5 brittle rockdefmn(petrology)

8/12/2019 5 Brittle RockDefmn(Petrology)

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1. Deformation mechanisms: classes ofdeformation response, elastic constants,

secondary effects, grain crushing

2. How do faults actually form???

3. Introduction to the Brittle to Ductiletransition

Tuesday, April 19, 2011


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The response of rock to applied stress

Classes of material:

- homogeneous

- inhomogeneous (heterogeneous)

Most rocks we will be dealing with can be considered: statisticallyhomogeneous

- have the same properties within defined limits

- e.g. a granite may be inhomogeneous when sampled at thecentimetre scale (only a few grains in the sample) but

statistically homogeneous at the metre scale (millions of grainsin the sample)

Even homogeneous materials may be:

- isotropic (properties independent of direction)

- anisotropic (properties vary with direction)

1. Rock Deformation



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We are primarily concerned with large rock masses which

we can consider as a mechanical continuum

We therefore consider only macroscopic descriptions ofdeformation and not the underlying micro-mechanismsresponsible

The macroscopic deformation response is characterised bythe stress-strain relation

There are 3 main classes of response: - Brittle: Localized Fracture and Faulting

- Transitional: Brittle -> Ductile

- Ductile: Distributed Flow and Folding

Classes of Deformation Response



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Summary of Rock Deformation Types



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Response to applied stress is instantaneous All strain is recovered on removal of stress

No permanent deformation

!

"

slope = E

Hookes Law: E = !/"

E = Youngs modulus of elasticity(one of the elastic constants)

Other examples of elastic response:

Elastic but not Hookean

Hysteresis

#1: Brittle Elastic Behaviour



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Poissons Ratio (#):

#= !"y/ "

x

For an ideal incompressible solid: #= 0.5

For most rocks: #= 0.15 to 0.35

Shear (Rigidity) Modulus ($):

$= shear stress / shear strain = !s/%

Bulk Modulus (K): a block of material subjected

to a pressure change (&P) undergoes a volumestrain (')

K = &P/'

!x

!

x

"x

#"y

Other Elastic Constants



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For isotropic materials, there are only 2 independent elastic

constants Therefore, if 2 are known we can determine the others

Relationships between elastic constants

Bulk modulus:

shear modulus:

Poissons ratio



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Pc= !

2= !

3

strength

Data is plotted as differential stress (!1 "!3) against axialstrain ("), as shown above R.

Rock Strength is defined as the maximum differential stress

that the rock is able to sustain.

Measured experimentally in the laboratory using a triaxial testingmachine as shown schematically below:

Measuring the stress/strain response of rocks



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Confining Pressure Shear Fracture Angle

N.B. The relationship can be expressed in terms of aMohr diagram by the straight-line envelope:

| (| = (0+ !tan )

where tan )is a constant, the slope of the envelope



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Effect of Anisotropy

#

0

90



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True triaxial tests

!3

!3

It is implicit in the widely usedCoulomb and Mohr criteria

of failure that the value of the

intermediate principal stress !2

does not affect the brittle

fracture strength; in particular,the Mohr envelopes for failure in

triaxial compression and

extension tests should coincide...

BUT

!2does have an effect, but is not

as strong as the combined effect

of !2+!3



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Haimson & Rudnicki, JSG, 2010

Failure occurs at increasingmaximum stress for increasingintermediate stress, for a givenfixed value of minimumprincipal stress.

Non-linear...

To date, data collected on dryrocks only

No experiments yet conductedat elevated temperatures...leading to enhanced stresscorrosion: strain rate alsoimportant!

True triaxial stresses

Intermediate principal stress,

Maximump

rin

cipalstress,

=

Low

Med.

