Earth Surface
Processes, GEOL 4880 Humphrey, fall 2014, Homework #2
Here are 4 questions to work on. The final question is the field trip we
talked about in class, I will email directions for the field work on
Saturday. Leave yourself enough time to
do the field work!
Please be careful… the homework gets posted just
before it is assigned. Links to homework
further on in the course lead to old homework.
I change some questions, and also change some of the data each year, so
you will be doing the wrong homework (the due date has to be this years for the
homework to be valid). The last part of
question 3 is hard.
Many of you are making simple mistakes, both algebraic and conceptual. Here is a summary table of most of the equations used so far, please use it and compare with your notes.
1
A soil with a porosity of 40% and a dry bulk density of 1600kg/cubic meter lies
2 meters deep over solid bedrock. Assume
the slope and the soil are horizontal and that
ground water motion is zero. After a
heavy rain the soil is saturated to the
surface.
a)
Calculate the water pressure at the soil/bedrock interface
b)
Calculate the effective normal stress across the soil/bedrock interface
c)
Calculate the shear stress on the bedrock interface.
d)
What is the Hydraulic Gradient from the surface to the soil/bedrock interface
(a fancy way of asking the Total Head difference from surface to bedrock)
2
Turbidity, or the opacity of water is often used as a rough estimate of the
amount of sediment in rivers. If the sediment size is fairly constant with time
this works well, with some initial calibration. However the turbidity depends
heavily on grain size and if the grain size varies, estimates of sediment
transport based on turbidity can have large errors. Investigate this problem by looking at the
turbidity created by two different crushed rock samples mixed into water.
a)
Calculate the amount (volume) of crushed rock that is needs to be suspended in
water to make a 1 meter cube of water 10% opaque, (in other words: so that 10%
of the light hits a particle while traveling through the 1 meter cube of
water). Use two different grain sizes, fine silt, and coarse sand.
(hint: it is x-section area of each grain that blocks
light, but the mass is due to the volume.
Make the simplifying assumption that no rock particles hide behind each
other.).
3 Is it
possible to create mountains by erosion?
Hint, think of isostacy and think of
dissecting a large region with deep valleys.
a To be precise, calculate the
maximum peak elevation you might achieve, if the Red Desert of Wyoming
(elevation about 2000m) was dissected by erosion, by a series of 2000m deep
valleys, with 45 degree side walls. Each
valley is 4 km
apart. (the resulting topography will look like a saw
tooth in profile. Only the ridge crests
do not erode. Assume complete isostacy and ignore any other factors.
b To see a possible example of this behavior, use GOOGLE EARTH to look at the Grand Canyon. Notice the rim elevation is higher than land away from the canyon. A particularly interesting example is the region of the Little Colorado River, a tributary of the main Colorado River, flowing north and west of Cameron Arizona (north of Flagstaff). It flows in the opposite direction to the topography. Could the elevation difference of the land from Cameron to the region of confluence with the main Colorado river be caused by downcutting of the Colorado river?
4 (part d is very difficult to do
correctly, but everybody should try part a,b,c:
HINT, it does not need any factor of
safety or other complex calculation(!), clear thinking is required, but very
little work)
a)
How
much does the block lengthen each day (and contract each night)?
b)
Calculate
the rate of motion, in meters per year of the slab, resulting from the diurnal
thermal cycle.
c)
Does
the angle of the slope affect the motion?
d)
(VERY
hard) Assume the slab touches the underlying rock along its entire length, not
just at the ends, now how fast does it move? A complete answer would give
a definite speed, however, a description of the details of motion is probably
sufficient, but such a description should include a comment on the speed
dependence on the slope angle, which is different from the answer to part c.