the greaFcirclejs a unique

representation of thePlane surface located in~ference sphere showingme. (b) Vertical section showing lower hemisphere~:great circle'and pole. (c) PI,lowing projections of great.

orientation of the piahalves of the sphere giand in engineering ap.'

:edure is to use the 10"';I. The projection is kno "lemisphere proje.etion. No:chniqueonly examines,;and there is no informalpace. Thatis, it is asSU;s through the centre of,he stereographic projectwhich the foundation c~the geological map wq

,pe examined to determine if it intersectedation.rnative means of representing the orien-

'plane is the pole of the plane. The poleIlt at which the surface of the sphereby a radial line in a direction normal

ne. The merit of the pole projectioncomplete orientation of the plane is

by a single point which facilitatesa large number'of planes compared toreat circles.

t convenient means of examining thedata provided by the great circles and

'is to project the lines and points onOntal reference plane which is a two-I representation of the surface of thee equal-area projection for any pointace of the reference sphere is accom-'drawing an arc about the lower end'ical axis of the sphere from the point

montal base plane, (Fig. 2.5(b. FigurebWS a plan view of the horizontal ref-'l.ne, and the positions of the pole and'~ of a plane with a dip of 3D' and a dip

f 150'. The great circle and the poleme' plane lie on opposite sides of the

,so the dip direction is measured from;fthe circle for the great circle, and from'in of the circle for the pole. Also, a plane

low dip has a pole close to the centre ofnee circle, while the great circle for thee is located close to the perimeter of the

graphic' projections of both planes anddes can be prepared by hand by plot-

Idata on standard sheets which contain"presenting dip and dip direction values'dix I). Alternatively, there are computerS available that will not only plot poles

'tcircles, but will also perform selections'(jala. This selection feature will preparerexample, of only faults, or of only

}Inengths greater than a specified length.~'plot$ have particular value where thereat quantity of geological data ,and it is

ant"to identify features that have a par-rgIlificance to stability.

Stereographic pro;ection 29

The analysis of structural geological data bystereographic methods is usually a three-stageprocess as follows:1. Plot poles to show the orientation of all the

data;2. Contour the data to find the prominent fracture

sets;3. Use great circles of the prominent fractures

or fracture sets to show the shape of blocksformed by the fractures, and the direction inwhich they may slide or topple.

Two different types of stereonet, the polar netand the equatorial net, are used when plottingthis data by hand. The polar plot is used to plotpoles, while the equatorial net can be used to ploteither poles or great circles.

These three stages of the analysis are describedin this section.

2.3.1 Pole plotsPole plots, in which each plane is represented by asingle point, are the most convenient means ofexamining the orientation of a large number offractures. The plot provides an immediate visualdepiction of concentrations of poles representingthe orientations of sets of fractures, and the

'analysis is facilitated by the use of differentsymbols for different types of fracture. A typicalpole plot generated by a stereographic projectioncomputer program is shown in Fig. 2.6. Thisis a lower-hemisphere, equal-angle projection of1391 original poles at a site where the rock typeis a highly metamorphosed phyllite. The rockcontains fracture sets comprising the foliation andtwo sets of joints; where more than one pole hasthe same orientation, a number is plotted showingthe number of poles at that p.oint on the net.The data can also be plotted with the symbol Frepresenting a foliation plane, and a J represent-ing a joint.

The dip direction scale (0' to 360') shownaround the periphery of the pole plot has zerodegrees at the bottom of the plot because thepoles lie at the opposite side of the circle tothe great circles (see Fig. 2.5(c). Therefore the

30 Structural geology

Figure 2.6 Pole plot of foliation planes and joints;'lower hemisphere, equal-area projection (plot byM. Goldbach). .

