ERTH2404 L14 RockMechanics Upload

7/28/2019 ERTH2404 L14 RockMechanics Upload

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ERTH2404

Lecture 14: Rock Mechanics

Dr. Jason Mah M a h

, 2 0 1 2


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Reading assignment

Please read Kehews book to complement thematerial presented in this lecture:

Chap. 7;

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Structural Geology Review

Strike and Dip Fractures are defined based on scale

Faults: Normal, Reverse, Strike-Slip faults Joints: fractures along planes of weakness

Folds formed when rocks are compressed andsee plastic deformation

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Lecture Objective & Contents

Objective: To review how rock materialsrespond under applied loads

Contents Mohr-Coulomb and its parameters Lab testing Classification systems: relating rock properties to

engineering properties

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Stress and strain

Stress (): Force applied per unit area [N/m2] = force/area

Strain ( ): Change in the shape and/or size of abody as a result of stress [dimensionless] = L/L

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Stress and strain

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Stress and strain

Elastic deformation: returns to original shape

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Slope = Modulus of Elasticity (E)

Strain ( )

Elastic deformation

Yield stress

Plastic deformation


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Stress and strain for rocks

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(yield stress)


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Deformation in rocks

Controlling factors: Rock type Temperature Pressure Time

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Strength

Strength [N/m2]: level of stress at failure

Above the elastic limit, two scenarios: Brittle rocks fail abruptly Ductile rocks undergo plastic deformation before

failing

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Strength

Compressive strength Resists crushing

Tensile strength Resists tearing apart

Shear strength

Most material have much higher compressivethan tensile strengths

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Measuring rock strength

The most important parameter for a rocksstrength is the uni-axial (unconfined)compressive strength (UCS)

12Stability Analysis in Mine Design, S. McKinnon


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Direct shear test Apply a constant normal stress Increase shear stress until failure Record the shear strength S Repeat test with higher value of normal stress

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Mohr-Coulomb S = C + N tan C = cohesion, = angle of internal friction

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Cohesion C [N/m 2]: inherent shear strength of soils and rocks due to interlocking grains,presence of cement or attracting forcesbetween particles For dry sand C =0

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Angle of internal friction [degree ] When granular materials are poured onto a

horizontal surface, a conical pile forms Angle between the surface of the pile and the

horizontal Maximum angle of a stable slope

Controlling factors: cohesion and density

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Angle of internal friction [degree ] Angle between the surface of the pile and the

horizontal

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Angle of internal friction

Source: Wikipedia


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Measuring rock strength: the problem

The fundamental problem with laboratorytesting: Often large discrepancies between laboratory and

in-situ results Laboratory measurements do not take into

account the effects of:

Structural trends Discontinuities within the rock mass Fluids

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Measuring rock strength: the solution

Develop empirical methods to assess rockmass strength Deere-Miller system RQD Rock Mass Rating system (RMR) Q-system

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Deere-Miller classification of intact rock

Borehole geophysical measurements are oftenmade to assess in-situ properties Gamma-ray logging to distinguish between sand

and shale, and assess porosity of potentialhydrocarbon reservoirs

Petrophysics : earth science discipline studying

in-situ rock properties

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Deere and Miller (1968) developed aclassification scheme based on thestress-strain behavior of intact rocks Stress-strain behavior chosen because it controls

the engineering behavior of rocks Applies only to internally continuous rocks, free of

large-scale weakness planes(e.g. shear zones, joints, bedding planes)

Based on laboratory measurements

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Classification scheme based on:1. Unconfined ( 3=0) compressive strength

a [N/m 2]

2. Tangent modulus of elasticity at 50% of unconfined compressive strengthEt50 [N/m 2]

Measure of stiffness

Modulus ratio MR [ ] = Et50 / a

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Point of failure a

50% a Et50 : slope of tangent at 50% a

Unconfinedcompressivestrength


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Description sigma a Example[kg/cm2]

A Very high > 2250 Basalt

B High 1125-2250 Most igneous rocksStrongest metamorphic rocksLimestone, dolostoneWell-cemented sandstone and shales

C Medium 562-1125 Most shalesPorous limestone and sandstoneSchist

D Low 281-562 Friable sandstonePorous tuff

E Very low < 281 Clay shaleRock saltHeavily weathered rocks

G e o m e t r i c i n c r e a s e


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Mineralogy affects strength: Coarse-grained rocks are weaker

Micro-fractures propagate faster

Fractures take a shorter, less circuitous path throughlarge crystals Some minerals are weaker

Minerals with well-developed cleavage are weaker

Rocks with interlocking crystals are stronger

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G e o m

e t r i c i n c r e a s e

Description E t50[kg/cm2 x 10^5]

