Midterm GEOL 4880             Humphrey 2017, in class, open book, open notes         2 pages

You may use any resource you want, except discussing answers with other (or previous) students in this class.

 

(There are ~25 questions, with point total ~35, (~2mins per point), don’t dawdle!)

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.

           

1    Assume you have gone down to the Laramie River.  The water discharge (total flux) is 2 m3/s.  The river is 4 meters wide and about 1/2 m deep.  The river slope is 2x10-4.  (hint, despite appearances, this question has little to do with rivers)

a){1}    What is speed of the water?

b){1}    What is the slope of the river in degrees?

c){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 back of your leg?

d){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.)

e){1}    Which is the larger storage term in the earth’s fresh water budget: surface water (including lakes), atmospheric water, or ground water?

f){1}     What is the baselevel for most of the geomorphic processes around Laramie?

 

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 1700 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 m/yr) based on the information from this slope?

d){1}    Use your Ccreep from above to estimate a time scale for this 100m long, 10m high, straight slope to become somewhat rounded by this rate of soil creep.

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  (c) 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:

•       shear stress at the bedrock-soil interface,

•       the normal stress,

•       the effective stress,

•       cohesion 

•       frictional resistance? 

(You only need to mention if each of these 5 terms increase, decrease or are not affected).

g){2} [you may want to skip this and come back at the end, since this is the most calculation intensive question] 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 some layering in the deposit, the layers have finer material underlying but grading up into noticeably coarser cobbles and gravels (inverse grading).  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 after the rain?

 

4    Consider a small drainage basin, with a map view appearance of a half circle.  A single short stream exits on the middle of the straight side.  A side view of the basin shows that it is basically ½ of a funnel or inverted cone, with 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}    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?

e){1}    (Very Hard) If the rains in (c) above were sufficient to cause Dunnian overland flow, modify curve ‘B’ to show the change in hydrograph (call it curve ‘D’) at the appropriate place on your plot to indicate how the hydrograph might change?

 

5   The top of the Laramie range (think Happy Jack or Vedauwoo), shows considerable evidence of diffusional processes rounding the landscape. 

a){1}  Until about 50 years ago, there was a small ski area at Happy Jack.  There is little evidence left, even the half meter diameter holes left by removing the lift supports are mostly gone.  Give a ‘really rough’ estimate of the diffusion coefficient ‘C’ for Happy Jack, based on the disappearance of these holes.

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 angle 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 (Hard, and several possible answers)?

 

6 {2}Draw a dimensionally correct response “hydrograph” for the output from a straight slope that is the response to a short, intense rain of total 1 cm.  You can choose the length of the slope, hydraulic conductivity, and anything else you need.  You can assume the slope already is at field capacity, and that the vadose zone transit time is 1 hour.

 

7  In one or two sentences tell me what, where, why about the ‘geomorphic feature’ you are planning on discussing for your term project.