Effects of Particle Shapes and Sizes on the Minimum Void Ratios of Sand

Table 2

The expressions and descriptions of the secondary shape parameters.

Secondary shape parameter	Expression	Description
Flatness		Describe the extended properties of the particle, where is the dimension along major axis of the particle plane and is the dimension along vertical axis of the spindle.
Sphericity		Describe how close the particle comes to the shape of a sphere, where is the maximum radius of the tangential circle of the particle and is the minimum radius of the circumferential circle of the particle.
Angularity		Describe the number of edges and the degree of protrusion of the surface of the particle, where is the minimum circumference of an external polygon along the boundary of particles, and is the circumference of a standard ellipse with the same area and flatness as particles.