Three-dimensional mathematical analysis of particle shape using X-ray tomography and spherical harmonics: Application to aggregates used in concrete

The propenies of composites made by placing inclusions in a matrix are often controlled by the shape and size of the panicles used. Mathematically, characterizing the shape of panicles in three dimensions is not a panicularly easy task, especially when the panicle, for whatever reason, cannot be readily visualized. But, even when panicles can be visualized, as in the case of aggregates used in concrete, threedimensional (3-D) randomness of the panicles can make mathematical characterization difficult. This paper describes a mathematical procedure using spherical harmonic functions that can completely characterize concrete aggregate panicles and other panicles of the same nature. The original 3-D panicle images are acquired via X-ray tomography. Three main consequences of the availability of this procedure are mathematical classification of the shape of aggregates from different sources, comparison of composite performance properties to precise morphological aspects of panicles, and incorporation of random panicles into many-panicle computational models. Published by Elsevier Science Ltd. Ke)'Words: Image and shape analysis; Aggregates; Modeling; X-ray tomography; Spherical harmonic~