Three-Dimensional Mathematical Analysis of Particle Shape Using X-Ray Tomography And Spherical Harmonics: Application To Aggregates Used In Concrete.
Three-Dimensional Mathematical Analysis of Particle
Shape Using X-Ray Tomography And Spherical Harmonics:
Application To Aggregates Used In Concrete.
Garboczi, E. J.
Cement and Concrete Research, Vol. 32, No. 10,
1621-1638, October 2002.
aggregates; concretes; shape analysis; spherical
harmonics; x-ray tomography
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