Midterm GEOL 4880 Humphrey 2014, take
home, open book, open notes
You may use any resource you want, except discussing answers
with other students in this class, or with past students of this class.
(There are ~25 questions, with point
total ~40.
Answer on a separate piece(s) of paper,
and make sure you number you answers, and add your name! Make it easy for me to find the answer; if I
don’t find it, it will be wrong (underline
or box is good). You must add units to your answers
if there are units. Unlike the homework,
where I try to figure out what you did incorrectly, I will just mark if you are
right or wrong, I will not try to figure out what you meant.
1 Assume you have
gone down to the
a){1} What is the total water flux (Q)?
b){1} What is the vertically integrated flux, or
the flux per unit width (q)?
c){1} What is the specific
water flux, flux per area?
d){1} What is speed of the water?
e){1}
What is the slope of the river in
degrees?
f){1} You wade out
into the flow to measure depth, how much higher is the water on the up-river
side of your leg, than on the bank-side of your leg?
g){1} What is the ratio
of basal water pressure to the basal (water) shear stress on the river bed? (This question illustrates why it is usually
assumed that the average pressure, (actually the normal stresses), in fluids,
even if moving [except at very high speeds], is isotropic.)
h){1} Which is the
larger storage term in the earth’s fresh water budget: surface water (including
lakes), atmospheric water, or ground water?
2 A tree covered hillslope
is mantled in 2.0 m of soil (perpendicular to slope), over solid bedrock. The soil has a dry density of 1600 kg/m3, and a porosity of 40%.
The slope is 27 degrees (tan 27 is 0.5, cos 27 is 0.9).
a){2}
The soil creeps downslope. The shear strain rate is constant with depth
and is about 0.01 per year. There is no
slipping at the bedrock interface. What
is the distance downslope that the surface moves in one year?
b){1} What is the
volume flux of soil per unit width of hillslope?
c){2} If we wanted to
model the creep movement as a ‘distributed’ process, we would need an estimate
of Ccreep
for this hillslope region. What would be
an estimate of Ccreep
(in units of m2/yr) based on the information from this slope?
d){1} If the soil was
saturated during a heavy rain, with the water table at 1 m below the surface
(water table thickness of 1m). What
would be the estimate of water pressure, at the soil/bedrock interface, using
the shallow-soiled hillslope approximation?
e){1} If the slope
where to fail as a debris flow, and stop on the toe slope at an angle of 5
degrees and a depth of 1 m, what was the critical yield stress (tc) in the
debris flow? ([hint] remember to add the
weight of water)
f){2} A heavy rain
occurs on this slope. How does the rain
affect the:
(You only need to mention if each of these 5 terms increase,
decrease or are not affected).
g){2} What is the approx. minimum bulk soil cohesion if the
internal angle of friction is 27degrees, and the soil is occasionally saturated
to the surface and doesn’t fail?
3 Consider an entire
landscape that has only slopes at angles that are less than the angle of repose
for the landscape materials.
a){1} Can there be landslides in this landscape?
b) {2} You find a fan of material at the foot of a mountain range,
and you find a road cut through it. The
exposure allows you to look at a cross-section of the fan. The rocks are broken
and there is a lot of fine grained material, but you notice that there is
layering in the deposit, which consists of several layers that have finer
material underlying but grading into noticeably coarser cobbles and
gravels. Somebody asks you how the
deposit was formed, which was..?
c){1} During a
subsequent rain on the unsaturated fan, the water infiltrates. The rainfall rate is less than the saturated
hydraulic conductivity. What is the
direction of the bulk water flow away from the surface? (vertical
to slope, parallel to slope or vertical to gravity)
d){1} After the rain,
you measure the soil moisture and find a water content about 8% water by
volume, and that the saturation is 25%.
What is the porosity of the soil.
e){1} Is the soil likely to be above or below
field capacity.
4 Consider a small
drainage basin, with a map view appearance of a half circle. A single stream flows across the basin and
exits on the middle of the straight side.
A side view of the basin shows that it is basically ½ of a funnel, with
a relatively constant gradient slopes down to the stream. A short intense rain occurs in this 1st
order stream basin. It takes 2 days for
the water to flow from interfluve to stream.
a){1} What is the
largest output term in the basin
budget, after stream discharge?
b){2} What is the shape
of the output hydrograph for the rain? Make a careful sketch/plot: of output discharge vs time, label the curve
‘A’ [hint, I want you to take into account the convergent flow]. Make the plot big enough to allow you to put
more lines on it for the next questions. Make sure the graph answers (at least) how the length of
the output hydrograph compares with the length of input rain; and how the shape
(amplitude) of the output hydrograph varies through time. Put labels on your axes.
c){1} Add a line to the
plot in part ‘b’, to show the hydrograph for a higher permeability (lets say: 2 times the conductivity) type of hillslope soil. [label the new line ‘B’].
d){1}
Another rain occurs on the following
day, on the original (low conductivity) basin.
Sketch and label on the above plot [line ‘C’] the total hydrograph that
results.
e){1} If the rains in
(d) above were sufficient to cause Dunnian overland
flow, add a curve ‘D’ at the appropriate place on your plot to indicate how the
hydrograph might change?
e){1}
Straight slopes are often transport
slopes with little erosion or deposition.
The major slope processes in this basin are diffusive with various creep
processes such as tree throw and soil creep.
Are the lower elevation parts of this basin undergoing: erosion,
deposition or merely transporting?
f){1} (Hard) If the basin had concave upward slopes, instead of
straight slopes, what would this do to the shape of the output hydrograph? (you can answer this in words if you want, or sketch)
5 The top of the Laramie
range (think Happy Jack or Vedauwoo), shows considerable
evidence of diffusional processes rounding the landscape.
a){1} Give a ‘really rough’ estimate of the
diffusion coefficient ‘C’ for that area, based simply on the fact that we see
evidence of diffusional smoothing, and explain your thinking. (hint: this is a
question about scaling, and you will not be marked on the value, only on your
logic)
b){1} What do you think are the dominant
diffusional processes operating on the Laramie range.
c){1} If you dig a hole in the soil on the low
slopes at Happy Jack, you often find that the material is inversely graded with
coarse rocks and gravel on top of fine grained material: what is the dominant
process in these areas?
6 A couple of tough
questions for bonus points: (these won’t affect your grade negatively,
but good answers will counteract incorrect answers above)
a) {1} What sets the elevation of the Laramie valley? (This is
asked on a time scale of 100Kyrs, and regarding the valley as having the
Laramie river as the local BASELEVEL).
b) {1} Directly between Laramie and Lake Hattie to the west is an
extensive shallow depression called the ‘Big Hollow’. (if you would like,
check it out on Google Earth and note
that the area is lower(!) than the nearby Laramie river.) What dating technique
could you use to find out when the Big Hollow was formed? (expected
age is less than 50Kyrs)
c) {1} Try to estimate
how long ago the water that comes out of your tap fell as rain and snow up at
Happy Jack and Vedauwoo?