Lectures on Rock MechanicsLectures on Rock Mechanics

• SARVESH CHANDRASARVESH CHANDRAProfessorD t t f Ci il E i iDepartment of Civil EngineeringIndian Institute of Technology KanpurKANPUR, 208016 Indiaemail: sarv@iitk ac inemail: sarv@iitk.ac.in

The problem in mathematics is black and white but the real ld i Alb t Ei t iworld is grey –Albert Einstein

Rock Mechanics ProblemsRock Mechanics Problems• How will rock react when put to men’s use?p• What is the bearing capacity of rock on surface an at

depths?• What is the shear strength of rocks?• What is the shear strength of rocks?• What is the response of rocks under dynamic /

earthquake type loading?• What is the modulus of elasticity of rock and how to get

it?• What are the effects of rock defects (jointing beddingWhat are the effects of rock defects (jointing bedding

planes, schistocity, fissures, cavities and other discontinuities) on its strength?

• What are the mechanisms of failure of rocks?• What are the mechanisms of failure of rocks?

Rock as a Construction MaterialRock as a Construction Material

• For laying structural foundations to supportFor laying structural foundations to support structures

• For constructing Underground openingsg g p g• For protecting slopes• For supporting railway tracks – BallastsFor supporting railway tracks Ballasts• As base and sub-base for roads and runways• As aggregate in concrete• As aggregate in concrete• Making facia for buildings.

Era Period Epoch Time Boundaries (Years Ago) Holocene - Recent Quaternary 10 000

Geologic

Quaternary 10,000 Pleistocene 2 million Pliocene 5 million Cenozoic Miocene 26 million Tertiary Oligocene ll gic

Timey g

38 million Eocene 54 million Paleocene 65 million Cretaceous 130 million M s z ic Jur ssic Scale Mesozoic Jurassic 185 million Triassic 230 million Permian 265 million Pennsylvanian Carboniferous 310 million Carboniferous 310 million Mississippian 355 million Paleozoic Devonian 413 million Silurian 425 million Ordovician 475 million Cambrian 570 million Precambrian 3.9 billion Earth Beginning 4.7 billion Greenland

What are we calling a rock?What are we calling a rock?

Grade Description Lithology Excavation Foundations

VI Soil Some organic content, no original structure

May need to save and re-use

Unsuitable

V Completely Decomposed soil, some Scrape Assess by soilV Completely weathered

Decomposed soil, some remnant structure

Scrape Assess by soil testing

IV Highly weathered

Partly changed to soil, soil > rock

Scrape NB corestones

Variable and unreliable

III Moderately weathered

Partly changes to soil, rock > soil

Rip Good for most small structures

II Slightly Increased fractures and Blast Good for II g yweathered mineral staining anything except

large dams

I Fresh rock Clean rock Blast Sound

Engineering classification of weathered rock

Primary Rock Types by Geologic OriginOrigin

Sedimentary Types Metaphorphic Igneous Types

GrainAspects

Clastic Carbonate Foliated Massive Intrusive Extrusive

Coarse ConglomerateBreccia

LimestoneConglomerate

Gneiss Marble PegmatiteGranite

Volcanic Breccia

Medium SandstoneSiltsone

LimestoneChalk

SchistPhyllite

Quartzite DioriteDiabase

Tuff

Fine ShaleMudstone

Calcareous Mudstone

Slate Amphibolite Rhyotite BasaltObsidian

Index Properties of Intact Rock

• Specific Gravity of Solids, Gs

• Unit Weight, γ• Porosity, n• Ultrasonic Velocities (Vp and Vs)( p s)• Compressive Strength, qu

• Tensile Strength, T0

• Elastic Modulus, ER (at 50% of qu)Elastic Modulus, ER (at 50% of qu)

Specific Gravity of Rock Minerals

itgalena

dolomiteolivinebaritepyrite

feldsparchloritecalcite

dolomite

halitegypsum

serpentinequartz Common Minerals

Average Gs = 2.70

0 1 2 3 4 5 6 7 8

Specific Gravity of Solids G

halite

Reference Value Specific Gravity of Solids, Gs(fresh water)

