Page 118 - Mechanics of Asphalt Microstructure and Micromechanics

110 Ch a p t e r F o u r

micro-strains. The strains, which occur in the mastic, are important parameters in the
evaluation of rutting and fatigue resistance of AC. The procedure developed in the pre-
vious sections was thus extended to include the capability of measuring the average
strains in the mastic only. Since mastic properties are both strain-rate and strain-level
dependent (Brown et al., 1980), the measurement of the permanent strain in the mastic
is only of interest in the analysis and experimental evaluation of the mechanical proper-
ties of AC.
The approach is best illustrated by considering the relative displacement between
the gravity center (cross-section area center) of any two particles i and j, as shown in
Figure 4.9. The displacement of particle i relative to particle j as a result of particle trans-
lation can be decomposed into two components:
The component along BA (see Figure 4.9):
Δu = ( u − u )cosθ + ( v − v )sinθ (4-9)
n i j i j
and the component normal to BA:
Δu =−( u − u )sinθ + ( v − v )cosθ (4-10)
t i j i j
Where u i , u j , v i , v j are the x and y components of the displacements of the gravity
center of the particles, while q is the angle of BA (j to i) relative to the x axis.
Since the particles are essentially rigid, actual deformation takes place in the mastic
only and therefore the relative displacement and the distance between A and B
(Figure 4.9) should be used for computing the strain measure of the mastic between the
two particles.
The average engineering strain along BA (normal strain) in the mastic is:
Δ u
ε = n (4-11)
n H

FIGURE 4.9 Illustration of particle kinematics.