Geo 147, The Landslide Problem

Due: Thurs, Feb. 25, 1999

Background

Recall that coefficient of friction is defined as: c=s/p,
where p is the force across the frictional contact, and s is the
minimum value of the tangential force to initiate sliding.
Look at picture below, the classic sliding block experiment.
In our classroom experiment, we discovered that the block would slide
when the vertical height of the ramp was about 1/4 the horizontal length.
(i.e., x=40 cm, y=10 cm (with some uncertainty!), when sliding would start).
Also recall that our analysis of the forces showed that: c = tan (dip angle).

The Problem (in six parts)

1. Use our measured values of the ramp height and length to calculate the coefficient of friction for our "slick book cover" material.

2. Use our measured values of the ramp height and length to calculate the dip angle associated with the above coefficient of friction.

3. Is the slope angle from (2.) "really steep", or "not so steep"?
Well, we need to compare it to something else, so:

Calculate the slope angle for a lower-Michigan ski hill.
For example, some of the slopes at Mt. Brighton have a vertical drop of 200 FEET,
the horizontal length of the run is about 200 METERS.
What is the slope angle? What is the minimum coefficent of friction for the material beneath Mt Brighton?

Let us return back to our idealized slider block example. You will use the value for c that you calculated in part (1.), but we will now refer to that value as the "dry friction coefficient", or "cdry". I will now specify how the friction coefficient decreases as we add water to the frictional contact zone:
cwet = cdry ( 1- f )
where "cwet" is the wet friction coefficient, and "f" is the volume fraction of water within the contact zone. The value of f can vary between 0.0 (i.e. dry), to a maximum value of 0.50 (i.e. completely saturated for this particluar material).

4. Make a graph that plots "cwet" versus "f", using the range of "f" given above.

Now, we have a slider block with "slick book cover" frictional contact resting on a slope with a dip angle of 10 degrees. Due to rain storms, the frictional contact will change from dry to wet.

5. Calculate the volume fraction of water in the contact zone that would initiate sliding.

6. (the open-ended question) Let us suppose that structures have been built on top of our idealized dry/wet slider block system (question 5. above), hence we want to mitigate the landslide hazard. Describe a system that you would design and build to monitor and/or prevent the slide.

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