Schedule

1
Schedule Problem Set 3- on line, due Monday
Oct.25 Updated Syllabus (with new PS due
date) MidTerm 1, Thursday, Oct. 20 study
guide online this week Field Trip 800 am
Saturday, Oct 22
2
Rheology, cont Review Two basic rock
rheologies 1) 2) Key attritutes of each
rheology 1) something to do with
stress/strain 2) something to do with strain
and time 3) something to do with
recoverability strain rate
3
Creep curve
Behavior of rocks to compression is not simple.
Deforms over time gt
Elastic Non-linear viscous Linear viscous Non
linear viscous
Instant deformation gt
4
Elastic behaviour and shear stress Shear modulus
(G) resistance of elastic solids to shearing.
Divide shear stress (ss) by shear strain (g) G
shear modulus ss/g
ss
5
Elastic behaviour and dilation (important in
seismology) Bulk Modulus (K) resistance of
elastic solids to dilation.
Another relationship between stress and volume
change Poissons Ratio n n-etransverse/eaxial
(perpendicular and parallel to compression
direction) Common values 0 to 0.5 (fully
compressible, to fully incompressible)
6
Poissons ratio, Greek letter nu (n). This
describes the amount that a rock bulges as it
shortens. The ratio describes the ratio of
lateral strain to longitudinal strain n
-etrans/eaxial Poissons 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 n are Fine-grained
limestone 0.25 Apilite 0.2 Oolitic limestone
0.18 Granite 0.11 Calcareous shale 0.02 Biotite
schist 0.01
7
Poissons 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 Poissons ratio are
significant.
8
rocks and deformation
Deformation experiments
Concrete strength test video
9
Nature rocks and deformation
Deformation experiments

• 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.

10
rocks and deformation
Deformation experiments

• Experiments are carried out in steel pressure
  vessels.
• Confining pressure (s2 s3) is often supplied
  by fluid that surrounds the specimen.
• Load is applied to end of rock, differential
  stress (s1 s3) is the important measurement
• Pore-fluid pressure can also be varied.

11
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

12
Natural rocks and deformation
Deformation experiments Strength vs Confining
Pressure
Elastic Deformation Non-Elastic
Deformation Fracture
Compression stress-strain curves at various
confining pressure at 25C
What is confining pressure in real
world? Lithostatic pressure High confining
pressure rock strength
13
Nature rocks and deformation
Deformation experiments Strength vs Confining
Pressure
Changing confining pressure on various rock types
Confining Pressure Lithostatic pressure
14
Nature rocks and deformation
Deformation experiments Strength vs Confining
Pressure At Higher Temperatures
Elastic Deformation Non-Elastic
Deformation Fracture
Compression stress-strain curves at various
confining pressure at 400C
15
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
16
Nature rocks and deformation
Deformation experiments
Summary Experiments demonstrate that rocks have
higher strength with increasing pressure (i.e.,
depth). However, in the Earths 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