Page 74 - Mechanics of Asphalt Microstructure and Micromechanics

Microstructure Characterization 67

(2001b) developed a simpler method—Linear Proportional Erosion (LPE) method. The
algorithm of the method is briefly summarized in the following steps:

Step 1: Obtain the difference image (ΔAB = B − A) between two adjacent images A
and B (image ΔAB in Figure 3.6.). For binary images, the pixel values of the difference
images will have the following combinations: 1-1=0, 0-0=0, 1-0=1, 0-1=-1. The interpola-
tion will be performed only on those pixels whose pixel value differences are equal to
1 or –1.

Step 2: The length, or the continuing counts of the pixels with the same pixel value
on the different image, will then be linearly proportionally scaled according to the dis-
tance of the image to its base Image A (see Figure 3.8). This is achieved by assigning
different pixel values (0, 1) to those pixels in a proportional length (Figure 3.8). The
pixel values (0, 1) are determined according to their adjacent pixel values at both ends
of the line sections. Figure 3.8 also presents the nine possible combinations of the adja-
cent pixel values, which can be further abstracted as five cases.

Step 3: Add the modified (to one phase it is erosion, to the other phase it is dilation)
image resulting from Step 2 back to the base image to obtain the interpolated image.
Images A1B, A2B, and A3B in Figure 3.6 are the three images interpolated between
images A and B. Figure 3.7b is a virtual cut through the stack of the 76 images with three
interpolated images between any two adjacent images of the 76 images. Compared
with Figure 3.7a, the interpolated stack results in smoother curves. It should be noted
that the images in Figure 3.7 have different resolutions in horizontal (0.3 mm/pixel)
and vertical (0.2 mm/pixel) directions.
There are several commercially available programs (for example, VoxBlast) that can
perform the interpolation conveniently.

3.4 Microstructural Quantities and Implications
3.4.1 Local Volume Fractions
As a heterogeneous material, the microstructure of AC is very complicated. It is related
to the gradation of aggregates, the orientation and number of contacts of aggregate par-
ticles, the properties of aggregate-binder interface, and the void structure. Voids in as-
phalt mixtures exist in different shapes, sizes, and interconnectivity. The influence of
voids on the properties of AC is related to not only the total void content, but also the
spatial distribution of the voids. The Strategic Highway Research Program (SHRP)
Phase I mix design actually determines the volumetrics of the constituents, including air
void content, voids in the mineral aggregates (related to the binder volume), and aggre-
gate volume and gradation. The volumetrics for all AC therefore is very similar. How-
ever, the performance of these mixes is sometimes quite different. This implies that
other parameters, in addition to the overall volumetrics, may also play important roles.
Local volume fractions of these constituents and their gradients may be of importance.
Among the three constituents, air voids have the properties that are more drastically
different from the other two. This can be illustrated through the comparisons of the
stress fields of two inclusions: an inclusion of a solid and an inclusion of a cavity. The
stress concentration also indicated the significant influence of voids (Wang et al., 2007).