Unit Weights of Rocks

26

28

3 ) γsat = γwater [ Gs(1-n) + n]

24

26

t, γ

T (kN

/m3 γ

20

22

Unit

Weigh

t

16

18

Satu

rate

d Dolostone GraniteGraywacke LimestoneMudstone SiltstoneSandstone Tuff

Gs = 2.80 2.65

140.0 0.1 0.2 0.3 0.4 0.5 0.6

Porosity n

2.50

Porosity, n

Geologic Mapping of Rock Mass FeaturesFeatures

INHERENT COMPLEXITIESINHERENT COMPLEXITIES

1 R k f t1. Rock fracture ─ under compressive stresses

2. Size effects ─ response of rock to loading affected by the size of

th l d d l ” (j i t & f t )the loaded volume” (joints & fractures)

3. Tensile strength ─ is low (similar to concrete); HOWEVER a rock mass

can have even less tensile strength

COMPLEXITIES….COMPLEXITIES….

4. Groundwater effects─ water in joints: if under pressure, reduces

normal stress (less resistance along joints)

─ water in permeable rocks (e.g. sandstone) → soil like response

── softeningsoftening of clay seams & argillaceous rocks (e.g. shales)

COMPLEXITIES….COMPLEXITIES….5. Weathering5. Weathering

─ chemical/physical alteration, reduction of engineering propertiesp p

─ limestone caverns, sinkholes: ”Karst”

─ basic rocks with olivine (e.g. basalt) and pyroxene ( g ) pyminerals are reduced to montmorillonite by hydrolysis

Cavernous limestoneCavernous limestone

Coffin Bay

STRUCTURAL FEATURES or DISCONTINUITIESDISCONTINUITIES

1) Bedding planes1) Bedding planes

2) Folds – tension joints at the crest of a fold (strike, dip

& shear joints)& s ea jo s)

– folding may cause shear failure along bedding planes (axialbedding planes (axial plane or fracture cleavage)

FoldingFolding

DISCONTINUITIESDISCONTINUITIES

3) Faults3) Faults– shear displacement zones - sliding

Faults may containF lt ( l ) k– Fault gouge (clay) – weak

– Fault breccia (re-cemented rock) – weakRock flour weak– Rock flour – weak

– Angular fragments – may be strong

DefectsDefects

DefectsDefects

DISCONTINUITIESDISCONTINUITIES

4) Shear zones4) Shear zones– bands of materials - local shear failure

5) Dykes5) Dykes – igneous intrusions (near vertical)– weathered dykes, e.g. dolerite weathers toweathered dykes, e.g. dolerite weathers to

montmorillonite– unweathered dykes attract high stresses

6) Joints – breaks with no visible displacement

Joint PatternsJoint Patterns

sedimentary rocks usually contain 2 sets of joints orthogonal to each other and thejoints, orthogonal to each other and the bedding plane

JOINTSJOINTS1) Open) p

FilledHealed (or closed)

2) SteppedUndulating

PlPlanar2B) each of the above can be Rough

SmoothSmoothSlickensided

JOINT CLASSES (AS 1726-1993)

I St d R hIIIII

Stepped RoughSmoothSlickensidedII Slickensided

IVV

Undulating RoughSmoothV

VISmoothSlickensided

VII Planar RoughVIIVIIIIX

Planar RoughSmoothSlickensidedIX Slickensided

Order of Description of Rocks (AS 1726-1993)

ROCK MATERIAL rock name

grain size (Table A6)COMPOSITION

g ( )texture and fabric (Table A7)

colour

e.g. Basalt, fine, massive, vesicular, dark grey to black

Order of Description of Rocks (AS 1726-1993)

ROCK MATERIAL CONDITION

strength (Table A8)

CONDITIONweathering (Table A9)

e.g. VL strength, XW

OR EH strength, FR

Order of Description of Rocks (AS 1726-1993)