Yielding

Highly Yielding

8 - 16

4 - 8

2 - 4

1 - 2

0.5 - 1

0.25 - 0.5

Very stiff

Stiff

Medium stifness

Low stifness


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Mineralogy affects strength: Coarse-grained rocks are weaker

Micro-fractures propagate faster

Fractures take a shorter, less circuitous path throughlarge crystals Some minerals are weaker

Minerals with well-developed cleavage are weaker

Rocks with interlocking crystals are stronger

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Modulus ratio classification MR [ ] = Et50 / a Three classes:

High > 500:1 Med 200:1 500:1 Low < 200:1

Logarithmic scale

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Unconfined compressive strength

M o

d u

l u s o

f E l a s t i c i t y

( E t 5 0

)


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M o d u

l u s o


( E t 5 0

) Intrusives

Extrusives

Igneous rocks


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Deere-Miller classification: Igneous Rocks

Intrusive rocks: Very strong, very stiff due to interlocking

crystalline texture and little anisotropy

Extrusive rocks: Show more variability than intrusive rocks Strength and stiffness related to formation

mechanism Lava flow vs pyroclastic material Texture: massive vs vesicular

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M o d u

l u s o


( E t 5 0

) Limestone / dolomite Sandstone

Sedimentary rocks

Shale


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Deere-Miller classification: Sed Rocks

Show largest variability in strength and stiffnessof all three rock groups

Clastic rocks MR depends on:

Grain size, sorting, mineral composition Lithification (compaction, cementation, crystallization) Non-clastic rocks

MR mostly depends on rock composition

Sedimentary rocks that tend to undergoplastic deformation (e.g. shale, evaporites)have a low M R

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M o d u

l u s o


( E t 5 0

) Marble Quartzite

Metamorphic rocks

Gneiss Schist


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Deere-Miller classification: Meta Rocks

Variable in strength and stiffness due to greatrange of mineralogy, texture and anisotropy

Generally, metamorphism increases strength Quartzites: similar to intrusive igneous rocks

because of dense, equigranular texture andinterlocking crystals

Gneiss: similar to granite, except slightly lowerstrength due to foliation

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Deere-Miller classification: Meta Rocks

Schist: M R strongly influenced by the directionof foliation

Steeply dipping foliation with respect to

compressive stress strength significantly reduced

Marble: less strength compared to originallimestone/dolostone due to increased grainsize from metamorphism

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Rock mass properties

Rock mass Exposed outcrops (road cuts) Underground rock (tunelling, mining) Containing joint sets

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Test results from intact rock samples cannotbe directly applied to an in situ rock mass Laboratory results are useful for comparison

between rock types

in situ : in its original position in the field

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Behavior of in situ rock mass under loadis controlled by: Mostly by

Discontinuities: the weakest link in the rockmass fabric

Pre-existing fractures in the rock mass

To a lesser extent Strength of intact portions of the rocks

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Rock mass properties: Discontinuities

Large scale Structural discontinuities: large-scale features

dividing the rock mass into different zones

Faults, shear zones, unconformities, etc.

Identify location and orientation of structuraldiscontinuities to delineate potentiallyproblematic areas

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Small scale Discontinuities in rock fabric: small-scale features

pervasive throughout the rock mass

In igneous rocks: cooling joints, pyroclasticmaterial, etc.

In sedimentary rocks: bedding planes, mudcracks, ripple marks, etc.

In metamorphic rocks: foliation Geo-statistical analysis required

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R e

f . : K e

h e w T a

b . 6 . 4 . S

h o w n w i t

h p e r m i s s i o n

.


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Rock mass properties: RQD

Rock Quality Designation [%]: index based onthe cumulative length of core pieces longerthan 10 cm in a run divided by the total length

of the core run Total length of core must include all lost coresections

Any mechanical breaks caused by the drilling

process or in extracting the core from the barrelshould be ignored

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P h o t o :

C . S

a m s o n


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44Hutchinson and Diederichs, 1996


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Stability Analysis in Mine Design, S. McKinnon


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Rock mass classification

Several classification schemes have beendeveloped for specific applications Objective:

Estimate the quality of the rock Strength of the rock Achieve a realistic assessment of factors influencing

engineering behavior

Challenge Large number of variables involved Most parameters are measured in-situ

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Dip direction = strike + 90


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S t a b i l i t y A n a l y s i s i n M i n eD

e s i g n , S . M c K i n n o n

Bartons surfaceroughness profiles

Used to measure

Joint Roughnesscoefficient (JRC)


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Two most common classification schemes: Geomechanics classification scheme

