5 Brittle RockDefmn(Petrology)
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Transcript of 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
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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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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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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
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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Compaction bands 101: basic concepts
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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Compaction bands 101: basic concepts
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...
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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
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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
Compaction bands: new data W.R.T. anisotropy
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C i b d d WR T i
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Compaction bands: new data W.R.T. anisotropy
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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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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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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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
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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)
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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
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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
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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
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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
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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
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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
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Alternate expression of the Mohr-
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Alternate expression of the Mohr-Coulomb criterion
where
!3
!1
gradient = b
a
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Griffith failure criterion (tensile)
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Griffith failure criterion (tensile)
parabolic in shape
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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
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3 Brittle-Ductile Transition
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3. Brittle-Ductile Transition
Effect of pressure
Effect of temperature
Volume change Simple physical models
Dehydration
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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
The Brittle-Ductile Transition
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The Brittle-Ductile Transition
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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
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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
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Geological view of brittle-ductile
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Geological view of brittle ductiletransition
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Rock mechanics view #1 of the
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Rock mechanics view #1 of thebrittle-ductile transition
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Rock mechanics view #2 of the
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Rock mechanics view #2 of thebrittle-ductile transition
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
Rock mechanics view #3 of the
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Rock mechanics view #3 of thebrittle-ductile transition
Summary
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Rock mechanics view of the brittle-
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Rock mechanics view of the brittle-ductile transition: Pressure
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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
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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
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Some real examples
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deformed Carrara Marble
deformed Diemelstadt Sandstone
p
Darley Dale Sandstone Icelandic Basalt
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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?
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Stress Drops
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Data from same sets of experiments shown earlier....
p
sandstone
serpentinite
dunite dolerite
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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
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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...
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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...
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Rock mechanics view of the brittle-
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ductile transition: Temperature
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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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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)
Tuesday, April 19, 2011
Laboratory examples of coupled processes
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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)
Tuesday, April 19, 2011
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?
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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...
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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!