MICROFINE AGGREGATES

 When rocks are crushed to different sizes, the dust of fracture, the residue left over after the usual construction sizes are removed, contains particles that usually have equivalent spherical diameters smaller than 100 mm. These particles can be imaged with x-ray computed microtomography. This dust, of the same material as the 12 rocks studied and collected from the same crushing process, was incorporated into narrow (2 mm diameter) samples, embedded in epoxy, and imaged at Brookhaven National Laboratory. The 3-D images were reconstructed in exactly the same way as were the larger particles, and spherical harmonic-based mathematical approximations were built for each of 332 particles. These particles had equivalent spherical diameters between 48 mm and 78 mm. The resolution used was 3.96 mm per voxel side (cubic voxels).

 The PMV and AFM were computed for each of these 332 particles, as before, but the L, W, and T dimensions were only computed for these microfine rocks, not measured, since direct physical measurements would be very difficult (but not impossible) and were not attempted for these particles. Table 9 below compares these microfines to the 12 rocks in a 2-D histogram using the calculated L, W, and T dimensions. Each bin contains a value computed from the 12 test rocks and a value computed from the microfine aggregates. The L, W, and T parameters computed from the spherical harmonic surface reconstruction were scaled by the T parameter to give L and W values as above, for both kinds of rocks. The number percent of rocks falling into each bin has been listed in Table 9, where the LI-WJ bin has I < L < I+1 and J < W < J+1. Note that all entries above the diagonal are blank, since the relation L > W must hold. Even though 12 rocks do not give very good statistics, it is remarkable how closely the two sets of materials match each other in Table 9, especially for the two bins, L1-W1 and L2-W1, which have the largest percentage of particles. This suggests that the shape of the microfines is similar to the shape of the larger rocks formed in the same crushing process. It is possible that different types of rock crushers will give a different form to Table 9. It is known that rocks from different sources can have markedly different versions of Table 9 (Garboczi and Douglas, 2005b).

  Table 9: LW histogram for microfines and 12 test rocks. There are two values in each bin - the values for the 12 test rocks are shaded in gray.

 Figs. 10-13 show the results of using three-parameter equivalent shape models in a manner similar to that of Figs. 6-9 but now for the microfine aggregates, showing how well the different types of models predict the volume and surface areas. Table 10 shows all the linear parameters of the various straight lines. All models have small values of the y-intercept compared to the maximum value of volume or surface area. Two special rows are marked in gray: the PMV box model – surface area row and the PMV box model – volume row. These rows both have slopes of 1.02, and very small y-intercepts compared to the maximum abscissa values. The same comment about not being exact relations that was made about Figs. 6 – 9 and Table 7 applies to  Figs. 10-13 and Table 10.

  Figure 10: Box surface area (microfines)                            Figure 11: Box volume (microfines)

 Figure 12: Ellipsoid surface area (microfines)                Figure 13: Ellipsoid volume (microfines)

Table 10: Linear fit parameters for the microfine aggregates for various choices of estimating volume and surface area from various choices of dimensions.

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