Alessandro Grippo, Ph.D.

 Sedimentary particles shape: SPHERICITY and ROUNDNESS

Sedimentary particles shape Last Updated  •  March 2, 2013

The shape of a sedimentary particle, or grain (what we called gravel, sand, silt, and clay) is essentially its geometric form.

The geometric form of a particle depends on two different concepts:

• the relative length of the particle intercepts along the three perpendicular axes A, B, and C, corresponding to three orthogonal axes X, Y, and Z (its sphericity)
• the sharpness or roundness of the corners and edges
The sphericity of a particle influences erosion, transportation, and deposition patterns. A "flat" particle would travel in a different way then a "spherical" particle.
The roundness of a particle instead is a direct measure of the distance that particle traveled and the harshness during transportation.

Sphericity Last Updated  •  February 28, 2013

Mathematically, sphericity can be expressed as the cubic root of the volume of a particle divided by the volume of the circumscribing sphere:

equation A

Consider a pebble of any shape, enclosed in a circumscribing sphere of a glass. If your pebble is nearly spherical, it will fill almost the whole circumscribing sphere. If instead your pebble is more like a thin disk, it will occupy a small piece inside the sphere.
Sphericity increases as the pebble occupies more and more space. Sphericity is 1 when the two volumes coincides while a thin, needle-like particle has a sphericity of nearly 0.

Notice that, given two particles with the same identical volume, the one with highest sphericity has the least surface area. Consequently, if a particle is non-spherical it will have more surface for the same volume, and hence will offer more resistance during erosion and transportation.

But, how do you actually estimate the sphericity of a pebble?
The volume of a large particle can be obtained by displacement in water in a graduated cylinder. It can be expressed using the diameter of a hypothetical sphere with that volume (d, or nominal diameter):

equation B

This pebble is circumscribed by a sphere with diameter a, higher than d. So the volume of the circumscribing sphere is π/6 a3.

If you replace these values in the previous equation (A), you can easily see that sphericity is simply the ratio between d and a:

equation C

This figure shows Zingg's classification of pebble shapes, based on ratios of intercepts.
(from Krumbein, W.C., and Sloss, L.L., Stratigraphy and Sedimentation, 1956, Freeman and Company, San Francisco CA)

roundness Last Updated  •  February 28, 2013

Roundness simply defines how 'smooth" a grain is. That is, a flat grain can be round, even if not spherical. Roundness can be defined mathematically as follows:

equation D
Average Radius of Corners and Edges
Roundness = _________________________