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Rock DeformationEOSC364

Dr. Dan FaulknerProfessor Dave Prior

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Rock Mechanics First 6 weeks: Rock mechanics/low

temperature rock deformation 12 lectures

6 practicals

Second 6 weeks: High temperature rockdeformation and microstructures 12 lectures

6 practicals

Assessment: 3 hour exam + 2 practicals

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Course structure: Rock mechanics

and low temperature rockdeformation

Lectures 1-4 Stress and strain

Lectures 5-8 Rock fracture

Lectures 9-12

Faults, friction and earthquakes

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Recommended texts

1st 6 weeks: Rock Mechanics Mechanics of Earthquakes and Faulting by

Chris Scholz (2nd Edition)

Stress and Strain by Win Means Fundamentals of Rock Mechanics by Jaeger and

Cook

Fracture mechanics of rock by Atkinson

Fracture mechanics by Lawn and Wilshaw

Structural Geology textbooks for stress/strain

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Why is rock deformation important?

For understanding how the Earth works

Plate tectonics

Fault mechanics (earthquakes, etc)

Lithosphere strength

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Big scale:

what drives plate tectonics?

Mantle convection

Controlled bydeformation of themantle driven by

heat

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Smaller scale:

crustal deformation Analysed by

structural

geology geometric, butwhat about the

mechanics?

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Controls on rock deformation Environmental

Pressure

Temperature

Fluids Material

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Mechanics and microstructure Nature deforms rocks leaving

microstructural signature We can reproduce microstructure by

laboratory deformation We can infer mechanics from observation

or remote sensing of microstructure

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Stress

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A demonstration of stress

F = M a

F = force, Newtons, NM = mass, kg

a = acceleration, ms-2

Stress = Force / Area

Units: Pascals, Pa

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Principal stresses In two dimensions, the principal stresses are

always the greatest and the least stresses. Theyare always at right angles to each other

They are termed 1 (greatest) and 2(least)

The same concepts apply in 3D, with threeprincipal orthogonal stresses, termed 1 2and3 where 2 is the intermediate principal stress

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Different types of stress Principal stresses, 1 2 3

Mean stress = (1+2+3)/3

Differential stress = 1-3

Deviatoric stress = 1- mean stress Isostatic or hydrostatic stress = 1=2=3

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22

1 1

Homogeneous stress Inhomogeneous stress

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What is the hydrostatic stress

(pressure) at 10 km depth?

Pressure (= hydrostatic stress) = g z = density, kg m-3, ~2700

g= acceleration due to gravity, m s-2, ~10

z= depth, m, 10000

Pressure = 2700 x 10 x 10000 = 270 MPa

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Two meanings of stress At any point, we may define

the stress acting on a plane in one direction(vector)

stress vectors for planes of allorientations at

that point complete state of stress (second-order tensor)

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Normal stress, n

Acts perpendicular to surface

Shear stress,

Acts parallel to surface

Normal stress, shear stress

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2

1

x

y

y-plane(normal toy direction)

x-plane(normal to

x direction)

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Stress as a tensor

y

x

xx

xy

yy

yx

=

yyyx

xyxx

ij

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The stress tensor in 3 dimensions

=

zzzyzx

yzyyyx

xzxyxx

ij

xx

xz

xyy

z

xwhere

i = j, normal stress (n)ij, shear stress ()

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What is the normal stress (n) and

shear stress () on a plane, given1 and 2?

2

1

xx

xy

y

x

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Equations relating the normal andshear stresses with the principalstresses

( )

( ) 222

22

1

42

1

2

4

2

1

2

++

=

+++

=

yx

yx

yx

yx

2

1

n?

?

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Mohr circle construction

normal

stress, n

shear

stress,

A state of stress can be represented by a circle

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2

1

The principal stresses are the greatestandthe leaststresses

The planes on which the principal stressesact have no shear stress acting on them

n

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2

1

The principal stresses are the greatestandthe leaststresses

The planes on which the principal stressesact have no shear stress acting on them

n

2

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2

1

yy

yx

x

y

n

xx

yy

(yy,yx)

(xx,xy)

2 2

xy

yx