Download Stress and Deformation I

Announcements
This week's lab: 1-3 PM with Andrew McCarthy.
Please come prepared with specific questions.
There will be no lecture this Wednesday!
Please use the time to:
1) Study important terms/concepts listed at end of
Powerpoint files
2) Study the practice problems
3) Fault project
Reminder: Midterm Oct. 14
What is it? (quiz)
s3
s1
s3
s1
instantaneous
strain ellipse
Stress and Deformation: Part I
(D&R, 122-126; 226-252)
The goal for today is to explore the stress
conditions under which rocks fail (e.g., fracture),
and the orientation of failure with respect to the
principal stress directions.
1. Coulomb law of failure
2. Byerlee's law
Experimental studies are fundamental in the
study of rock failure
Common types of deformation experiments
Compressive strength tests: The Goal
Compressive strength tests: The Approach
#1
#2
#3
Compressive strength tests: The results
Linear envelope of failure. The fractures form at
angles of 25 to 35 degrees from s1- very
consistent!
Coulomb's Law of
Failure
sc = s0 + tanf(sn)
sc = critical shear stress required for failure
s0 = cohesive strength
tanf = coefficient of internal friction (f = 90 - 2q)
sN = normal stress
Tensile strength tests with no confining pressure
Approach: Similar to compressive strength tests
Results: (1) Rocks are much weaker in tension than in
compression (2) Fracture oriented parallel to s1 (q = 0)
Tensile + Compressive strength tests
Result: Failure envelope is parabolic
0 < q < 30
Failure envelopes for different rocks: note that
slope of envelope is similar for most rocks
sc = s0 + tanf(sn)
sc = critical shear
stress required for
failure
s0 = cohesive
strength
tanf = coefficient of
internal friction
sN = normal stress
Byerlee's Law
Question: How much shear stress is needed to cause movement
along a preexisting fracture surface, subjected to a certain normal
stress?
Answer: Similar to Coulomb law without cohesion
Frictional sliding envelope: sc = tanf(sN), where tanf is the
coefficient of sliding friction
Preexisting fractures of suitable orientation may
fail before a new fracture is formed
What about pore fluid pressure?
Increasing pore fluid pressure favors failure!
-Also may lead to tensile failure deep in crust
Effective stress = sn – fluid pressure
What is it?
What is it? Tensile fracture filled with vein during dilation
s1 is parallel to the structure. What does this suggest about
very low
the magnitude of effective stress?
What mechanism may help produce this structure within the
deeper crust? high fluid pressure to counteract lithostatic stress
What happens at higher confining pressures?
Von Mises failure envelope
- Failure occurs at 45 degrees from s1
Next Lecture
Stress and Deformation II
...A closer look at fault mechanics and rock
behavior during deformation
( D&R: pp. 304-319; 126-149)
Important terminology/concepts
Uniaxial vs. axial states of stress
Coulomb law of failure: known how it is determined and
equation
q values for compression
q values for tension
Cohesive strength
Coefficient of internal friction
Byerlee's Law / frictional sliding envelope- know equation
Important role of pore fluid pressure