High

Mohr

Criterion;

=

"3

"3

"3

"2

"1

" 1

" 2

" 2

" 3

"1

"2

"3



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Shear Fracture Angle

Shear Fracture

Cleavage orientation



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Other types of deformation... graincrushing



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Hydrostatic Compaction P*



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Compaction bands: Formation and features

The transition from axial splitting, through faulting, to cataclastic flow andlocalised compaction proceeds as a function of increasing confining pressure:

Confining pressures increase >> axial splitting >> shear failure atdecreasing angle >> cataclasis >> compaction bands



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Localised compaction thought to be important in range of geoscience disciplines,such as fluid compartmentalisation in reservoirs



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Compaction bands 101: basic concepts

As before CBs can be monitored in the lab using Rock Physics as a tool: As the cylindricalsamples are loaded, Grain crushing (C*) occurs due to the application of stress, as a function ofconfining pressure (P=110MPa)... leading to CB formation

C* is largely constrained by the acceleration in AE activity which results from the brittleprocesses associated with shear-enhanced compaction.



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Yield envelopes for four sandstones, covering the transition from shear-induced dilatancy (opensymbols) to shear-enhanced compaction (closed symbols). [Max stress at given Pc]

Plotted in P-Q space [P: is the effective pressure, Q: differential stress.]



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Yield envelopes for four sandstones, covering the transition from shear-induced dilatancy (opensymbols) to shear-enhanced compaction (closed symbols). [Max stress at given Pc]

Plotted in P-Q space [P: is the effective pressure, Q: differential stress.]

No obvious / intuitive link between porosity and grain

crushing / CB onset... whats going on?

Hypothesis: to test the influence of anisotropyon thisphenomenon...


C b d d WR T


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P-axis samples:

Cored parallel tobedding

Bands normal to bedding

C* marks the onset of

shear-enhancedcompaction:

Here, C*p~150MPa

Compaction bands: new data W.R.T. anisotropy


C b d d WR T


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N-axis samples:

Cored normal tobedding

Bands parallel to bedding

P-axis samples areconsistently strongerthan N-axis samples:

C*n~140MPa



C i b d d WR T i


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C*p~150 MPa

C*n~140 MPa



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The evolution of the compactionbands through time is very rapid

(seconds)...

...As is evident in these movies

There is a considerable influencefrom the rock anisotropy

Compaction bands: spatio-temporal evolution



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(seconds)...






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(seconds)...





C i b d bili


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P-axis cores:

A similar overall reduction,but much more gradual.

Permeability response to the growth of compaction bands, sample axis parallel to bedding

Compaction bands: permeability


C i b d bili


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N-axis cores:

Massive and rapid drop in K

with growth of the firstband.

Apparent reduction of 3orders of magnitude(actually greater than 4orders of magnitude).

More gradual reductionwith growth of more bands

Compaction bands: permeability

Permeability response to the growth of compaction bands, sample axis normal to bedding



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2. But how do faults actually form???

they are macroscopic shear cracks

coalescence of mode I fractures

Healy et al., 2006, Nature



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Fault formation

Wing cracks

stress



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Real material contain imperfections

Imperfections concentrate stress

Failure at lower stress than theoretical strength

Griffith applied a thermodynamic approach

strength of real materials can be explained by the

presence of microcracks ~1 !m long

these Griffith cracks were entirely hypothetical untilthe advent of electron microscopy

Griffith theory (1920, 1924)


F ti f i l k (M d I f t )


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Formation of axial cracks (Mode I fractures)

Many small fractures (e.g. mode 1 microcracks) can link together to form a

larger macro fault... based on the stresses at the fault tip, typically a maximum

at 300

... explaining why fault angles are also close to 300


Q i i f l h f i i i


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Quasistatic fault growth from acoustic emissionsLockner et al., 1991



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Using fracture mechanics tointerpret fault displacements and

structure

Non-linear elastic approach needed

fault damage zones displacement/length relationships

see Scholz (2002)



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F l d


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Fault damage zones have been suggested to be thedamage wake of a migrating process zone.

