Homework #4 GEOL 4880 Humphrey fall 2016, mainly debris flows and water in debris questions

Please note that if you are completely stumped by a question, then come and ask me about it. (You are supposed to learn, not just be stumped! This is true each week.) I recommend using MATLAB (available in the student labs) or EXCELL or PYTHON for question 2.  Question 2 will need some computer learning for some of you!

1 Suppose you see a debris flow, moving down a small gully. The flow is about 1 meter deep and a couple of meters wide. The slope of the gully is 15o. A sample of debris material yields a bulk density of about 1,800 kg/m3 ("wet"). Mud on the front of a tree stump in the path of the flow is about 10cm above the mud lines on the bank of the gulley. You got the impression that about half of the depth of flow was moving as a "plug".  Make sure you look at the summary of debris flow equations.

a) Based on the above, give an estimate of the surface velocity? (hint: tree stump)

b) Estimate the critical shear stress ( tc).

c) Estimate the effective viscosity

d) What is the angle of the slope upon which the flow would probably stop?

2. Plot (using a computer!) the following for the debris flow in question 1. Title the graphs, label the axes, and include the dimensions (ie meters, sec, kg whatever).  Plot depth on the vertical axis of your plots, and make sure the surface is at the top, and the bed is at the bottom.  Include the full depth of the flow.

a) The shear stress as a function of depth

b) The slope parallel shear strain rate as a function of depth

c) The slope parallel velocity as a function of depth

3. A lot of geo problems can be solved using mass conservation concepts. And a particularly useful mass conservation approach is to define a single box or reservoir in your problem, and look at the inflow or outflow pathways.  If the amount of material flowing into and out of the box is equal over time, the box is in steady state. The ratio of the amount of material in the box to the flow rate (in or out) is called the residence time. (Check that the dimension(s) on this ratio is actually time). In a well mixed reservoir the residence time is the same as the average age, spent in the reservoir, of the exiting stuff. Simple box models are surprisingly powerful in dealing with mass flow problems.

a.       UW has an undergraduate enrollment of about 10,000 students. Assume that they are all model students, and that they all graduate in 4 years: ie. the residence time of students is 4 years. How many graduate each year?

b.      Graduate students tend to hang around a lot longer. Assume our department accepts on average 5 PhD candidates a year, and that they stick around for about 4 years (and that they all graduate). How many PhD students do we have on average?

c.       Calculate the residence time for water in the atmosphere of the earth? (you might need to know that the atmosphere has about 1.3 x 1013 m3 liquid water in vapor form, try to assess probable values for the other required variables... or look them up). The lower atmosphere is a fairly good example of a well mixed reservoir, in which the residence time is a good estimate of how long particles actually do spend in the reservoir.

d.      What is the residence time for water in the Seminoe Reservoir?

e.       What is the residence time for the rocks that make up the continents of the earth? The continents are a good example of a poorly mixed reservoir, where much of the output is from recent inputs, and the bulk of the mass is therefore much older than the residence time. (Note you have the data for this question in a previous homework)

f.       Residence time can be calculated for any type of reservoir.  However, it works better for some types than others.  Does residence time give a reasonable average age estimate for a “first-in first-out” (or “piston”) type of reservoir, even though it is not well mixed?

4 We are going to analyze one of the experimental debris flows at the USGS debris flow flume.  The flume is 2m wide and 1.5m deep, with a slope of 31degrees, and a slope length of 95m.  There is a concrete apron on which the debris flow stops.  Here is the data from the USGS debris flow flume experiment.  The green line is data from just above the fan area where the flow stopped.  You can clearly see the arrival of the coarse, heavy front (at 12 secs), followed by the viscous body (12-22secs), and then the flow starts to stop and pile up (25-40secs).  There is still some trailing stuff coming down the flume after that and piling up.  (The questions below are based mainly on the greenline data, although you will need the other data for a and b.  Big hint, most of this question uses the same thinking as question 1)

a.    Estimate the surface velocity of the flow?

b.    Is there any acceleration down the flume?

c.    Calculate the bulk density of the material?

d.    Using the data, estimate the approximate porosity of the mass? (a little hard)

e.    From the photographs on the USGS web page, it looks like the plug thickness was only a few centimeters.  Assume the plug was 4cm thick and Estimate the critical shear stress ( tc).

f.     Estimate an effective viscosity.

g.    (Hard) Explain why the water pressure (greenline) declines slightly at 22secs and then stays constant in the debris fan, whilst the debris depth increases by 50%?  There is not enough time (30secs) for significant water flow or drainage.