Predicting Compaction Effects on Asphalt Mixture Microstructure Using 2D Digital Image Analysis

The paper's priorities are to characterize the aggregates brought from seven sources in Iraq as shown in Figure 1, used in the production of hot mix asphalt by, among other properties, describing the distribution of aggregate in asphalt mixes using DIA, intending to match laboratory compaction methods with those actually occurring in the field, and quantitatively realizing the 2D orientations of aggregate particles with a diameter greater than or equal to 2.36 mm. The following methodology in research was used to achieve this goal:

1. Enables a valuable, faster, and reliable DIA technique for analysing the aggregates' behavior during the compaction process and understanding their possibility to randomize precisely.
2. Define recognizable indicators that highlight remarkable characteristics of aggregates' interactions and packing in asphalt mixtures and categorize them into two aspects: The first concerns the aggregates' geometrical morphologies, while the second concerns the aggregates' interlocking characteristics.
3. Accurately measure the consequences of compaction variables on aggregate structure and choose the optimal option compared to the field and ideal aggregate sources.

4.1 Aspects of aggregates’ geometric forms

4.1.1 Geometric indicators of aggregate

As mentioned earlier, the DIA could be used to quantify morphological indicators characterizing the geometry of an aggregate cross-sectional area. Numerous researches have examined the typical Area (A_c), Equivalent diameter (E_D), and Feret Diameter (F_D) [28-30]. In addition, a newly calculated Crofton Perimeter (C_P) has been employed to assess this study's findings accurately. E_D is the diameter of the disc of the same area, which is calculated as in Eq. (1):

$E_D=\sqrt{\frac{4 A_c}{\pi}}$                              (1)

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Figure 11. Analysis of aggregate’s geometric indicators

In all directions [0^o-180^o], Accurate C_P, producing by an average value of 8 Var-Diameter measured as the product of intercepts by distance between interception nodes. F_D can be estimated as the separation of two tangents of the particles that run parallel to one another. Based on Eqs. (2) and (3), the principles for the two indicators are shown in Figure 11.

$C_p=\propto a N_o+\left(\frac{\pi}{2}-\propto\right) b N_{90}+\frac{\pi}{4} c\left(N_{\infty}-N_{\pi-\alpha}\right)$                           (2)

Cauchy's Formula is used to construct the aforementioned equation, where the N is the intercept count along the directions 0^o, 90^o, α, and α-π. a, b and c are the distances between horizontal, vertical, and diagonal lines as well.

$F_D=\frac{C_p}{\pi}$                            (3)

AVISO characterizes aggregate two-dimensional morphology. Seven aggregate sources are specifically selected. The geometric indicators of their projected two-dimensional images are quantified, as shown in Table 6.

Geometric indices are often used as a start in specifying other characteristics. Because of differences in compaction conditions, the amount of the geometric indications may vary. Consequently, the coefficient of variation (CoV) is employed in the analysis to quantify the degree of dispersion of the average DIA findings of vertical and horizontal segmentation of various aggregate sources. Geometrical indicators were evaluated, and the results of the standard deviation and variation coefficient of the A_c, E_D, C_P, and F_D were provided to investigate the correlation between the variability of the two-dimensional outline index of the different aggregates under various compaction approaches.

Compared to the Field compaction approach, all vertical segmentation parameters for Marshall compaction have decreased by 29, 17, 20, and 18%, respectively, and for Roller compaction by 32, 21, 12, and 15%. The CoV data revealed that Marshall compaction had a more significant degree of variability for the A_c and E_D indicators than roller compaction. However, for the C_P and F_D indicators, Roller compaction had lower variations than Marshall compaction.

In contrast to the Field compaction method, all horizontal segmentation parameters for Marshall compaction have been increased by 31, 20, 1, and 10%, while Roller compaction has been raised by 6, 4%, and dropped by 4, 1%. According to the conclusions of the CoV, Marshall compaction has more considerable variability than roller compaction when all indicators are evaluated. Increasing the average portion of aggregate indicators increases the probability of contact points and interference between the aggregate during the compaction process.

