Page 78 - Mechanics of Asphalt Microstructure and Micromechanics

Microstructure Characterization 71

Where g d denotes the absolute value of the difference of volume fractions of voids
in the two adjacent small squares. For example, the following equation was used to
calculate the gradient in X-direction for Square 1 in Figure 3.9:
γ − γ
gradφ = 2 1 (3-12b)
d
Where d = 21.2 mm, g 1 represents the void volume fraction of Square 1, and g 2 rep-
resents the void volume fraction of Square 2. The gradient of Square 1 in Y-direction can
be expressed as in the following equation:
γ − γ
gradφ = 6 1 (3-12c)
d
Where g 6 represents the void volume fraction of Square 6. However, the gradient of
squares in the centered area is calculated using a different method. For example, the
gradient of square 7 in X-direction is represented by the following equation:
γ − γ
gradφ = 6 8 (3-12d)
d
Where d = 42.2 mm. The gradient in Z-direction is calculated as the ratio between
the absolute of the difference of volume fractions of slices between the upper and lower
position and the spacing between these two slices.
There is one gradient in each of the three directions for one point. The gradients will
be related to the anisotropic properties of the materials. For simplification of data pre-
sentation, an effective gradient is defined by the following equation:

gradφ = φ + φ + φ 2 (3-13)
2
2
x y z
Where f x , f y , and f z represent the gradients of local void volume fraction in X, Y,
and Z directions.
Wang et al. (2002) presented a study on the WesTrack specimens. Six specimens,
two for each of the three mixes, were studied. Specifically, TM06 and TM07 were the
fine mix cores; TM08 and TM09 were the fine plus mix cores; and TM10 and TM11 were
coarse mix cores. Eighty sectional images were captured for each specimen except for
TM08, which had only 62 images. Table 3.1 and Table 3.2, respectively, show some sta-
tistical information of the local volume fractions and gradients.

Statistical Information
TM06–TM11 Standev Mean Maximum Minimum
TM06 0.02146 0.015836 0.20327 0
M07 0.018812 0.018052 0.178246 0
TM08 0.05623 0.053774 0.353412 0
TM09 0.05288 0.051661 0.35322 0
TM10 0.049723 0.072603 0.338013 0.006545
TM11 0.060915 0.0770255 0.436568 0.004937
TABLE 3.1 Statistical information of local volume fraction of TM06–TM11.