Homework #1
Humphrey Geology 4880 Fall 2015
Notes:
Try to couch your
answers at the appropriate level of accuracy that is implied by the question.
You are free to use data from any source or to make reasonable
assumptions, but state what you assume, or show the data you use and give the source
of the data. Be aware that data and
ideas from the Web are of highly variable quality. To do the homework you will have to take 4
steps: figure out how to do the problem, decide on the data you need (if any),
collect the necessary information, and finally produce the answer.
Your work must be neat, legible, and organized. I am not willing to wade through a mess and I will just give it back to you to re-do. You can work with others, but be aware that you will have to do similar questions on exams and quizzes, by yourself.
Often the homework
will include one or more questions that are quite hard. Usually the last one(s)
are virtually impossible to get correct, however I expect an attempt, since I want
to see how you approach a difficult question.
1 On the
slopes above I-80, (East up to the Lincoln Memorial) are limestone blocks
sitting on the steep side hills, which are composed of the underlying
a) What would the factor of
safety be, if the cohesion is 0?
b) Calculate a minimum value of
cohesion, for the block to be stable?
c) If the mass fails (and cohesion
goes to 0), what velocity will the block reach by the time it hits the road?
d) Will the chicken (block)
cross the road (5 lane highway, plus shoulder and median)?
2 Rivers currently carry about 1010 cubic
meters of soil and eroded rock to the sea each year, throughout the world.
a) Roughly how long
will it take, at the present rate, for all the continents to shrink by an
average of 1 meter in elevation (if all other processes, such as tectonics, are
ignored)
b) This implies a world averaged erosion rate of what (in mm per year)?
c) If the Platte
River basin above the Seminoe reservoir (see Google
Earth) is lowering at the average rate of 0.2 mm per year from erosion, what is
the approximate total sediment and dissolved load (kg per year) entering the reservoir? You can assume that all the material leaves
the upper basin via the Platte (a fairly good assumption), but you will need to
find the drainage area of the basin above the reservoir. (You may find data at the USGS site water.usgs.gov to be useful, although it is not an
easy site to navigate). Note you will
have to convert from volume eroded to mass, which will require a density for
the material removed by surface lowering.
d) (Tricky) Most of
the eroded material will be weathered rock and soil from the surface Should you
use the density of unweathered rock, or the lesser density
of soil, or what density(?) in part c?
3 We argued in class
that mountains are mostly held together by friction.
a)
Check
out this idea by finding the approximate average slope of the Grand Teton
(south side gives longest steep slopes), Everest (east face is probably the
longest and steepest), Denali (see if you can find the longest steepest face)
and a typical volcano such as Rainer or Fuji.
(Google Earth is a good tool for this).
(Don’t look for the steepest local slope, but try to find the steepest
slopes that are several 1000 ft high). How do these
crude estimates of slopes compare with the typical friction angle of rocks of
30-35degrees.
b)
See
if you can find slopes for a steep crater on the moon.
c)
(Hard)
Although for solid to solid friction, the angle of repose is independent of
gravity, it is not so obvious that this is true for the complex interactions of
a granular pile of material. Question:
Should the slope angle of a sand pile or a talus change with changing gravity?
4. Many processes in
geomorphology are non-linear in the sense that the results are not linearly
related to some of the controlling variables.
We have already talked about exponential decay. I want you to get more familiar with some of
the typical geomorphic non-linearities, which are
often logarithmic, exponential or power-law relationships in time or space.
a) Plot the
following 4 functions of X and Y, with X going from about 0 to 10 (use more
than 10 steps, 100 would be good):
linear Y =
X, logarithmic Y = 10* log10
X, exponential Y = e(X/4.4), power law Y = X2
/10
(linear,
logarithmic, exponential, power law (square))
Plot 3 different graphs (with the 4
functions on each graph) as follows:
1- a graph with linear x-y axes that go from 0 to 10,
2- a graph with
horizontal linear scale (0-10) and a vertical logarithmic scale (0-1), and
3- a log-log plot
with a scale from 0-1 on both axes
(in
all cases x will go from about 0 to near 10, however the values of y will not
all plot on some graphs).
Use different
colors or symbols for each curve, and label them, either by hand or have the
computer do it. The purpose of this
question is to get you to think about non-linear relations, but also to get you
to figure out how to plot with various axes.
I recommend either MATLAB or EXCELL (or some other computer or
spreadsheet program).
5 A major jargon
phrase in Geomorphology is “Magnitude and Frequency.” It refers to the idea that huge, infrequent
events may dominate the evolution of a landscape, or conversely that small very
frequent events may dominate. To get you
thinking concretely, contemplate your possible death by infrequent, but large
magnitude events:
The Cretaceous probably ended with a major asteroid impact on earth. Large (10km. diameter or more) impacts appear to occur randomly, but with an average time spacing of order 75 million years. Most of the larger life forms all over the globe suffer near complete mortality rates as a result of such an impact. Meteor impacts are an extreme example of a process dominated by high magnitude, not high frequency events.
a) What are the odds, or more precisely the probability, of a catastrophic impact somewhere on earth in your life time? (that would probably end your lifetime)
b) Since we are now
talking about Landslides, which is more likely: that you will die from a
landslide, or that you will die (with the rest of us) by an asteroid
impact? (Data on landslide deaths in the
c) (Hard) A good example of a process that is dominated by Frequency
is the background chemical erosion of the near surface rocks of the world. If you refer back to question 2c, not all the
0.2mm of yearly erosion is physical, some is chemical. Some of the chemical erosion products leave
the basin dissolved in the water, not as particulates. If 15% percent of the erosion of the Platte
river basin is by dissolution and by solution of chemical weathering products,
what is the dissolved load concentration in
the water in the Seminoe reservoir (in milligrams per
liter)? (Note this a ‘back of the envelope’ type
of calculation, since chemical weathering often produces products that weigh
more or less than the original rocks, [however, pure dissolution would lead to
an accurate answer]. Here we ignore the
chemical details.)