How to Calculate Modulus of Granular Material

Sand is an example of a granular material.

Granular material is a collective substance that comprises discrete macroscopic objects. An example of a granular material is sand, which is made up of countless numbers of grains of sand. A granular material has properties that are reminiscent of solids, such as tensile properties, liquids, such as flow, and gases, such as large velocities of the individual granular components. One important solid property that you can apply to granular materials is the bulk modulus, which is a substance's resistance to compression. Calculating this property requires only a few short steps.

Things You'll Need

• Piece of paper
• Balloon
• Sand
• Tape measure

Instructions

1. Roll a piece of paper up, and place one end inside the balloon. Pour the sand onto the piece of paper, which acts as a funnel, until the balloon is spherical in shape.

2. Determine the initial volume of the sphere. As an example, the volume of a sphere is 1.333 multiplied by the constant pi -- 3.1415926 -- multiplied by the cube of the radius of the balloon. If the radius is 1 meter, or m, then the volume is 4.18 meters cubed, or m^3.

3. Exert a measured amount of pressure uniformly on the surface of the balloon. Measure the corresponding change in the volume of the balloon. For example, assume that a pressure of 400 Pascals, or Pa, the unit of measurement of pressure, results in a change of volume of 1.2 m^3.

4. Find the relative change in volume of the balloon by dividing the change in volume of the balloon by the initial volume. In the example, dividing 1.2 m^3 by the initial volume of 4.18 m^3 gives 0.287. This number is dimensionless.

5. Divide the pressure exerted on the balloon by the relative change in volume. In the example, dividing 400 Pa by 0.287 gives 1393 Pa. This is the bulk modulus of the material.

Tips & Warnings

• This method is only applicable for a granular solid material; that is, a granular material that is not subject to any shaking or sudden movements.

• Although the bulk modulus was calculated here, you may not be able calculate other moduli (e.g., Young's modulus, shear modulus) for granular material.

References

• Engineering Toolbox: Bulk Modulus and Fluid Elasticity

Resources

• Particle Technology Learning Resources: Fundamentals of Particle Technology