5. Four kinds of real aggregates: Image acquisition and sieve analysis

As an application of the x-ray CT/spherical harmonic technique, we examined four different kinds of aggregates: granite (GR), limestone (LS), Indiana (IN), and Arizona (AZ), which had all passed a 12.7 mm sieve [15, 16] and were retained on a ** sieve. These four kinds of aggregates were intended to cover a wide range of aggregates commonly used in the U.S. in terms of shape and texture. The GR and LS aggregates, both from Oklahoma, were crushed aggregates. The AZ and IN aggregates were siliceous river gravels and were not crushed. A qualitative petrographic analysis is given in Table 3 [15]. All x-ray CT samples were 100 mm diameter by 200 mm high cylindrical samples of coarse aggregates cast in cement paste. The image analysis procedures described earlier were performed to separate particles and eliminate internal porosity, ring artifacts, etc. These aggregates were imaged at approximately the same horizontal resolution, 0.2 mm per voxel, but at differing vertical resolutions: GR − 0.7 mm per voxel, LS − 0.8 mm per voxel, IN − 0.8 mm per voxel, and AZ − 0.4 mm per voxel.

Once the spherical harmonic coefficients were generated for several hundred examples of each kind of aggregate, some statistical analysis could be done. A sieve analysis can be simulated, since the volume of each particle is known via spherical harmonic techniques [1]. For a sieve analysis of a single kind of rock, mass fractions are the same as volume fractions if we assume that the specific gravity of each kind of rock is the same. There is usually some distribution in specific gravities [11], but only of order 10 %, so we neglect that here. The only choice to be made when constructing a sieve analysis is how to devise a length from the known volume of each non-spherical particle. We chose to compute the equivalent spherical diameter. If V is the true volume of the aggregate, then D, the equivalent spherical diameter, is given by D = (6V/π)^1/3. An experimental sieve analysis of the particles that went into the sample was also performed, and so the experimental and simulated results could be compared.

Table 4 shows this comparison for the four kinds of aggregates in terms of mass percentage retained at each of six sieve sizes. There is good qualitative agreement in the overall distributions among sieve sizes, although there are some significant disagreements within individual bins. There are two primary reasons for these differences. The first is that the equivalent spherical diameter based on particle volume is not exactly the same as the effective length of a square-holed sieve. The second reason is that the image-based analysis only uses a few hundred particles. So, especially for sieves for which the mass percentages were small, there can be a high degree of statistical fluctuation. It can be seen in Table 4 that the largest relative quantitative disagreements are at sieves where the experimental mass percentage is small.

Figure 5: VRML images of four typical particles each selected from the four different kinds of aggregates studied in this paper. The relative aggregate sizes are approximately accurate. For comparison between rock types, the AZ particles are all about 12 mm in size.

Figure 5 shows four aggregates each of the four kinds of rocks investigated, taken from VRML images, which can have different viewpoints and hence different apparent magnifications. The sizes have been adjusted by hand to approximate the scaling of the equivalent spherical diameter. Table 5 lists the equivalent spherical diameter, D, for each rock in Fig. 5 as a measure of size, as well as the ratio of its true surface area, as measured by the spherical harmonic series, to the surface area of a sphere with the same equivalent diameter, denoted by the letter "h." Left to right and up and down in Table 5 corresponds to left to right and up and down in Fig. 6.

Figure 5 shows four aggregates each of the four kinds of rocks investigated, taken from VRML images, which can have different viewpoints and hence different apparent magnifications. The sizes have been adjusted by hand to approximate the scaling of the equivalent spherical diameter. Table 5 lists the equivalent spherical diameter, D, for each rock in Fig. 5 as a measure of size, as well as the ratio of its true surface area, as measured by the spherical harmonic series, to the surface area of a sphere with the same equivalent diameter, denoted by the letter "h." Left to right and up and down in Table 5 corresponds to left to right and up and down in Fig. 6.