(synonym: Rock Mass Rating (RMR))

Rock tunnelling quality index (Q) Empirical systems Common practice to use both

Both schemes use RQD(Rock Quality Designation)

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Rock Mass Rating (RMR)

Proposed by Bieniawski (1973; revised in1989)

Combination of: Laboratory results Visual inspection of in situ rock mass

Common in North America

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Rock Mass Rating (RMR)

Six criteria1. Strength of intact rock material (UCS)2. RQD

3. Joint spacing4. Joint condition (surface roughness, separation)5. Groundwater conditions6. Others (infilling, weathering, orientation)

Each parameter is ranked and sum estimatesquality (strength) of rock mass

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Q-System

Developed by Norwegian GeotechnicalInstitute

Common in Europe

Developed by Barton, Lien and Lunde in 1974

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Q-System

Q = ( RQD / Jn ) * ( Jr / Ja ) * ( Jw / SRF )= block size * inter-block shear strength * active stress

RQD = Rock Quality Designation Jn = joint set number Jr = joint roughness number

Ja = joint alteration number Jw = joint water reduction number SRF = stress reduction factor

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Rock mass classification: 3D Laser Imaging

Research project to measure surface roughness using3D laser imaging

Surface roughness is related to shear strength Rock blocks slide against each other High surface roughness resists motion Low surface roughness (smooth surfaces) do not

Significant is road cuts, slope stability, mining

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Vale, T1 nickel mine (Thompson, Manitoba)

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Mah, 2012


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Surface roughness measured manually Joint Roughness Coefficient (JRC) relates asperity

amplitude and length JRC = 20, maximum roughness

JRC = 1, smooth surface



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3D laser imaging Significant amount of data acquired 3D data acquisition at safe distance Regions typically inaccessible can be scanned Efficient data processing Digital archive


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Mah, 2012


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JRC measured at10 increments toproduce

anisotropy map

Mah, 2012


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Joint orientationand surfaceroughness map

Imposed on 3D

image

M a h

, 2 0 1 2


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Example 1: Impact of orientation

A tunnel is to be driven through a slightlyweathered granite with a dominant joint setdipping at 60 against the direction of drive.

Strike is perpendicular to the axis of thetunnel.

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Drive against dipDrive with dip


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Example 1: Impact of orientation

A tunnel is to be driven through a slightlyweathered granite with a dominant joint setdipping at 60 against the direction of drive.

Strike is perpendicular to the axis of thetunnel.

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Drive against dip45 - 90 20-45 45 - 90 20-45 20-45 45 - 90

0 -2 -5 -10 -5 -12

Strike parallel to tunnelaxisOrientation of discontinuities in tunnelling Drive with dip

Strike perpendicular to tunnel axis

Rating


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Example 2: Application of RMR

Core testing gives a uniaxial compressivestrength of 150 MPa.

Logging of diamond drilled core gives averageRDQ values of 70%.

The slightly rough and slightly weathered joints with a separation of


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Drive against dip45 - 90 20-45 45 - 90 20-45 20-45 45 - 90

0 -2 -5 -10 -5 -12

Uniaxial compressive strength [MPa] >250 100 - 250 50 - 100 25 - 50 5 - 25 1 - 5 2000 600 - 2000 200 - 600 60 - 200 < 6020 15 10 8 5

Very rough surfaces Slightly rough surfaces Slightly rough surfaces Slickenslided surfacesUnweathered walls Slightly weathered wall Highly weathered walls or gouge < 5 mm thickNo separation Separation < 1 mm Separation < 1 mm Separation 1-5 mm Separation > 5 mm

Dry Damp Wet Dripping Flowing15 10 7 4 0

Strike parallel to tunnelaxis

RatingGeneral ground water conditions

Orientation of discontinuities in tunnelling Drive with dipStrike perpendicular to tunnel axis

0

Condition of discontinuitiesSoft gouge > 5 mm thick

Rating

Rating

Rating

Rating

Rating 30 25 1020

Final rating = -5 + 12 + 13 + 10 + 25 + 7 = 59


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I II III IV VDescription Very good Good rock Fair rock Poor rock Very poor rockRating 81 - 100 61 - 80 41 - 60 21 - 40 < 21Cohesion [kPa] > 400 300 - 400 200 - 300 100 - 200 < 100

Angle of internalfriction

[degree] > 45 35 - 45 25 - 35 15 - 25 < 15

Tunnellingstand-up time

20 yr for 15 m span

1 yr for 10 m span

1 week for 5 m span

10 hr for 2.5 m span

30 min for 1 m span

Rock mass classes

Rating of 59 corresponds to a fair rock

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