1. Introduction

Mathematical (spherical harmonic series) and experimental techniques (X-ray computed tomography) to characterize the particle shape of aggregates used in concrete have been demonstrated [1], and a general case has been made for the important effect on composite properties of inclusion particle shape [2-5]. But acquiring true, full three dimensional (3-D) shape information is not an easy task, although X-ray computed tomography (CT) is the method of choice at present [6, 7]. The sample preparation techniques needed for successful imaging of particles in 3-D are not obvious. Uncertainty analysis of the spherical harmonic mathematical procedure has been carried out using analytical ellipsoidal particles, but not on real aggregate shapes. Visualization of images that have been reconstructed from the spherical harmonic series process have been made [1] using POVRAY [8], a ray-tracing program specialized to mainly Unix and Linux machines^*. This package and imaging techniques are not easily accessible to the average aggregate researcher. And having the surface of an aggregate in terms of an analytical function like the spherical harmonic series allows many interesting computations to be carried out on these aggregates [1].

In this paper, lessons learned in sample preparation and image analysis and reconstruction are described. The spherical harmonic/x-ray CT procedure is further evaluated using individual rocks that can be imaged with the x-ray CT scanner, and then directly compared with the resulting images that come from spherical harmonic reconstruction. This comparison is both qualitative and quantitative. The Virtual Reality Modeling Language (VRML) is used to generate images quickly, simply, and automatically, which can be easily visualized and manipulated on popular web browser software. Novel shape analysis procedures, made possible by the spherical harmonic series information, are applied to four different kinds of coarse aggregates. The results are used to show how analysis of shape data can be done, and to suggest other possibilities.

* Certain commercial equipment and/or materials are identified in this report in order to adequately specify the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the equipment and/or materials used are necessarily the best available for the purpose.