;i:Eaf(bst

slTIIIof

\

-

ent sets, and to find the most likely odentationof each set. However, by contoudng the plot,the most highly concentrated areas of poles canmore readily be identified. The usual method"of generating contours is to usethe"Gontoudng:rpackage contained with most stereographic pro-:}cjection computer programs. However,contouringIcan also readily be carried out by hand using the,~techniques descdbed by Hoek and Bray(1981).~'

Figure 2.7 shows a contour plot of the pOlesfiplotted in Fig. 2.6. The pole plot in Fig. 2.6 ShOW$!that the odentation of the foliation planes h~...,relatively little scatter; the contour plot of thes2.3.2 Pole densityAll natural fractures have a certain amount ofvariation in their orientations'whieh"resUlts. inscattedn the poIeplots.IHhep]oicol1tainsijolesfrom a number of fracture sets, it can be difficultto distinguish betweeri the poles Il'orilthe differ-

Stereographic projection 31

counts 28 poles out of a total pf 1391 poles in a1% area, then the concentration level in that'areais 2%. By successively counting each area, acontour plot showing the pole cOncentrations ofall the data can be developed.

A further use of the stereographic projectionprogram in analysing structural data is to prepareplots of data selected from the total data collected.For example, joints with lengths which are only asmall fraction of the foundation dimensions areunlikely to have a significant influence On stability.or settlement. Therefore it would facilitate designto prepare a stereo plot showing only those frac-tures which have lengths greater than a specifiedlength. Figure 2.8 is a pole plot of the same datashown in Fig. 2.6 in which only fractures ,with

.,7 Contour plot of the poles shown in Fig. 2.6.

N(180)~~---'----,~ ~ 1391 original poles

/-= "'>g S:7"B '\~~>-85/135 ~~-__ \

r=-, -~..~ \;:=-::=-' Foliation -:m '.ffi=_ \t=- = =- 65/245 ,- 11$ Jr ..:: -J... --.. -.. ', + - :l' 'c, E(270)~ ~J\ S5

\ 'i~)o~o ~~\ ' -:-=-]

. \ Set B---..#Legend' (0/,) ~ J

:..:-- 1 to 4

32 Structural geology

great circles of each of the fracture set orien 1tations, as well as the orientation of the face ofthe cut on which the foundation is located. In thisway the orientation of all the surfaces that havean influence on stability are represented on asingle diagram. Figure 2.9 shows the great circlesof the joint sets identified on the contoured poleplot in Fig. 2.7. It is usually only possible to havea maximum of about six great circles on a plot,because with a greater number, it is difficult toidentify all the intersection points of the circles. JThe procedure for plotting great circles using an',equatorial net is shown in Appendix L .

The primary purpose of plotting great circles of ,fracture sets in a foundation is to determine theIshape of blocks formed by intersecting fractures,:and the direction in which they will slide. For

+234 .5-9A-Z

N---'I---'~ 163 original poles/ ~"')

/ ++ + + + ~\r ++ + +: + +: 12~;' \r + + + 22 + ~~++ ~

w fr

:++++ ~ t:>~:; ~ ~ +:;;++JJ E+ + ++;+++ +: ... + +\ .::.:::"~ ,..:' . .. J

Legend \\ : : + + -I1 Pole /2 Poles ~ V c3Poles/' Scatter plot4 Poles (. V lower-hemisphere5,6,7,8,9 "-..~ . V equal-area projection10.11.... L..-L----

S

Figure 2.8 Seleclivepole plOI of dala in Fig. 2.6 for all fractures with lengths greater than 4m (pial by M.' Wise).

lengths greater than 4m (13 ft) have been plotted.This plot shows that only 163 fractures, or 12% ofthe toial number have lengths greater than 4m,and that virtually all these fractures are eitherthe foliation or joint set A. Similar selectionscan be made, for example, of fractures that havea certain type of infilling, or are slickensided, orshow evidence of seepage.