The overall statistics of two segmentations and according to the preceding results, relying on roller compaction results, the AlNibaa'e, AlDoz, Southern AlRumela, Alsimawa, AlKut, Jalawlaa, and Dyala aggregate sources are considered in that sequence from the different kinds of aggregate sources due to their relative values that are closer to the average and possess a lower standard deviation. Even so, it is still challenging to describe the morphological aspects of the aggregate using only one parameter of the two-dimensional geometric index. Thus, additional complicated indices will be studied to guarantee the reliability of results.

Table 6. Geometric indicators for all quarries under different methods of compactions

4.1.2 Shape indicators of aggregate

Three indicators have been employed to magnify their impact on the distribution of aggregates for assessing aggregate shape using the DIA analysis. Shape index (SI), Aspect Ratio (AR), and a new index measure the symmetrical property of aggregate called Symmetry (S(p)).

SI, as presented in Eq. (4), measures aggregate cross-section uniformity. Lines have a SI of 0, while perfect circles have 1. The more elongated the particle cross-section, the lower the shape index.

$S I=\frac{4 \pi A_c}{\left(C_p\right)^2}$                                    (4)

AR of the matched ellipse for the particle as shown in Figure 12(a) is found using the Eq. (5). It is defined as the proportion of the longer to the shorter feret axes [31].

$A R=\frac{X F_{\text {max }}}{X F_{\text {min }}}$                             (5)

The measure of S(P) indicates whether or not a form is symmetric. It approaches 1 for symmetric shapes and declines with symmetry. It is reduced to 0.5 if the gravity centre is located outside the particle, as seen in the Figure 12 (b). Eq. (6) for aggregate particle P is used to calculate it.

$S(P)=\frac{1}{2}\left(1+M I N_n\left(\frac{R_{\min }}{R_{\max }}\right)\right)$                            (6)

where, R_min and R_max are ${MIN}\left(\overline{I_a G_c}, \overline{I_b G_c}\right)$  and ${MAX}\left(\overline{I_a G_c}, \overline{I_b G_c}\right)$, respectively.

MIN_n is the minimum value operator over all the angles ϴ_n within [0, π].

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Figure 12. Analysis of aggregate’s shape indicators

Aggregate performance in asphalt concrete is enormously affected by the aggregates' SI, AR, and S(P). The C_P of a particle is compared to the perimeter of a circle of the same area using the SI. The particle's area is proportional to that of a circle. An orientation angle is required to characterize the spatial distribution of particles inside asphalt concrete when the AR is more significant than one. Another signifier that DIA uses to identify aggregate architecture is symmetry, and it has strong indications for values that fall within the range of more than 0.5 and less than 1 [32].

The SI of the aggregates on the two cross sections is between 0.273 and 0.640, as shown in Figures 13 and 14. Comparing the two compaction techniques to the Field, the findings for all sources indicate that Marshall compaction is valuable for vertical and horizontal segmentation, indicating that most aggregate particle cross sections tend to lay vertically and horizontally, respectively. In contrast, Roller compaction implies that the results are superior to Marshall's for two reasons. The first is associated with a reasonable variation in SI, which indicates an ideal aggregate orientation. In contrast, the second is closest to its average value from the Field compaction.

AR related to the effects of SI to limit the indications regarding the effects of compaction on the aggregate distribution and the orientation angles. All values of Marshall and Roller compaction recorded more than one. Still, the Roller method performed best in the vertical and horizontal segmentation. SI and AR provide better aggregate results for AlNibaa'e than other indices. The two indicators, as mentioned earlier, determine the S(P) indicator as a function of aggregate size and depending on the aggregate centre's eccentricity from the bally centre. All values are evaluated as more than 0.5 and less than 1. Roller compaction provides better indicators than Marshall for the two segmentations compared to the Field, even considering AlDoz source.

