Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Some Properties of Irregular 3-D Particles



Michael A. Taylor, Edward Garboczi, S T. Erdogan, D Fowler


This paper discusses some of the properties of irregular particles that are of interest to engineers, including volume, density, & surface area. Numerical and statistical information on these properties is essential (a) for a better understanding of particulates, (b) to suggest more efficient ways to utilize particulate materials, and (c) to permit the creation of mathematical models that can reduce the need for lengthy real-world testing. While the motivation, examples and applications are from the construction materials industry, the results should be of interest to others. Measurement techniques used included x-ray computed tomography & multiple projected images, augmented by traditional laboratory techniques. To compare the results of these techniques a set of 12 rocks were studied of which six were between 19 mm and 12.7 mm in size, and six were between 12.7 mm and 6.3 mm in size. Microfine versions of these rocks (< 80 um equivalent spherical diameter) were also studied and compared. The shapes of the rocks were studied by relating three dimensions to their volume and surface area. These three physical dimensions were defined in two different ways: direct measurement of three unique orthogonal dimensions on the rock surface, and dimensions obtained from the use of absolute first moments of volume and principal moments of volume. These measurements and calculated moments allowed the development of three-parameter equivalent shape models based on rectangular parallelepipeds and tri-axial ellipsoids. All types of three-parameter equivalent shape models considered provided acceptable accuracy in predicting both vol-ume & surface area, with the box models generally more physical and realistic than the ellipsoid-based equivalent shape models.
International Journal of Powder Metallurgy


equivalent shape models, irregular particles, microfine, multiple projected images, rectangular parallelepipeds, tri-axial ellipsoids, x-ray computed tomography


Taylor, M. , Garboczi, E. , Erdogan, S. and Fowler, D. (2021), Some Properties of Irregular 3-D Particles, International Journal of Powder Metallurgy (Accessed February 29, 2024)
Created October 12, 2021