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Three-Dimensional Mathematical Analysis of Particle Shape Using X-Ray Tomography And Spherical Harmonics: Application To Aggregates Used In Concrete.


pdf icon Three-Dimensional Mathematical Analysis of Particle Shape Using X-Ray Tomography And Spherical Harmonics: Application To Aggregates Used In Concrete. (4437 K)
Garboczi, E. J.

Cement and Concrete Research, Vol. 32, No. 10, 1621-1638, October 2002.

Keywords:

aggregates; concretes; shape analysis; spherical harmonics; x-ray tomography

Abstract:

The properties of composites made by placing inclusions in a matrix are often controlled by the shape and size of the particles used. Mathematically characterizing the shape of particles in three dimensions is not a particularly easy task, especially when the particle, for whatever reason, cannot be readily visualized. But even when the particle can be visualized, as in the case of aggregates used in concrete, three-dimensional (3-D) randomness of the particle can make mathematical characterization difficult. This paper describes a mathematical procedure using spherical harmonic functions which, by operating on x-ray tomographic images, can completely characterize concrete aggregate particles and other particles of the same nature. Three main consequences of the availability of this procedure are: classification of the shape of aggregates from different sources, comparison of composite performance properties to morphological aspects of particles, and incorporation of random particles into many-particle computational models.