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Figure 13. Analysis of aggregate’s shape indicators (Vertical segmentation)

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Figure 14. Analysis of aggregate’s shape indicators (Horizontal segmentation)

4.1.3 Texture indicator of aggregate

DIA using AVISO program provides quick and straightforward access to aggregate texture properties, which aids in developing more accurate and realistic parameters [33].

Rugosity (Ru(P)) is also known as ‘Spike Parameter’ is a factor determines if the contour of a shape is smooth or not. Its value close to 1 for an abrasive shape and decreases for smooth boundaries. It is given by using Eq. (7) where E_d is the mean operator over all the triangle bases d within [40, L/15]. The step length d represents the distance $\overline{I_n I_{n p}}$ as shown in Figure 15. L is defined as the shape perimeter in pixels. Ru_d (P) is defined as E_N(ru_n) where E_N is the mean operator over all valid [ln, lnp] bases for the current d length, and ru_n=cos(ϴ(n)/2). ϴ(n) is the angle associated to the point P maximizing the spike value cos(ϴ(P)/2)⋅h. The angle ϴ and the distance h are defined as in mentioned figure, with ϴ<2.9 rad. If ϴ≥2.9 rad the spike value is counted as 0.

$R u(P)=E_d\left(R u_d(P)\right)$                            (7)

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Figure 15. Analysis of aggregate’s texture indicator

The DIA quantifies texture as a function of rugosity by measuring particle boundary irregularity in high-resolution black-and-white images. Gray-level intensities from 0 to 255 show surface abnormalities. Surface texture is described with this term. A smooth particle has a minimal gray-level intensity variation, whereas a rough surface has a considerable variance. To determine how compaction variables affect the aggregate texture, it measured various aggregate sources under varied compaction conditions Compared to Field compaction as presented in Figures 16 and 17.

Marshall method has a noticeable influence on texture for vertical segmentation, while Roller compaction influences horizontal segmentation. This may be due to the direction of compaction and their ways of contributing to aggregate particle friction, a vital mix property that resists pavement deformation. Nevertheless, the Roller approach outperformed Marshall's impact, especially for AlNibaa'e, AlDoz, and Alsimawa aggregate sources.

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Figure 16. Analysis of aggregate’s texture indicator (V.S.)

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Figure 17. Analysis of aggregate’s texture indicators (H.S.)

4.2 Internal structure of aggregates' interlocking

A comprehensive microstructural statistical analysis was performed to determine how many variables affect HMA specimens' interior structure. AVISO program as shown in Figure 18 divided the data into zones with equivalent diameters greater than or equal to 2.36mm. The data analysis allocates estimated findings into class intervals (CI) for all vertical and horizontal sample segmentations. The recent internal structure equations of the study depend on using 20 CIs of frequency distribution (approximately an average orientation angle of 10^° per CI).

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Figure 18. Frequency distribution of aggregate orientation

4.2.1 Orientation and anisotropy of aggregate

The orientation as shown in Figure 19 (a) is its principal inertia axis. Physical and mechanical particle qualities vary with orientation. The covariance matrix's biggest eigenvalue's eigenvector is (M). whereas its minor inertia axis is its secondary orientation. It is the covariance matrix's lowest eigenvector (M). With regard to the barycentre, the values reflect the shape's bounding box orientated along the associated eigenvector. the average of all particles' inclination angles assessed by the orientation angle as given in Eq. (8):

$\theta=\frac{\sum_1^{C I}\left|\theta_{C I}\right|}{C I}$                             (8)

