Midterm GEOL 4880 Humphrey 2020, 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)

 

Rules:

-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 your answer. 

-You must add units to your answers if there are units. 

-FOR CALCULATIONS, YOU MUST WRITE YOUR WORK, NOT JUST THE ANSWER, OR IT WILL BE WRONG.

           

1    Assume you have gone down to the Laramie River.  The average water speed is 0.5m/s.  The river is 4 meters wide and about 1/2 m deep.  The river slope is 2x10-4.  (BIG hint, despite appearances, this question has very little to do with rivers)

a){1}    What is the water discharge (total flux) of the river?

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 shear stress that the water exerts on the river bed?

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

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

 

2    A tree covered hillslope is mantled in 1.0 m of soil (perpendicular to slope), over solid impermeable bedrock.  The soil has a dry density of 1700 kg/m3, and a porosity of 40%.  The angle of the slope is a uniform 27 degrees.

a){1}    The soil is creeping downslope.  The shear strain rate is constant with depth and is about 0.01 per year.  There is no slipping at the bedrock interface.  Sketch a side view of the soil, showing the strain rate profile (dashed line), and the velocity profile (solid line).

b){1}    What is the distance downslope that the surface moves in one year? 

c){1}     What is the volume flux of soil per unit width of hillslope?

d){2}    If we wanted to model the creep movement as a ‘distributed’ or diffusion process, we would need an estimate of the rate coefficient Ccreep for this hillslope region.  What would be an estimate of Ccreep (in units of m2/yr) based on the information from this slope? (tan 27 is 0.5, cos 27 is 0.9).

e){1}    Use your Ccreep from above to estimate a time scale for this 100m long, 50m high, straight slope to become somewhat rounded by this rate of soil creep.

 

3  More questions about the slope in question 2

a){1}    If the soil was saturated to the surface during a heavy rain.  Estimate the water pressure, at the soil/bedrock interface, use the shallow-soiled hillslope groundwater flow approximation?

b){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)

c){2}    If a heavy rain occurs on this slope.  How does the rain affect the:

a-shear stress at the bedrock-soil interface, b-the normal stress, c-the effective stress,

d-cohesion, e-frictional resistance? 

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

 

4  Again for the slope in question 2

a {3} [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 (probably supplied by the tree roots) if the internal angle of friction is 30 degrees, and the soil is occasionally saturated to the surface and doesn’t fail?

 

5    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}     After a dry period subsequent rain falls on the unsaturated fan.  The rainfall rate is less than the saturated hydraulic conductivity.  What is the general direction of the 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, which implies a saturation of 25%.  What is the porosity of the soil.

e){1}    Is the soil likely to be above, at or below field capacity after the rain?

 

6    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 ˝ of a funnel or inverted cone, with relatively constant gradient slopes down to the stream.  A short intense 1 hour 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 [hint, I want you to take into account the convergent flow]. Include the rain input on the plot, so I can see the relationship between the amount and time of the input to the output. 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.  You must put labels and units on your axes.

c){1}    (Very Hard) If the rains in (b) above were sufficient to cause Hortonian overland flow, modify your output plot to show the change in hydrograph at the appropriate place on your plot to indicate how the hydrograph might change? (use a dashed line to show this)

 

7 a{1} All other things being equal (Cohesion, water table, angles, friction coefficient etc) would a slope made of a silty soil or a sandy soil be more stable under a heavy rain?

 b{1} (Hard) Is a tilted (planar) fan (a 3D feature) erosional or depositional under creep processes?