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Geol 344: Earthquakes and Seismic Hazards
Fall 2013
Homework Set 2: Stresses, Elasticity, Frictional Sliding, and Mohr Circles
1. i) What is meant by the term lithostatic stress, how is it calculated, and why is it pretty much the same thing as
a “pressure” inside the Earth?
(3)
ii) What are normal stresses and shear stresses?
(2)
iii) What is a principal stress and why are there three of them?
(2)
iv) If a principal stress is also a normal stress for a particular plane, what can we say about the likelihood of
sliding on that plane, and why?
(2)
v) Faults can only slide if the principal stress from one direction is different to that from an orthogonal
direction, allowing a change in shape (strain). What do we call this state of stress?
(1)
vi) Given the requirement in (v), can earthquakes happen if the only stress inside the crust is the lithostatic
stress? Explain your reasoning with the aid of a s vs n graph.
(4)
vii) What is meant by elasticity when referring to rocks?
(2)
viii) Draw a conceptual 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.
(4)
ix) 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.
(4)
2. Explain the difference between stick-slip sliding and stable sliding and what this means for earthquakes.
(4)
3. i) What is meant by the coefficient of static friction () and what defines its magnitude?
(3)
ii) Does  have any units of measurement? Explain your answer.
(2)
iii) Conceptually, how is  different from the coefficient of dynamic friction and why is this important?
(2)
Geol 344: Earthquakes and Seismic Hazards
Fall 2013
4. i) Draw a hypothetical s versus 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 So = 10 MPa and that the slope of the line  = 0.6. (i.e., at an angle of 30° to the
n axis).
(10)
ii) What is the equation of this frictional failure line?
(2)
iii) For stress conditions where 1 = 80 MPa and 3 = 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).
(4)
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)? Draw this new Mohr circle that
now touches the failure line.
(4)
v) Label 2 on your new Mohr circle where it touches the failure line and measure this angle using a protractor.
What value did you get?
(2)
vi) Given this value of 2, draw a figure showing how this relates to the angles between the fault and the
principal stress orientations in nature (i.e., in physical space). Note: only 1 and 3 are important for the
faulting.
(3)
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