2.3.3 Great circlesOnce the orientationofthdracture sets,as wellas important singlfracturessuch as faults, havebeen identified on the pol" plots,th~..nextstepin the analysis is to determine if these fractUresform potentially unstable',blocks in thefoundation. This analysis is' cai-riedout by plotting

NI,

Foundation failure 33

Figure 2.9 Plot ofgreat circles representing the threefractnre sets identified on the contour plot of Fig. 2.7.

the block is unlikely to slide if the plunge is at ashallow angle. The orientation of the line of inter-section b.etween two planes is represented by thepoint where the two great circles intersect. For.the data shown on the pole plot (Fig. 2.6), inter-sections occur between joint sets A and B (1,),between set.B and the foliation (12) and set A andthe foliation (13)' The orientation of the inter-section line 13 is shown in Fig. 2.9, and the methodof determining the trend and plunge of lines isdescribed in Appendix 1. For the conditions shownin Fig. 2,9, the wedge formed by intersection 13will slide towards a direction of 1580 at a shallowdip angle of 80

2.4 Types offoundation failureA great circle stereographic plot of fracture setscan be used to identify the shape of blocks inthe foundation, and m'ake an assessment of theirstability conditions (Fig. 2.10). Four distinct typesof slope failure can be distinguished" and charac-teristicsof which depend on the relative orien"tations of the slope face and the fracture (Hoekand Bray, 1981). For each of the failure types

[901 Dip directionof great circles

I,

Wedge:line of intersection=08/158

8[1801

,.in Fig. 2.1 the foundation failure only.,at the location where the fractures inter-

form a wedge with a particular shapentation with respect to the face. It is,e, important to identify such potential

ibefore ,movement and collapse actually, is requires an ability to visualize the)mensional shape of the wedge from the, J the fractures On the face of the original'The stereographic projection is a con-means of carrying out the required three-

':onal analysis, keeping in mind that this, ure examines only the orientation of the"~s and not their position. If the stereonet(he possible, occurrence of a potentially

Ue block; examination of the location of the,)es on the geological map would determineeyiIitersect the foundation.

::o:i~tersecting planes will form a wedge-'~:,blbck as shown in Fig. 2.1. The direction':lithis block may slide is determined by the

:.Qlthe line of intersection, with failure only'.-possible if the trend is out of the slope face.,lunge of the line of intersection gives an

""',.,. ,'" the stability condition 'of the block:

1poles

tan 4m (plot by M. Wise).'

f the fracture set orie,rientation of the face '.ndation is located. In thall the surfaces that hity are represented on:~.9 shows the great circl,ed on the contoured po!tally only possible to haXix great circles on a plo,number, it is difficult, '

:tion points of the circl'1,ting great circles using ~I in Appendix 1. ,.of plotting great circles';

jation is to determine tI by intersecting fractureNhich they will slide. F

\, ~+ JEJ)

)I

ltter plot'erhemisphereJsl-area projection

Ifssfi

at

NKinematic analysis 35

Or dip direction of faceas direction of slidingU 1 direction of toppling

Randomlyorientedfractures

, /" /

.... __ ....

stability conditions. This procedure is known askinematic analysis. An application of kinematicanalysis is the failure shown in Fig. 2.1 where twojoint planes form a wedge which has slid out ofthe face and towards the photographer. If theslope face had been less steep than the line ofintersection between the two planes, or had astrike at 900 to the actual strike, then the wedgeformed by the two planes would not have beenable to slide. This relationship between thedirection in which the block of rock will slide andthe orientation of the face isteadily apparent onthe stereonet. However,' while analysis of thestereonet gives a good indication of stability canditions, it does not, account for external forcessuch as foundation loads, water pressures or reoinforcement comprising tensioned rock, bolts,

LEGENDPole concentrations.

Great circle representingslope face.

Great circle representing~plane corresponding to centres. of pole concentrations.

Main types of block failures in foundations and the structural geology conditions likely to cause theser.Hoek ,and Bray, 1981): (a) plane failure in rock containing continuous fracture(s) dipping out ofdstriking parallel to face; (b) wedge failure on two intersecting fractures; (c) toppling failur"in '

.'\mtaining fractures dipping steeply into the face; (d) circular failure in rock fill, soil and closelyJ:k with randomly oriented joints.

ill only occur in closely fractured rocke'major portion of the sliding surface is'd of fracture surfaces. It is found that

" failure' occurs under these conditions,illg surface can be approximated by adius circular arc forming a shallow failure,>Stability analysis of this failure mode in, 'be carried out in an identical manner to'soil, with the use of appropriate strengthrs.