The $M$ matrix is defined as $\left[\begin{array}{cc}M_{2 x} & M_{2 x y} \\ M_{2 x y} & M_{2 y}\end{array}\right] M_{1 x}=1 / \mathrm{A}(\mathrm{X})$ $\sum_X M_i$, and $M_{1 y}=1 /(\mathrm{A}(\mathrm{X})) \sum_X M_i M_{2 x}=1 /(\mathrm{A}(\mathrm{X})) \sum_X\left(x_i-M_{1 x}\right)^2$, $M_{2 y}=1 /(\mathrm{A}(\mathrm{X})) \sum_X\left(y_i-M_{1 x}\right)^2$, and $M_{2 x y}=1 /(\mathrm{A}(\mathrm{X})) \sum_X\left(x_i-\right.$ $\left.M_{1 x}\right)\left(y_i-M_{1 y}\right)$, where, $A(X)$ is the area, $\left(x_i, y_i\right)$ is the points on particle, and $M_{1 x}, M_{1 y}, M_{2 x}, M_{2 y}, M_{2 x y}$ are the first and second moments of inertia, respectively.

Anisotropy depended on the particle orientation angle and measures the deviation of a region from a spherical shape. It describes the orientation, structure, and morphology of the particles. Anisotropic materials have directions-dependent characteristics. The percentage value of anisotropy as shown in Figure 19 (b) can be estimated using Eq. (9):

$Anisotropy =\left(1-\frac{ { Eigen \,Value }_{\max }}{ { Eigen \, Value }_{\min }}\right) * 100 \%$                             (9)

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Figure 19. Analysis of aggregate orientation and anisotropy

The DIA results of vertical and horizontal orientation angle and anisotropy are presented in Figures 20 to 23, respectively.

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Figure 20. Analysis of aggregate orientation (V.S.)

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Figure 21. Analysis of aggregate orientation (H.S.)

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Figure 22. Analysis of aggregate anisotropy (V.S.)

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Figure 23. Analysis of aggregate anisotropy (H.S.)

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Figure 24. Analysis of aggregate orientation, normalized, and harmonic data (AlDoz quarry, V.S.)

Table 7. Amplitude ‘A’ values for aggregate quarries under different methods of compaction

It is required to assess the impact of various compaction processes on the orientation of contact and central lines from various aggregate sources. The average vertical and horizontal segmentation aggregate orientation is specified by 10^° intervals from -90 to 90. It has been shown that the average vertical and horizontal orientations concentrate at -10 to 10 degrees and -20 to 20 degrees, respectively. Compared to the Field compaction, Marshall achieves better vertical orientation outcomes than the Roller compaction and vice versa for horizontal segmentation. The findings demonstrate a significant fluctuation in the negative and positive results of the Marshall technique, which may need to be more reliable in predicting the actual state. According to previous studies, the anisotropy is more significant in samples with 0° orientation and vice versa. The findings demonstrate that Marshall compaction provides strong recommendations for vertical segmentation. However, Roller compaction provides better results for horizontal segmentation than Marshall compaction, corresponding to lower percentages of aggregate anisotropy. The explanations also agree with the results of aggregate shape indicators and textures, particularly for the aggregate sources of AlNibaa'e, AlDoz, and AlKut, respectively.

4.2.2 Homogeneity of aggregate in HMA

Pavement deterioration begins with asphalt mixture inhomogeneity. Due to the difficulties of defining homogeneity using typical testing techniques, DIA has been used for field cores, and laboratory compacted specimens to define it directly, related to connection with the pavement performance. Instead of indirectly measuring asphalt mixture homogeneity by density, % air voids, and texture depth, DIA can directly define its morphological properties [35, 36]. Variation of homogeneity is essential to determine each aggregate orientation relative to the aggregate's major axis. Figure 24 displays a histogram for AlDoz aggregate sample presented by distributing an aggregate orientation into approximately 10^° intervals. Perfectly, fitting normalized data to the harmonic occurrences considering a sinusoidal wave's function as shown in Eq. (10).

