Angle of Repose - Measurement

Measurement

There are numerous methods for measuring angle of repose and each produces slightly different results. Results are also sensitive to the exact methodology of the experimenter. As a result, data from different labs are not always comparable. One method is the triaxial shear test, another is the direct shear test.

If the coefficient of static friction is known of a material, then a good approximation of the angle of repose can be made with the following function. This function is somewhat accurate for piles where individual objects in the pile are minuscule and piled in random order.

Where:

• μ_s is the coefficient of static friction
• θ is the angle of repose

Procedure to measure and calculate the angle of repose

1. Pour the dry sand into a pile on a level surface allowing it to build a pile from the top. This will result in a pile with a relatively circular base, making measurement easier.
2. Using the ruler and a tape measure, measure the height (h) of the pile of sand from the peak to the ground. Stand the ruler next to the pile so it can be read easily. Extend the tape measure carefully to the top of the pile without disturbing the pile and allow the other end of the tape measure to intersect the ruler. While keeping the tape measure level, observe the intersection of the tape measure with the ruler. Write the value on the paper. (For example: if the height of the pile is 12 units, write h = 12)
3. Using the tape measure, measure the horizontal distance (d) from the middle of the pile to the edge. Place the tape measure on the ground beside the pile. Line up one end with one side of the pile and extend the tape measure to the other end of the pile. Write the value on the paper and divide by 2. This will give you the distance from the centre of the pile to the edge. (For example: If the total distance on tape measure from one end of the pile to the other is 30 units, divide by 2 to get 15. d= 15)
4. The equation for calculating the angle of repose is tan-1(h/d) . Using your scientific calculator, divide height (h calculated in Step 2) by the distance (d calculated in Step 3). Then, hit the inverse tangent key (or tan-1) and the answer just calculated. This will give you the angle of repose, α.
5. Place the protractor on the level surface next to the pile of sand. Using the ruler, create a straight line from the peak of the sand pile down the slope. Read the angle of repose value (α) and write the value on the paper.
6. Compare the calculated angle of repose from Step 4 and the measured angle of repose from Step 5. If the values are not within 1 degree of each other, repeat Step 5.