(e.g. Vermilye + Scholz, JGR, 1998)

Damage also occurs from Earthquake rupture (Rice et al., BSSA, 2005) Geometric irregularities (Chester and Chester, JGR, 2000)

Fault damage zones


Brittle failure of a cylinder in axial


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Brittle failure of a cylinder in axialcompression

Axial cracks are Mode I fractures volume increase

Brittle deformation is always accompanied byvolume increase (as fracture density increases)

Brittle deformation is highlypressure sensitive(as illustrated in last lecture) increase in pressure suppresses the formation

of new fractures


Unconfined uniaxial compression test


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Unconfined uniaxial compression test

axial strain

circumferential strain

volumetric strain

Stress

Failure

Yield

extension compression

Strain

elastic


Mohr Coulomb failure envelope revisited


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Mohr-Coulomb failure envelope revisited

shearstress

normalstress

confining pressuresfor three tests

failure stress forthe three tests

Another example... applied toreal data


Mohr Coulomb failure envelope revisited


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shearstress

normalstress

)

!3 !1

C

unstable

stable

Mohr-coulomb

failure envelope

Mohr-Coulomb failure envelope revisited

where:

tan*= coefficient of internal frictionC = cohesive strength

Mohr-coulomb failure criterion


Alternate expression of the Mohr-


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Alternate expression of the Mohr-Coulomb criterion

where

!3

!1

gradient = b

a


Griffith failure criterion (tensile)


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Griffith failure criterion (tensile)

parabolic in shape


S mmar


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Summary

Real materials contain imperfections(Griffith cracks)

Brittle deformation involves opening ofcracks pressure sensitive

Mohr-Coulomb failure criterion is empirical

Griffith failure criterion is mechanistic,although it only describes tensile failure


3 Brittle-Ductile Transition


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3. Brittle-Ductile Transition

Effect of pressure

Effect of temperature

Volume change Simple physical models

Dehydration


The Brittle-Ductile Transition


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In geology and geodynamics it is important to know ifrocks will behave in a ductile or a brittle manner under agiven set of conditions at depth in the Earth

The brittle-ductile transitioncan be studied by

seeing how the brittle strength and the ductile strengthboth vary with temperature and pressure

Since we know how temperature and pressure both

increase with depth in the Earth, we can then determinethe depth at which the brittle-ductile transition occurs





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Brittle strength is stronglyinfluenced by pressure

Ductile strength is almostindependent of pressure

Brittle strength is virtuallyindependent of temperature

Ductile strength decreasesdramatically as temperature

increases

temperature

pressure

Brittle

Ductile

Combined effects of pressure and temperature



The Brittle-Ductile Transition in the Earth


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Depth

Strength (pressure, temperature)

Shear strength from Coulomb Criterion

Ductile flow stress from Dorn Equation

Max. strength of the Lithosphere

Maximum strength occurs at the Brittle-Ductile Transition

Depth to B-D Transition depends on properties of the rock

The Brittle Ductile Transition in the Earth


Geological view of brittle-ductile


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Geological view of brittle ductiletransition


Rock mechanics view #1 of the


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Rock mechanics view #1 of thebrittle-ductile transition




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Byerlees law and Goetzes criterion bound an approximate zone, inside of

which the deformation is neither brittle or ductile

AND, as we saw from the grain crushing, even brittle processes can manifest

themselves as ductile under certain P/T and pore pressure conditions...Tuesday, April 19, 2011



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Summary


Rock mechanics view of the brittle-


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Rock mechanics view of the brittle-ductile transition: Pressure


Transition from Brittle Faulting to Cataclastic Flow


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!S

!N

Amontons Law

Combined Fracture StrengthEnvelope (parabolic)

stress drop

Transition from faulting to cataclastic flow

Below the transition frictional sliding is easier than fracture

Above the transition fracture is easier than frictional sliding

g


Stress-strain curves as a function of confining pressure for four very different


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rock types with very different strengths:

sandstone

serpentinite

dunite dolerite


Some real examples


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deformed Carrara Marble

deformed Diemelstadt Sandstone

p

Darley Dale Sandstone Icelandic Basalt


What similarities do we see in all cases?


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Strength increases with increasing!

3.

Strain at failure increases with both strength

and !3.

