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300 Ch a p t e r N i n e

Limestone Aggregates Sponge
Young’s
Size Specific Aggregate Modulus Thickness Stiffness Container Axial Load
(mm) Gravity Number (Gpa) (mm) (MPa) Size (mm) (g)
9.5~12.7 2.674 173 37 24 36.2 100H,103D 39.1 kN
TABLE 9.4 Properties of materials, specimen size, and load magnitude.

acquired by XCT, they can be converted into binary images and the digitized geometric
characteristics of individual particle cross-sections, such as the mass center coordinates
and area, can be obtained. Each particle cross-section (i) in each slice (z) was denoted as
PC(i, z). The next step was to identify which particle cross-sections in sectional slices
belong to a specific particle, namely a 3D reconstruction procedure. A similarity index
(SI) method to identify individual particles from granular media was presented else-
where (Wang et al., 2004, 2007). Further research has shown that some enhancement
could be made to improve the efficiency of identification. Recognizing that the particle
identification is very sensitive to mass center coordinates, a modified similarity index
method was employed in this study. Two particle cross-sections in two adjacent slices
were considered to belong to the same particle, if a minimum SI (SI min ) was obtained
using the following equation:
(,
SI i z) = min( x − x + y − y )
min iz , jz+1 iz , jz+1
,
,
i = 12, … n (9-24)
,
2
j = 12,, … m

Where n and m represent the number of particle cross-sections in adjacent slices z
th
th
and z+1; x and y are mass center coordinates of the ith particle in z slice or j particle
th
in (z+1) slice. Using this equation, each particle cross-section in slice z could find its
corresponding cross-section in slice z+1.
There are three possibilities that could confuse the computer judgment in individu-
al particle cross-section identification:
th
1. A new particle emerges in the (z+1) slice. In this case, no corresponding particle
th
cross-section could be found in the z slice (Figure 9.14a). Then a new code is
assigned to this new particle.
2. Existing particle cross-sections disappear in the next slice (z+1). In this case,
n>m. One particle cross-section in slice (z+1) would correspond to two or more
particle cross-sections in slice z with SI min . Then, the pair of cross-sections PC(i,z)
and PC(j,z+1) with the smallest SI min are considered to belong to the same
particle. Any other particle cross-sections in slice z corresponding to the particle
cross-section PC(j,z+1) are those that disappear in slice (z+1) (Figure 9.14b).
th
3. An existing particle disappears in the (z+1) slice while a new particle emerges
in that slice almost at the same location, having similar mass center coordinates
(Figure 9.14c). Then the trend of the area change of the particle cross-section at
slice z-1, z, z+1, z+2 is traced. In this case, the trend must satisfy the relationship
Area > Area & Area , < Area , otherwise, those cross-sections are still
z−1, i z i , z+1 i z+2, i
considered to belong to the same particle.