ScheduleProblem Set #3- on line, due Monday Oct.25 Updated Syllabus (with new PS due date)MidTerm #1, Thursday, Oct. 20

study guide online this weekField Trip 8:00 am Saturday, Oct 22

ScheduleProblem Set #3- on line, due Monday Oct.25 Updated Syllabus (with new PS due date)MidTerm #1, Thursday, Oct. 20

study guide online this weekField Trip 8:00 am Saturday, Oct 22

Rheology, con’t

Review:Two basic rock rheologies:

1)2)

Key attritutes of each rheology1) something to do with

stress/strain2) something to do with strain

and time3) something to do with

recoverabilitystrain rate

Rheology, con’t

Review:Two basic rock rheologies:

1)2)

Key attritutes of each rheology1) something to do with

stress/strain2) something to do with strain

and time3) something to do with

recoverabilitystrain rate

Creep curve

Behavior of rocks to compression is not simple.

Instant deformation =>

Deforms over time

=>

Elastic:

Non-linear viscous

Linear viscous

Non linear viscous

Elastic behaviour and shear stress

Shear modulus (G): resistance of elastic solids to shearing.

Divide shear stress (s) by shear strain ()G = shear modulus = s/

Elastic behaviour and shear stress

Shear modulus (G): resistance of elastic solids to shearing.

Divide shear stress (s) by shear strain ()G = shear modulus = s/

€

s =G∗γ

s

€

=tan(Ψ)€

Ψ

Elastic behaviour and dilation (important in seismology)

Bulk Modulus (K): resistance of elastic solids to dilation.

Elastic behaviour and dilation (important in seismology)

Bulk Modulus (K): resistance of elastic solids to dilation.

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=K ∗ V −V0( ) /V0[ ]

Another relationship between stress and volume changePoisson’s Ratio =-etransverse/eaxial (perpendicular and parallel to compression direction)

Common values 0 to 0.5 (fully compressible, to fully incompressible)

Another relationship between stress and volume changePoisson’s Ratio =-etransverse/eaxial (perpendicular and parallel to compression direction)

Common values 0 to 0.5 (fully compressible, to fully incompressible)

Poisson’s ratio, Greek letter nu ().

This describes the amount that a rock bulges as it shortens.

The ratio describes the ratio of lateral strain to longitudinal strain: = -etrans/eaxial

Poisson’s ratio is unit-less, since it is a ratio of extension.

What does a low ratio mean?What does a high ratio mean?

Typical values for are:

Fine-grained limestone: 0.25Apilite: 0.2Oolitic limestone: 0.18Granite: 0.11Calcareous shale: 0.02Biotite schist: 0.01

Poisson’s ratio

If we shorten a granite and measure how much it bulges, we see that we can shorten a granite, but it may not be compensated by an increase in rock diameter.

So stress did not produce the expected lateral bulging.

Somehow volume decreases and stress was stored until the rock exploded!

Thus low values of Poisson’s ratio are significant.

rocks and deformation

Concrete strength test videoConcrete strength test video

Deformation experiments

Nature rocks and deformation

Specimens are drilled out cores that are ‘machined’ to have perfectly parallel and smooth ends.

Specimens are carefully measured to determine their initial length (lo) and diameter (to get initial cross-sectional area, Ao).

Specimens are jacketed with weak material - copper or plastic.

Deformation experiments

rocks and deformation

Deformation experiments

Experiments are carried out in steel pressure vessels.

Confining pressure (2 = 3) is often supplied by fluid that surrounds the specimen.

Load is applied to end of rock, differential stress (1 – 3) is the important measurement

Pore-fluid pressure can also be varied.

Nature rocks and deformation

Deformation experiments

Pressure chamber – confining pressure (Pc)

Pore-fluid pressure (Pf)

Difference between Pc and Pf (Pc – Pf ) is effective pressure, Pe

Adjust pressures

Natural rocks and deformation

Deformation experiments

Strength vs Confining Pressure

What is confining pressure in real world?

Lithostatic pressure

High confining pressure & rock strength

€

Pc= ρ ⋅g ⋅h

Compression stress-strain curves at various confining pressure at 25°C

Elastic DeformationNon-Elastic DeformationFracture

Nature rocks and deformation

Deformation experiments

Strength vs Confining Pressure

Confining Pressure= Lithostatic pressure

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Pc= ρ ⋅g ⋅h

Changing confining pressure on various rock types

Nature rocks and deformation

Compression stress-strain curves at various confining pressure at 400°C

Deformation experiments

Strength vs Confining Pressure

At Higher Temperatures

Elastic DeformationNon-Elastic DeformationFracture

Nature rocks and deformation

Deformation experiments

Role of temperature and rock strength

Yield strength decreases with increasing temperatures

Yield strength: the maximum stress that a rock can support elastically (recoverable)

Temperature & rock strength

Nature rocks and deformation

Deformation experiments

Summary:

Experiments demonstrate that rocks have higher strength with increasing pressure (i.e., depth).

However, in the Earth’s crust, as pressure increases, so does the temperature (both typically increase with depth). At some depth, rock strength decreases with depth.

(strength-depth diagrams) Temperature & rock strength