Geol 333
Brittle Failure Lab Exercise
J. Louie and R. Schultz, Spring 2001
- Define and contrast plane stress and plane strain, using
both words and equations for the appropriate conditions.
Draw diagrams illustrating the differences in physical interpretation.
Give an example from structural geology or tectonics of a
process or phenomenon explainable under the plane stress assumption,
and an example explainable under the plane strain assumption.
- Discuss the conditions under which a rock may respond
elastically to stress. (Note: simply stating ``high strain rates
or cold temperatures'' is not enough although aspects of these may appear
in a correct answer.)
- Write two simple equations that express stress as some function of
strain; a) for linearly elastic materials; and b) for linearly
viscous materials. Your equations should contain nothing more than
sigma for stress, epsilon for strain, a time derivative, and two
material constants.
- Use your equation for the linearly viscous material to
derive the units of viscosity in the MKS system. Show your
entire dimensional analysis.
- Discuss the conditions under which a rock may respond
plastically to stress. Identify what parts of the stress-strain curve
are plastic.
- Discuss the conditions under which a rock may respond
in a viscous manner to stress. Identify what parts of the stress-strain
curve are viscous or frictional.
- Define Young's modulus and describe how it can be estimated.
For what geologic situations might you want to use this parameter?
- Sketch and describe the modes of failure of a concrete building
support column where a) it has little or no lateral steel reinforcement;
and b) it has substantial steel reinforcement (but still fails).
Which failure has Mode I fractures, and which has Mode II fractures?
- Consider the 1857 San Andreas fault rupture, which extended from
the Carrizo Plain in central Calif. to Cajon Pass in southern Calif.,
and to 15 km depth. Was it a strike-slip or dip-slip earthquake?
Sketch a rough map, and show where you would
find a) the Mode II parts of the rupture; and b) the Mode III parts
of the rupture.
- Consider the Genoa fault zone, which extends from southwestern
Carson Valley to downtown Reno. Assuming it dips 45 degrees east
and ruptures in a magnitude 7.2 purely normal-slip earthquake,
describe where you would find a) the Mode II parts of the rupture;
and b) the Mode III parts of the rupture.