$\begin{gathered}\text { Harm. }=\text { Norm.* }\left(1+A_1 \operatorname{Cos}\left(2 \theta_{C I}\right)+\right.  \left.2 B_1 \operatorname{Sin}\left(2 \theta_{C I}\right) \operatorname{Cos}\left(2 \theta_{C I}\right)-A_1 \operatorname{Sin}\left(2 \theta_{C I}\right)\right)\end{gathered}$     (10)

where, $A_1=\frac{2 \sum_1^{I I} \cos \left(2 \theta_C\right)}{C I}$, and $B_1=\frac{2 \sum_1^{C I} \sin \left(2 \theta_{C I}\right)}{C I}$.

The study fit determines the harmonic amplitude (A), which measures severity or variation from a uniform distribution. Horizontal line would have zero ‘A’ if aggregate orientation were uniform. Thus, orientation non-uniformity decreases with increasing ‘A’. The results of ‘A’ for all quarries of aggregate are presented in Table 7.

Comparing compaction modes' influence on aggregate homogeneity. The findings show that the compaction method significantly affects the computed harmonic amplitude (A). The comparison relies on evaluating ‘A’ for all aggregate sources and estimating the CoV range relating to the average value. The vertical segments indicated that the Marshall and roller compaction rates of ‘A’ are substantially higher than those of the field compaction, although the rate of CoV across aggregate types is around 60%, which may call into doubt the evaluation procedure. In the horizontal segments, the results process showed that the roller compaction with a rate of ‘A’ is most influential than it is in the Marshall method, compared to the field compaction with an approximated average CoV of 20% and less than it is in the Roller compaction, which implies that it has the highest tendency to orient the aggregate homogeneously to a particular angle. The AlNabai, AlDoz, and AlKut sources of aggregates were given priority since they produced the most significant results.

4.2.3 Directional distribution of aggregate

As indicated in Eq. (11), the vector magnitude (∆₀), a statistical indicator, has been employed to characterize the directional distribution of aggregates. Each compaction energy is determined as the average of the values measured on the two segments of each specimen produced at that compaction level [37]. Marshall specimens were prepared using 75 blows, while Roller slabs were progressively applying with 5 kN load for a variable number of cycles to achieve the same Marshall density for each aggregate source. Conversely, the ∆₀ improved with compaction until it reached a peak value, after which it began to decline when the compaction level was raised further. As a result, the aggregates' preferred orientation seemed more noticeable with compaction until an optimal value was realized. After that, aggregates tended to have randomized orientation.

$\Delta_0=\frac{100}{C} \sqrt{A_2{ }^2+B_2{ }^2}$                            (11)

where, $A_2=\sum_1^{C I} \operatorname{Cos}\left(2 \theta_{C I}\right)$, and $B_2=\sum_1^{C I} \operatorname{Sin}\left(2 \theta_{C I}\right)$.

The average value of ∆₀ range from 0% to 100% at any time. If the orientation is wholly distributed randomly, it will be 0%. However, if it is 100%, all observable orientations point in the same identical direction. Figures 25 and 26 show ∆₀'s vertical and horizontal segmentations.

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Figure 25. ∆₀ analysis of aggregate (V.S.)

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Figure 26. ∆₀ analysis of aggregate (H.S.)

The results demonstrated that Marshall and roller compaction had a higher ∆₀ value in vertical segments than in situ compaction. For the horizontal segments, their importance in Marshall compaction remained virtually greater than in field compaction for most of the aggregate types while being lower in roller compaction. The Marshall and roller compactors tilt the aggregate, reducing fullness. Field compaction, whereas throughout the vertical segments, the vector magnitude of Marshall compaction is higher than roller compaction and with the average of an aggregate spreading percentage of 54 and 63%, respectively, since in the Marshall method, the stresses are perpendicular to the estimated area of the sample, which may well lead to the possibility of organizing the aggregates transversely and then tending to take a path towards the circumference of mould because of its small dimensions, maintaining somewhat the spreading process in the other direction. With the Roller technique, shear stresses affect the aggregate horizontally with a spread proportion more significant than Marshall, then stabilize may be due to the large size of the mould, resulting in more aggregate distribution randomization than Marshall, especially for AlNibaa’e, AlDoz, and Jalawlaa sources of aggregate.