STABLE ANGLES OF SLOPES

Marie Morisawa
Department of Geological Sciences
State University of New York
Binghamton, NY 13902-6000

Estimated Time Required: 45 minutes collecting data, 45 minutes discussion

Anticipated Learning Outcomes

• Students will learn about factors controlling the angle of repose (the stable angle of a slope).
• Students will see what happens when slopes are oversteepened.
• The experiment results can be related to a general understanding of instability of slopes.

Background

Slopes composed of loose debris can be seen all around us. The angle at which such a mass of debris rests under given conditions is called the angle of repose. It has generally been accepted that such slopes tend to have an angle varying from 25 to 40 degrees. The exact angle depends upon conditions such as size, shape, and density of the grains, roughness of the grain surfaces, sorting or mixture of sizes, and height of fall of the grains. Studies of the effects of these various characteristics determining the angle of repose of loose material have produced diverse results. In general, an increasing fragment size results in lowering the angle of repose.

Materials

• Soils from local slopes
• Sands - these may be from anywhere. It would help if there were several sands of differing sized grains, mixed sizes, etc.
• Several clear plastic shoeboxes, cut in half.
• Plastic protractors, also cut in half
• Glue
• Cardboard squares large enough to cover the open ends of the cut shoeboxes
• Large sheet of paper to catch the sand or soil as it falls from the box

Procedures to Prepare the Boxes

These should be prepared in advance, by the teacher. However, once made, they can be used repeatedly. Allow one box per student team (of 2 - 4 students).

1. Cut the shoeboxes in half, with a hacksaw made to cut plastic.
2. Cut the protractors in half.
3. Glue the protractors on the outside of the shoebox, on the open edge of the box (see Figure 1a).

Figure 1. Set-up for the stable slope measurement. a) Plastic box for the experiment. b) Box filled with sand before removing the cardboard at the end. c) Box and slope formed on the sand after the cardboard at the end is removed.

Procedures

1. Slowly and carefully spill the grains into a plastic box (Fig. 1a) piling the grains loosely against the open end which is closed by holding a cardboard against it (caution: do not pack).
2. When all the sand is in the box quickly remove the cardboard so the sand can fall freely onto a large sheet of paper placed below the box opening (Fig. 1b).
3. Read and record the angle which the sand (or soil) assumes within the box (Fig. 1c). Repeat the procedure until you have 10 readings.
4. Repeat the procedure with the other soil/sand samples.

Results and Discussion

Discuss the results among the group using the following questions as a guide.

What is the variation in angle of repose for any one sample?
Not much, I hope.

How do the different materials differ in angle of repose?

Can you deduce any relations between characteristics of the material and angle of slope from your results? (e.g., what is the relation between size of material and angle of repose? Do your observations indicate that the slope angle decreases with an increase in grain size?)

Why does the angle of repose of the soil material differ from that of the sands? I hope it does.

Are there any landslides in your area? Along roadcuts or other slopes? Of what practical use it it to know the angle of repose of a given material?