Page 123 - Mechanics of Asphalt Microstructure and Micromechanics

Experimental Methods to Characterize the Heterogeneous Strain F ield 115

FIGURE 4.14 Gray-scale
image and separated
aggregates.

process, particle parameters such as volume, surface area, and aspect ratio remain con-
stant. The recognition algorithm was based on the above assumption.
To identify the matching particles in the specimen, a method presented by Wang et
al. (2004) was applied in this study. It involved two identification procedures. One is to
identify particle cross-sections between adjacent slices; the other is to identify the par-
ticles before and after testing.
The first procedure is implemented through the following steps. The first step is to
measure the sectional characteristics such as mass center coordinates Xi, Yi, and Zi,
th
area, and perimeter of the particle i on the j slice. Image-Pro Plus software was used to
obtain these geometric parameters of the particles. The second step is to find the match
particle cross-sections between adjacent slices based on comparing the similarity index
(SI), which was defined in Equation 4-13.
SI = x − x + y − y + A − A + P − P (4-13)
−
,
,
,
ij , m j+1 ij , m j+1 ij , m j+1 ij , mj , +1
th
Where x i,j and y i,j represent the mass center for particle i on j slice; A i,j represents the
th
particle cross-sectional area for particle i on the j slice; P i,j represents the particle cross-
section perimeter for particle i on the j slice; m is the dummy index representing the
th
top five nearest neighbors for the particle cross-sections on (j+1) slice. The nearest
th
neighbors are defined by the distance between two cross-sections as shown by Equa-
tion 4-14.
2
D ( x − x ) + y ( − y ) 2 (4-14)
,
,
ij , m j+1 ij , m j+1
th
To find the nearest neighbors (denoted by dummy index m) in (j+1) slice, distances
from particle i in j slice to all the particles in (j+1) slice are compared. Only the top five
th
th
nearest neighbor particle cross-sections are used for SI matching. However, the differ-
ences of particle perimeters or areas between two adjacent slices could be relatively
large while the mass center coordinate difference is small. Consideration of the area and
perimeter may actually increase noises for particle cross-section identification. Research
indicated that mass center was the most important factor for particle detection (Wang
et al., 2004). Therefore, Equation 4-13 was modified as:
SI = x − x + y − y (4-15)
,
,
ij , m j+1 ij , m j+1
The section that has the minimum SI is considered the matching particle cross-sec-
tion between two slices. Practically, SI cannot be the only factor that controls the particle