GEOL 3700 STRUCTURE AND TECTONICS
STRESS PROBLEMS 1
General hints and instructions
Always visualize the problem first. It is usually best to draw a sketch. Label the sketch with arrows, etc.,
to represent the forces etc., that are involved in the problem. Be neat and careful. It can be useful to jot
down the useful, applicable mathematical relations next. Then solve the problem step by step. Be neat and
label what you do. It generally is easiest to work out the problem using variables (e.g., x, y, s, etc.), then
plug in the numerical values to compute the answer to the problem at the very end. Finally, use your
intuition and common sense by always looking at your answer and asking yourself: "is that result
reasonable?" Follow these instructions and hints to earn full credit for your work.
This homework is due at 5 pm on Friday February 1.
The problems
1. This problem involves only unit conversions.
a. Convert 2.47 g/cm3 to units of kg/m3. Show your work!
b. Convert 13 lbs (weight, which is a force) to Newtons (be careful; this can be a tad tricky).
c. Convert 13 lbs/in2 to MPa (mega-Pascals).
d. Convert 10 Pa to MPa.
e. Convert 17 x 108 Pa to MPa.
f. Convert 17 x 108 Pa to kb.
2. Look up and list the densities of the following minerals and rocks:
a. Quartz
b. Calcite
c. Magnesium-rich olivine
d. Potassium feldspar
e. Plagioclase feldspar
f. Granite
g. Basalt
3. This question involves a cube of granite that is 10m on a side and has a density 2.6 g/cm3.
a. If the cube of granite is resting on a solid horizontal surface, what is the vertical stress (i.e.,
pressure) at the cube’s base?
b. If the cube of granite is resting on a pedestal that is 2 m by 2 m in horizontal crosssectional area, what is the pressure at the base of the granite cube?
c. If the cube of granite is resting on a pedestal that is 1 m by 1 m in horizontal crosssectional area, what is the pressure at the base of the granite cube?
d. Why are the answers to a, b, and c different from each other?
4. Calculate the vertical stress (pressure) at various depths in the Earth’s crust at a location where
porosity is negligible. Assume the density of the crust is 2.6 g/cm3 and give your answers in
MPa and kb. This question will be much easier if done on a spreadsheet program such as
Microsoft Excel. If you are unfamiliar with generating plots in Excel, there is a handout
online that explains how to do it.
a. What is the pressure at 1 km depth?
b. What is the pressure at 2 km depth?
c. What is the pressure at 4 km depth?
d. What is the pressure at 10 km depth?
e. What is the pressure at 20 km depth?
f. What is the pressure at 40 km depth?
g. Plot all of your answers (a-f) on a graph. Construct your graph this way: make the x-axis
pressure and the y axis depth. But make depth increase downwards , as it does in the
Earth. Your axes should look like an upside-down capital L.
5. This question asks you to calculate the water pressure in the pores and fractures of rocks at
various depths in the Earth’s crust. As an approximation, we assume that the pore pressure
equals the pressure from a column of water as high as the pores are deep – analogous to the
way you solved for pressure in problem 3. For all questions, assume the density of water is
1.0 g/cm3 and give your answers in MPa and kb. Like the previous question, this one will be
much easier if done using a spreadsheet program than by hand or with a calculator.
a. What is the pore pressure at 1 km depth? What is the effective vertical stress on the rocks
at this depth?
b. What is the pore pressure at 2 km depth? What is the effective vertical stress on the rocks
at this depth?
c. What is the pore pressure at 4 km depth? What is the effective vertical stress on the rocks
at this depth?
d. What is the pore pressure at 10 km depth? What is the effective vertical stress on the rocks
at this depth?
e. What is the pore pressure at 20 km depth? What is the effective vertical stress on the rocks
at this depth?
f. What is the pore pressure at 40 km depth? What is the effective vertical stress on the rocks
at this depth?
g. Plot all of your answers (a-f) on the same graph as you used for question 3. Label the three
curves (lines) ‘lithostatic load,’ effective vertical stress,’ and ‘pore pressure.’
6. All of the rock in the hanging wall block of a horizontal thrust fault has been eroded away
except for one large piece (called a klippe). The piece is composed of sandstone, is roughly
circular in map view and is very steep - sided. We can treat it as a perfect right cylinder that
is 1 km in diameter and 300 meters high. A well cemented, 10% porosity sandstone has a
density of about 2.4 g/cm3. What is the stress on the thrust fault along the base of the
sandstone klippe? What assumption(s) must you make to calculate the stress load?
Parameters and their units
time (t): seconds (s); scalar
length (l): meters (m) or feet (ft); scalar
mass (m): kilograms (kg) or sometimes pounds (lb), but be careful because pounds also are used
to represent a force; scalar
density (ρ): g/cm3 or kg/m3
velocity (V): meters/second (m/s); vector
acceleration (a): m/s2; vector
force (F): Newtons (N); kgm/s2; pounds also are a measure of force; vector
Pressure (P): Pascals (Pa) kg/ms2 or bars (b); generally a scalar (also kilopascals, Kpa;
megapascals, MPa; bars, b, and kilobars Kb)
Stress (σ): Pascals or bars; tensor
How the parameters relate to each other
F=ma
V = l/t
V = at
P = F/A
σ = F/A
Metric unit naming conventions commonly used in geology:
centi: one hundredth
milli: one thousandth
micro: one millionth
kilo: one thousand
mega: one million
giga: one billion
Conversions:
1 inch = 2.54 cm
1 kg (weight equivalent) = 2.2 lb
1 kb = 100 MPa
acceleration due to gravity is about 9.8 m/s2