ROCK MASSPROPERTIES

structuredefects (much information required)PROPERTIES defects (much information required)

weathering of joints

Structure:

sedimentary rocks – bedded, laminatedsed e ta y oc s bedded, a ated

metamorphic – foliated, banded, cleaved

igneous rocks massive flow bandedigneous rocks – massive, flow banded

DEFECTS – information needed

ti httightness

cementation or infill

smoothness or irregularity of surfaces

class of jointclass of joint

water in joints

joint orientation

joint spacingjoint spacing

DESIGN IN ROCKDESIGN IN ROCKTake into account:Take into account:• Local geological structure• Shear strength of the rock mass• Shear strength of the rock mass• Impact of water on stability

R k h i ?• Rock anchoring?• Drilling and blasting procedures• Monitoring of stability

– the observational method

Intact RockIntact Rock

H t• Heterogeneous • Anisotropic (soils less so)• Spatial variability (soils the same)• Yield mechanisms are non-linear & depend on

stress level and rock type• Failures are often brittle (soils strain

soften or harden past the peak strength)

Rock MassesRock Masses

C t i di ti iti ith littl t il• Contain discontinuities with little tensile strength

• Scale effect─ response is dependent on stressed volumeresponse is dependent on stressed volume

• Affected by groundwater & weathering

• In-situ stresses difficult to estimate

Rock MassesRock Masses

DEFINITIONSDEFINITIONS

• Dip angle, βw:

the acute angle measured in a vertical plane between the line of maximum dip in a non horizontal plane and the horizontalof maximum dip in a non-horizontal plane and the horizontal plane

i e 0° ≤ β ≤ 90°i.e. 0 ≤ βw ≤ 90

• Dip direction, αw: the geographical azimuth measured in a clockwise direction from north (0°) of the vertical plane in which ( ) pthe dip angle is measured i.e. 0° ≤ αw ≤ 360°

Dip AngleDip Angle

North

Horizontal

ββw

Line of maximum dip

Dip directionDip direction

Azimuth is the direction of an object, measured clockwise around the observer's horizon from North, i.e. an object due north has an azimuth of 0°

Dip DirectionDip Direction

N thNorth

Horizontal

αw

Line of maximum dip

Quantitative Classification of Rock MMass

• Description of Joints:Description of Joints:Orientation, Persistence, Roughness, Wall Strength Aperture Filling SeepageStrength, Aperture, Filling, Seepage, Number of sets, Block size, spacing.ISRM i i ’ tISRM commission’s reportClassification of Rock MaterialBased on Uniaxial Compressive Strength

Uniaxial Compressive Ranges for someUniaxial Compressive Strength

Ranges for some Common Rock Material

Term Kg/cm2 Schist, Silt stone VW-W, Sand Very Weak- VW < 70Stone, Lime stone –VW-M,Granite, Basalt Gneiss

yWeak- WMedium Strong-MS

70-200200-700 Basalt, Gneiss,

Quartzite, Marble –MS-VS

Medium Strong MSStrong- SVery Strong- VS

200 700700-1400> 1400 MS VS

|

Very Strong VS > 1400

|

Classification for Rock Material StrengthStrength

Intact Rock ClassificationIntact Rock Classification• Rock TypeRock Type• Geologic Formation and Age

I di• Indices:– Specific Gravity, Porosity, Unit Weight,

W V l itiWave Velocities– Strength (compressive, tensile, shear)– Elastic Modulus

• What is Rock Mechanics?

R k h i iRock mechanics is a discipline that uses the

principles of mechanics top c p es o ec a cs todescribe the behaviour ofrock of engineering scale.

• How to correlate the properties of rock studied inHow to correlate the properties of rock studied in the laboratory with in-situ properties?

• What in-situ test methods will provide actual in-psitu conditions and properties of rock?

• What design parameters are to be used for rock g pslope design?

• How to stabilize slopes and underground openings?