~inatic analysis,,,,:,~:.,

'i:;,fypeofblock failure, has been identified"'Steteonet; the same diagram can also

/tRexamine the direction in which a,slide and give an indication of possible

N

N

N

(c)), the structure dips':reonet the poles are on's the great circle of the

tilure, circular failure". closely fractured rockfractures dipping out 0For cuts in fracturedforms partially alan

I approximately parallelIlly through intact rock,high shear strength 0

f fractures, this type 0

stlne

2.Api:fwHIwiIjff.

., c(3.2) and (3.3) can be combined to'e,deformation modulus of a rock mass"several sets' of fractures inclined at . 3.2.5 Modulus ofanisotropic rock-Ilentations with respect to the applied Many rock types e"hibit anisotropic strength and

,ppell and Maurice, 1980). These equa- elastic properties, and it is important that the

fractures that deterrnin,n the modulus of tthe rock mass are tof the fractures in ea

ormal stiffness k n, 0{e normal closure 0

;-o..tll'.1irn;~I;~ressG a'

1cture tends to be h'or portion of.J.b..J' clos:s levels.1e fractures is defined,iiffiiless kn and k, res .'S,QRe...Q normlrv G/o" an.$L.k.-16~!!I9jspLaCe=utll.,ters can be obtained fr,ar tests to determinee surfaces. If the spathe modulus of the in

,lication of a stress 0',follows (Fig. 3.7(b:

m can be developed foi,lulus (Om) in the caslodel shown in Fig. 3.7

ss equation is as foliO'Jetermined by laboratof Em by in situ metli..ts. For a particular se,. the stiffness can be..n lhen be used to estirpmass modulus of diff~

Tal

and.-sixtheof \calc

1datiselladj.ori(;ad

'reStThiWitl

B. J

, Reference

80

olE9O

1.36-2.861.7

1.28-1..331.3~3.2

60

3.2.6 Modulus/rock mass qualityrelationshipsWith rock mass modulus being highly dependenton both the geological structure and the size ofthe test sample, Bieniawski (1978) has proposeda method of estimating in situ modulus froin an.index which characterize,s the oVerall properties -:~of the rock mass. This index is known as the ,.rock mass rating (RMR) and i~ widely used inthe assessment of tunnel support requirements(Bieniawski, 1976). The advantage of this ap-proach is that the index is determined fromreadily measured parameters: the compressivestrength ofthe'intact rock, the characteristics oftheiractures determined by mapping and driWng,

ment will take place more readily along theseplanes (Section 3.4). Therefore it is important toexamine both the direction and type of loadingwith respect to the orientation of the geologicalstructure in the design of any foundation in'_,anisotropic rock: y

Table 3.3 Modulus ratios of anisotropic tack

Rock type

Clay shaleSlatePhylliteSchist

.20 40

Deformation modulus E(GPa)

40 f:=:~-:.~.L--'-.1",

90' / \/'/\20 ---160' A \1'" /' \, \

/ )(30' \ \/' \=00 I \

E(GPa)

figure 3.8 Variation in modulus of elasticity with direction oOoading in anisotropic (schistose) rock'(Pinto,1970).

values used in design are appropriate for thedirection of' loading. Typical anisotropic rocktypes are the sedimentary-metamorphic se-quence of shale-slate-phyllite-schist which willusually contain sets of parallel fractures, and inthe case of schist and phyllite, have low-strengthmica aligned with these fractures. The massmodulus of these rock types is likely to be lowerin the direction normal to the orientation of thepredominant geological structure as a result ofclosure of these fractures (Fig. 3.8).

Laboratory and in situ testing programmes'have been conducted to determine elastic con-stants in directions parallel and perpendicularto the orientation of the predominant geologicalstructure in anisotropic rock. The modulus ratio isknown as the degree of anisotropy, and is giventhe term Eo/E90 - modulus parallel/perpepdicularto anisotropy. Surveys conducted by Lama andVutukuri (1978a and b) of rock modulus testingprogrammes show that the modulus is usuallyhigher in the direction parallel to the structure'and that the degree of anisotropy varies betweenabollt 1 and 3 (Table 3.3).

