Geol 542: Advanced Structural Geology
Fall 2013
Problem Set #1: Rheology, Fractures, and Physical Quantities
Answer the problems below. Please pay attention to specificity when answering questions that require a written
explanation of a concept. All answers must be typed. Equations and sketches may be drawn in by hand.
1. The rheology of geologic materials can be described using a number of constitutive behaviors.
a)
What is meant by constitutive behavior?
(2)
b) Which of the following can or cannot be considered rheologic constitutive behaviors?
If not, explain why:
elasticity; strength; viscosity; density; plasticity; visco-elasticity; Prandtl number
2. What is a fracture?
(5)
(4)
3. The three different modes of fracturing are mode I, mode II, and mode III, defined according to the relative
motions in the near-tip region. Give examples of geologic fractures for each of these three modes, explaining
your reasoning. In developing your answer, think very carefully about the nature of a tipline and how the
motion along a fracture relates to the tipline orientation. Also provide one example of a mixed-mode fracture
(i.e., involving more than one mode simultaneously).
(8)
4. The SI unit for the measurement of pressure is the Pascal (Pa). Nevertheless, we often see pressure-versusdepth diagrams in geology expressed in kilobars (kb). For example, the invariant point for kyanite-andalusitesillimanite is frequently taken to be at 3.5 kb.
a)
How many Pascals is 3.5 kb equivalent to?
(2)
b) How many megapascals is this (MPa)?
(2)
c)
(2)
What is the direct conversion factor for kilobars to megapascals?
d) Which is the simpler unit of measurement for pressures in the Earth's crust: Pa or MPa? Give your
reasoning.
(1)
5. All physical quantities are characterized by some form of mathematical dimension: scalar, vector, or tensor.
Indicate the mathematical dimension of the following physical quantities that are relevant to geomechanical
studies:
(8)
velocity
time
stress
force
strain
length
temperature
acceleration
Geol 542: Advanced Structural Geology
Fall 2013
6. The three types of coordinate systems we typically use in geomechanical analyses are Cartesian, polar, and
spherical.
a)
What are the three coordinates used to define each of these three coordinate systems?
b) Which of the following Cartesian systems (A, B, or C) is shown in its correct, right-handed form?
A.
c)
B.
(3)
(2)
C.
What are the polar coordinates in terms of the Cartesian coordinates (i.e., the transformation
equations from Cartesian to polar systems)? These were provided in class.
(1)
d) What are the spherical coordinates in terms of the Cartesian coordinates (i.e., the transformation
equations from Cartesian to spherical systems)? These were provided in class.
(1)
e)
Now use basic trigonometry to determine the reverse transformation equations:
(i)
(ii)
f)
polar to Cartesian
spherical to Cartesian
(4)
(5)
For each of the three types of coordinate systems, list one geologic process or geologic system for
which the use of that particular coordinate system would be a logical choice in a geomechanical
analysis. Explain your reasoning in each case.
(6)
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