Stress drop at first increases and then

decreases with !3until it eventually

becomes zero.

Overall we see qualitatively similarbehaviour for all these very different rocktypes with very different strengths.

What similarities do we see in all cases?


Stress Drops


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Data from same sets of experiments shown earlier....

p

sandstone

serpentinite

dunite dolerite


Stress Drops


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Stress drop is a key parameter because it provides the energy

release that drives earthquakes.

Stress drops are low at low !3= shallow depth: so only small

earthquakes in shallow crust.

Stress drops are highest at intermediate !3= intermediate depth:

so largest crustal earthquakes occur at depths of 5 to 12 km. Stress drops decrease to zero at high !3= very deep: so no large

earthquakes below about 15 km in normal crust (deep

earthquakes generally occur only in subducting lithospheric slabs).

NB: the point where the stress drop goes to zero marks the

transition from localized shear faulting to distributed cataclastic

flow.

Overall we again see qualitatively similar behaviour for all four very

different rock types.

p


Mohr-Coulomb Failure Diagram


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gWe have now looked at a number of phenomena associated with rock fracture and faulting:

Initial compaction

Elastic deformation

Onset of new cracking leading to dilatancy Rock strength at peak differential stress

Dynamic stress drop

Frictional sliding on the shear fault

Transition from shear faulting to cataclastic flow

All of these phenomena can be represented on a

single Mohr-Coulomb failure diagram...


Mohr-Coulomb Failure Diagram


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Increasing

strain

Cataclastic Flow

Tensile Fracture

Extensile ShearFracture

Compressional Shear

Fracture

SHEARSTRESS

NORMALSTRESS

SccScc

Cracks open Cracks closeStrain softening

(fracture)Strain hardening(cataclastic flow)

Initial crackpropagation

CATACLASISA

NDDILATANC

Y

Sliding

frictio

nonfr

acture

gWe have now looked at a number of phenomena associated with rock fracture and faulting:

Initial compaction

Elastic deformation

Onset of new cracking leading to dilatancy Rock strength at peak differential stress

Dynamic stress drop

Frictional sliding on the shear fault

Transition from shear faulting to cataclastic flow

All of these phenomena can be represented on a

single Mohr-Coulomb failure diagram...


Rock mechanics view of the brittle-


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ductile transition: Temperature


Laboratory examples of coupled processes


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Uniaxial press

LOAD

AE

AE

Sample

y p p pCoupled Processes:

- Episodic Tremor and Slip (higher pressures)- Seismogenic lavas and eruption forecasting (i.e. very high/representative temperature)




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Uniaxial press

LOAD

AE

AE

Sample

y p p pCoupled Processes:

- Episodic Tremor and Slip (higher pressures)- Seismogenic lavas and eruption forecasting (i.e. very high/representative temperature)




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Furnace

~1200C

Uniaxial press

LOAD

AE

AE

Sample

Coupled Processes:- Episodic Tremor and Slip (higher pressures)

- Seismogenic lavas and eruption forecasting (i.e. very high/representative temperature)


Seismogenic lavas: when does melt fracture?


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- Transition from ductile behaviour to brittle deformation- Can we elucidate this process using Laboratory AE Rock Physics tools?


Seismogenic lavas: when does melt fracture?


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- Transition from ductile behaviour to brittle deformation- Can we elucidate this process using Laboratory AE Rock Physics tools?

Remember this...


Brittle --> ductile rocessesf


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7 % strain 14 % strain 21 % strain 28 % strain 35 % strain0 % strain

As we move from ductile tobrittle behaviour (applied stress20 MPa, T=870 C) : more

cracks, more AE...

AE/time relationship revealsincreasing AE, and fewer, moreenergetic, AE.

Colima

Fracturing initiates in crystals, then coalesces into macroscopic extensional fracturesobservable on barreled sample surfaces from 20 to 35% strain (ductile -> brittle):



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End of Lecture 2, part 2.

Coffee!

5 brittle rockdefmn(petrology)

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