__Homework
Set 2__: Stress, Elasticity, and Frictional Sliding

1. i) What is meant by the term *lithostatic
stress* and
why is it pretty much the same thing as a "pressure" inside the Earth? (3)

ii) What is
a *principal stress*
and why are there three of them? (4)

iii) Faults
can only slide if the compression (stress) from one direction is different to
the compression from a different direction, allowing a change in shape
(strain). Given this requirement, can earthquakes happen if the only stress
inside the crust is lithostatic stress? Explain your reasoning. (2)

iii) What
is meant by *elasticity* when referring to rocks? (2)

iv) Draw a
hypothetical stress vs strain graph for rock and label the portion where the
behavior of the rock is elastic. Also label the location on the graph where the
behavior becomes brittle. (5)

v) Describe
what actually happens in the rock at the instant where the behavior becomes
brittle. Be sure to describe the type of feature that forms and how it is
oriented within the rock. (5)

2. If the maximum principal stress is
oriented perpendicular to a __vertical__ fault inside the crust, would this
fault be able to slip and produce an earthquake? Explain your reasoning in a
few sentences. (*Hint*: think about what causes sliding in any situation) (4)

3. Explain the difference
between *stick-slip*
sliding and *stable*
sliding and what this means for earthquakes. (8)

4. i) What is meant by the coefficient
of static friction (m) and how is it measured? (4)

ii)
Conceptually, how is m different from the
coefficient of dynamic friction and why is this important? (3)

5. i) Draw a hypothetical t versus s_{n}
graph in which you show the line that separates the stable from unstable fields
(i.e., the frictional failure line defined by the Coulomb failure criterion).
Label each field. __The axes must be drawn at the same scale as each other__.
Each axis should range in values from 0 MPa to 100 MPa. Assume that the cohesion of the rock S_{o}
= 10 MPa and that the slope of the line m
= 0.6. (i.e., at an angle of 30¼
to the s_{n} axis). (10)

ii) What is
the equation of the frictional failure line? (2)

iii) For
stress conditions where s_{1} = 80 MPa and s_{2} = 30 MPa, draw a Mohr circle on
your graph and indicate whether or not rocks would be prone to frictional failure
under these conditions (explain why). (5)

iv) How
much pore fluid pressure would need to be added in order for frictional failure
to occur here (i.e., by how much would the Mohr circle need to shift to the
left to cause failure)? (3)

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