Seismic testing to (Ietermine ihe dynamicmodulus shows values of E,o/Eooratio of between1.0 and 1.2. These low ratios can be attributed to;he fact that, at theJows;resslevels

When calculating roek strength using Tahle 3.5. rating = Ill; ground wlltcr pressures aCClluntcd for in slahility ;m;llysi~.,

(3.4)

-25

Very unfuvllunlble

Compressive strength 53

-15

UnfaVlluralllc

-7

F~lir

.Em = 2RMR - 100.

be in a direction parallel to the load direction(Chappell and Maurice, 1980).

The empirical relationship betwecn the RMRrating value and the in situ rock mass modulus isshown in Fig. 3.9. For the seven different projectsstudied by Bieniawski in developing this relation-ship, Em is given by:

The obvious deficiency of this equation is that itdoes not give modulus valucs for RMR valuesless than 50. Additional studies carried out onrock masses with qualities ranging from poor tovery good indicatcs that the modulus is related

-2

Favourahte

(I

When euleuluting rock strength usingT;lble 3,5. adjustmenl = U: joint orientation accounted fllr in shlbility ;malysis.

>11 MP(l 4-1' MPa 2-4 MPa 1-1 MPa For this low ran~c.>1.2 ksi 0,(1-1.2 ksi O.J-Il.(} ksi Il.X-CD ksi uniaxial 21KI MPa IlMI-2(l(l MP(l ;1I-IlKl MPa 25-$11 Mr,l M[>a MPa MP..

strength---------.

......-_._.--

"12 4 2 \I

-_..._-----_._--_.- - ..._---_._---

9t1%_ltKl'y" 75%-90'X, 5U'X,-75% 25%-50% 5 mm

H;lrd jllint wall Hard joint wall roek Stlft joint wlill roek Continuous joints Continuous joints"

-------------------------

54 Rock strength and de!ormability

>,8

6

4

2

10

(p,S,i.X106 )12

90 100

machine or a point load tester. The compression~machine gives the more precise results but it is ;"

.. necessary to prepare the samples in the manner'described in Section 3.2.2 on modulus testing.

Determination of approximate compressive'strength values made with the point load testingequipment has the advantage that tests can beconducted on lengths of unprepared core in axialand diametral directions, as well as on irregularlumps of rock (ISRM, 1985). The equipment isportable 'and can readily used in the field. ~principle of operation is that a compressive loadis applied through two conical platens whichcause the rock to break in tension between thesetwo points. If the distance between the platens'is D and the breaking load is P, then the point +load indexJ, is given by: "

I, = PID;, (3.6) ~_~ Figurewhere De, the equivalent core diameter, is given c,, equipnby: "

"~De = D2 for diametrial testsj l,(~~~

=4Ahc for axial, block and lump tests 'i the VIandA = WD'is the minimum cross-sectional are~~. by a Iof a plane through the platen contact points (W i'~i condu

, ' '~~the specimen width). t"

GPa90

80

70

In situ 60modulus of 50deformationEM(GPa) 40

30

20

10

Rock mass rating RMR

Figure 3.9 Relationship between in situ modulus and rock mass ratiug (Bieniawski, 1978; Serafun and Pereira,1983).

to the rock mass rating over the range of about20 to 85 by (Serafim and Pereira, 1983):

Em = lO(RMR-lOj/40. (3.5)

3.3.1 Compressiv~ strengthofintactrockThe compressive strength of ,intact rock canreadily be measured using either, a cOmpression

,

3.3 Compressive strengthCompressive strength values of rock are used inthe determination of bond strengths at the rock!concrete interface in drilled piers and tensionedanchors, and for the bearing capacity of spread ,footings. In the case of bond strength values,

. 'empirical relationships have been developedbetween compressive strength of intact rock andworking bond strengths that have been found tooperate satisfactorily in practice. In the case ofspread footings where the bearing area is largerthan the spacing between fractures, the bearingcapacity can be calculated from the compressivestrengtJ1 of the rock mass. The following is a

.discussion on methods of determining the com-pressive strength of both intact rock, and therock mass.

a size-corrected point load strength index byapplying a correcHon factor kPLT as follows:

1'(50) = 1, kPLT' (3.7a)The value of the size correction factor kPLT isshown in Fig. 3.10(b) and is given by:

1 ~~

7/

V

1.0 1.5 2.0 2.50n)20

.

