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 sn 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 m = 0.6. (i.e.,  at an angle of 30¼ to the sn axis).       (10)

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

iii) For stress conditions where s1 = 80 MPa and s2 = 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)

[60]