34
N. Abdul Hassan et al. / Construction and Building Materials 54 (2014) 27–38
Topp reggionn
Midddlee reegioon
Botttom
m regiion
ITZ
Z craackss
Fig. 10. Comparison of image slices of asphalt mixture specimen, before (top images) and after (bottom images) the deformation at 25 °C.
in which the micro-cracks tend to bridge between proximal aggregates. After being formed, the micro-cracks and air voids are
thought to have propagated to form macro-cracks, thereby
decreasing the specimen’s strength. From the observations made
on a number of specimens, it was determined that damage governed by the changes in air voids structure occurs in a variety of
ways. First the changes might contributed by the increase in the
size of the existing individual air voids and propagate to form
cracks. Second, two separated air voids might coalesce and propagate to form cracks within the vicinity of the damage. Third, as a
result of the deformation, new air voids are also formed having potential for crack initiation. These observations concur with those
that were previously recorded in Table 2. It is also noteworthy that
they are not mutually exclusive and can act simultaneously to initiate micro-cracks and macro-cracks under the loading.
3.5. Quantification of crack formation and crack propagation
This investigation is intended to apply the concept of fractal
analysis to study the formation and propagation of cracks in the
mixtures. For decades this concept has been used in many
3×3
disciplines including medicine, geology and material sciences. For
asphalt mixtures, it has been used to measure the geometry of
irregular shapes and the surface roughness of aggregate particles,
which are both important factors with potential to affect the
mechanical properties of asphalt mixtures [26,27]. In cement and
concrete research, fractal analysis has been widely adopted for
crack analysis [28–31]. Outputs of interest derived from fractal
analysis, containing crack information include fractal dimension,
crack tortuosity, crack branching factor and crack density.
Fractal dimension, D, is an application of fractal analysis to
characterise the shape of a crack’s boundary or contour. It is a
non-integer number that measures the degree of fractal boundary
fragmentation or irregularity over multiple scales. The fractal
dimension of cracks was determined using the ‘Box Counting
Method’ under the application of FracLac in ImageJ developed by
Karperien [32]. The approach measures the lengths or distances
between points on the border of a shape using sets of square boxes
or grids. Fig. 11 displays images showing the grids or arrays of
boxes of different sizes (e) overlaying the crack images. The boxes
that contained the pixels of the cracks image were counted (N) for
the plot of ln(box count, N) versus ln(box size, e), which is used to
11×11
24×24
Fig. 11. Example of a crack image analysed with different grid sizes (in pixels).