30 40 50 6O(mm) Sample Dcdi~meterAO SO NO HO Series Qdrill core

0.9

1.0

1.

56 Rock strength and deformability

3.3.2 Compressive strength of fractured rockFractured rock will, ofcourse, have a much lowercompressive strength than intact rock. Studieshave been conducted on the load capacity ofmine pillars which demonstrate the decrease instrength that occurs asthe sample size is increased(Ilieniawski, 1975; Pratt, 1972). These-tests showthat once the side length is greater than about 1m(3 ft) there is little decrease instrenglh with larger

samples, and that this minimum strength is about20 to 30% of the maximum strength (Fig. 3.11).

Laboratory testing to determine the compress.ive strength of fractured rock is difficult becauseof the problem in obtaining undisturbed samplesof fractured rock, and then testing a sufficientlylarge sample that is representative of. the frac.ture conditions. To avoid the expense of carryingout laboratory testing, it is usual to use empiricalrelationships between the rock mass strength andthe fracture characteristics. ~

For most foundations, the rock is loaded in atriaxial stress field consisting of the foundationload and the confinement produced by the sur.rounding rock. Therefore, in calculating the ,}bearing capacity of the rock, it is necessary to '~have a strength criterion that is expressed in termsof the principal stresses acting on the rock, andtakes into account the characteristics of thefractured rock mass. Such a criterion will allowthe state of str~ss at any point in the foundation . ~.;to be compared with the rock mass strength at ,that point, which will identify overstressed areas .so that the design can be modified accordingly.This approach is useful in the case of dam foundations where the stress distribution is usuallynon-uniform across the bearing surface, andalso for foundations located on the crest of steepslopes.

A strength criterion for fractured rock has beendeveloped by Hoek (1983) and Hoek and Brown',(1988) which can be applied readily to the design,of foundations. This is an empirical criterion thaihas beeh developed by trial and error and is based.on the observed behaviour of rock masses, modelstudies to simulate the failure mechanism 01:jointed rock, and triaxial compression tes~tof fractured rock. Hoek's expression .. for the!maximum principal stress 0'1 at failure is '

- r,

0'; = 0'3 + (mO'u(,) 0'3 + S

4.5

I,,

1.51.0

Uniaxial compression

O'v(m) = (serU(,):?)1/2

UniaxialtensionO'l(m) = 1f20"u(.)[m ~ (m2 + 45)112)

0.5

Minor principal stress 0'3

4.0

3.5

Compressive strength 57

3.0

1.5

0.5

Figure 3.12 Strength offracturedrock (Hoek, 1983).

iate principal stress has no particular'failure (Jaeger and Cook, 1976).. ts m and s depend on both thed !be fracture characteristics. The

.lind s given in Table 3.5 are those: rock because of the loosening that

ace excavations made for founda-g Table 3.5 it is necessary to define

in terms of one of five categories'a.nd six categories of rock quality. ality varies from intact rock, toeavily fractured rock, or rock fill,Jegory defined either by a descrip-rock mass Or by the RMR qualityTable 3.4). Where possible, thees determined from equation (3.8)

'ct with other sources of rock strength"se obtained from the back analysis of

lopes in similar geological conditions.al shape of strength envelope de-uation (3.8) is shown in Fig. 3..l2.radient of this curve clearly demon-.increasing confining pressure has a

ect on improving the strength' andacity of the rock. Foundations on

.8 where there is little confining press.psening of the rock mass occurs, willer bearing capacity than foundations

'jhuous horizontal surface. The curve in.,so shows that the uniaxial compressivef the rock mass O'u(m) is defined by the

