Page 310 - Mechanics of Asphalt Microstructure and Micromechanics

302 Ch a p t e r N i n e

9.4.1.3 Particle Identification
After being sustained under a compression force, the microstructure of the granular
material would change accordingly. If the change of locations and orientations of the
individual particles were recorded, the kinematics of the particles can then be calculat-
ed based on the mathematical relationships. For the confined compression test, the par-
ticle displacements were relatively small compared to the size of the aggregates, and
the coordinates of the mass center of individual particles changed little in radial direc-
tion. Judgment can still be made based on the SI method for individual particles. The
particle similarity index (SI p ) is defined as follows:
Δ h
SI = x − x + y − y + z − ( z + * z ) (9-25)
p b a b a b a h a

where x b , y b , z b = mass center coordinates of individual particles before test
x a , y a , z a = mass center coordinates of individual particles after test
Δh = vertical global deformation of the specimen
h = height of the specimen

The pair of particles giving the smallest SI p is considered to be the same particle. If
two or more particles are paired to the same original particle after testing, then their
volumes are compared and the one whose volume is closest to that original particle is
recognized. The same procedure of finding another original particle giving the smallest
SI p is followed for the remaining particles. This process is repeated until all the particles
after testing are recognized.
9.4.1.4 Quantification of Particle Translational Kinematics in 3D
th
Once a particle is identified, the magnitude of particle translations (for the k particle)
can then be calculated as:
DISP = u + v + w 2 (9-26)
2
2
k k k k
Where u = x − x v =; y − y w =; z − , and the superscript a denotes after the test-
b
a
b
a
a
b
z
ing and b denotes before testing. The rotation can be determined following the same
procedure presented in Chapter 4. Due to the insignificant rotations in the compression
test, only translation displacements are presented.
9.4.1.5 Computation of Micro Motions and Local Strains in 3D
With the displacement information, strains at the micro-level can be calculated. The
displacements thus quantified can be used for comparison with numerical simulations.
The procedures followed those presented in Chapter 4.
The global strains of the entire specimen are measured by:
ε = Δh (9-27a)
1 h
ε = ε = Δr (9-27b)
2 3 r
ε − ε
ε = ε = 1 2 (9-27c)
12 13 2