Page 85 - Mechanics of Asphalt Microstructure and Micromechanics

78 Ch a p t e r Th r e e

number of particles in contact acquired from the specimen scanned. The specimen con-
tains a total of 52 particles. At a 0-pixel threshold distance, just 12 particles (six pairs) are
involved in contact. With so few particles in contact, the particulate system would not be
able to achieve equilibrium. It may be reasonable to assume that all 52 particles are in
contact with at least one other particle. The relation presented in Figure 3.14 indicates
that when the threshold distance is 5 pixels, each particle will contact with at least one
other particle. Therefore, the threshold distance is determined as 5 pixels. In other words,
when two surface points on two different particles have a distance of 5 pixels or less, the
two points are considered in contact. If two particles have more than one pair of points
having a distance less than 5 pixels, the point pair that has the shortest distance will be
selected as the contact point. When more than one pair of points between the two parti-
cles has the same shortest distance, the point closer to the central part of the particle
surface (i.e., point O in Figure 3.15) is selected as the contact point. In some cases, when
more than one portion of two particles has a distance smaller than the threshold distance,
especially for two flat particles, only the portion that has a larger number of point pairs
that have distance below the threshold distance is considered as the contact point. In
other words, only one contact between two particles in contact is counted.
Based on the above criteria and the calculation and ordering of the distances be-
tween any point pairs on two particles, a total of 102 contact pairs were detected using
a 5-pixel threshold distance for the specimen. Each contact is also visualized for verifi-
cation of the contact. Correspondingly, the average coordination number for this speci-
men is 3.92 (102 2/52). It is anticipated that the coordination number would increase
if particles at the boundaries were removed from the calculations.

3.4.2.4 Contact Normal Vectors and Their Distribution
Among the very many fabric terms for a granular system, the contact normal vector is
one of the most important fabric quantities. Contact normal vector is defined as a unit
vector of the normal to the tangent plane at the contact point as shown in Figure 3.16.
The tangent plane should be tangential to the surfaces of both contacting particles at the

FIGURE 3.15 Illustration of
the selection of the contact
point.