>equation:" 1=; (s~(,)2 (3.9)

'=st (3.10)I.~X3.10) shows that the ratio O'u(mj!O'u(,)... es.rapidly as the rock becomes more-d'and that the rock mass has essentiallyJj)pressive strength when the fracture

. --ress than about 0.3 m. This relationshipIi:Jbe compressive strengths of the rock

~~.intact rock can be compared With the..eprease in rock mass strength ""ith speci-"shown in Fig. 3.11.

nimum strength is abdurn strength (Fig. 3.1'determine'the compr'rock is difficult beca)

ling undisturbed samphen testing a sufficienlresentative of the frj the expense of ca .is usual to use empiri

e rock mass strength'ics., the rock is loaded;listing of the founda',nt produced by the s'are, in calculating)rock, it is necessary

that is expressed in tel. acting on the rock, ,e characteristics of,'lch a criterion will aly point in the foundal1e rock mass strengtlentify overstressed a'be modified accordinin the case of dam fa

ss distribution is. ustiIe bearing surface, ,ated on the crest of sf

Jr fractured rock has 083) and Hoek and Brgplied readily to the de~an empirical criterion .:rial and error and is b'Jur of rock masses, mqte failure mechanismiaxial compression '(Jek's expression for'JSS 0', at failure is

1.+ S~(,2mum principle stress,; the uniaxial compre~rock; and m and s

s.~ failure procesS is deli.. principal stresses and'

Table 3.5 Approximate relationship between rock mass quality and material constants ~Hoek, 1988)

Empirical failure criterion u..J l-arser grained rocks such as granites tend tohave higher friction angles than finer-grainedlimestones.v

fu~ of the tests also determined residual shear~Ilgth values. It was found that the residual'c!.ion angle was only about 2 to 4 less than thelFfriction angle, while the residual cohesion

51essentially zero.'n additional factor to consider regarding'lir strength is the shear strength/displacement

'~viour of the fracture infilling. This behaviour"be divided into three general categories, as'ws (Nicholson, 1983):train softening- fractures which show signi-ant loss of strength with displacement, or

"e already close to their residual strength.xamples are brittle infillings such as hardalcite, faults containing clay mylonites, shearones, and bedding plane slips. Also, over-

"onsoldated fnfillings often show significanttrain softening, with the decrease in strength,eing more significant in silts and clays than in, 'nds and gravels.':.For these types of infillings, residual sheartrengths should be used in design.(astic-plastic - fractures which show no,ecrease in shear strength with displacement'lice the maximum shear strength has been

,ched.train hardening - fractures that show an'crease in shear strength with displacement;p'to a poorly defined break in the curve, after'!Iich the stress-deformation slope flattens

Shear strength 63

somewhat, although the shear resistence con-tinues to increase with displacement.

Both elastic-plastic and strain-hardening in-fillings will usually be undisturbed, such as near-surface weathering products, or normally con-solidated clay. These materials generally arenot susceptible to progressive failure, and peakstrength values may be used in design.

3.4.3 Shear strength testingThe friction angle of a fracture surface can bedetermined in the laboratory using the directshear box shown in Fig. 3.17. This is portableequipment that can be used in the field if required,and is ideally suited to testing samples with di-mensions up to about 75 mm (3 in), such as NQand HQ drill core. The most reliable values areobtained if a sample with a smooth, planar sur-face is used because it is found that with anirregular surface, the test results can be difficult tointerpret.

The test procedure consists first of using plasterof paris or sulphur to set the two halves of thesample in a pair of steel boxes. Particular care istaken to ensure that the two pieces of core are intheir original, matched position and the fracturesurface is parallel to the direction of the shearforce. A normal load is then applied using canti-levers, and the shear load is gradually increaseduntil a sliding failure occurs. Dial gauges areused to measure both the shear and normaldisplacements from which a pair of plots ofshear displacement against shear stress, andshear displacement against normal displace-ment is produced (Fig. 3.18(a)). Examinationof the shear stress/shear displacement plot willusually show an approximate peak shear stress. 'The normal stress at this shear