Three-dimensional quantification and classification approach for angularity and surface texture based on surface triangulation of reconstructed aggregates

Construction and Building Materials 246 (2020) 118120

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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Three-dimensional quantification and classification approach for angularity and surface texture based on surface triangulation of reconstructed aggregates Can Jin a, Feilong Zou a, Xu Yang b,c,⇑, Kai Liu a, Pengfei Liu d, Markus Oeser d a

School of Automotive and Transportation Engineering, Hefei University of Technology, 193 Tunxi Road, Baohe District, Hefei, Anhui 230009, China School of Highway, Chang’an University, Xi’an 710064, China Department of Civil Engineering, Monash University, Clayton, VIC 3800, Australia d Faculty of Civil Engineering, RWTH Aachen University, 52074 Aachen, Germany b c

h i g h l i g h t s
Three-dimensional angularity and texture indices of the aggregate were proposed and quantified.
Statistical indices were proposed to compare the similarity of aggregates by the angularity and texture.
Adaptive classification of aggregates by angularity and texture was conducted.

a r t i c l e

i n f o

Article history: Received 25 September 2019 Received in revised form 25 December 2019 Accepted 6 January 2020

Keywords: X-ray computed tomography (CT) Three-dimensional aggregate reconstruction Angularity and surface texture Morphology quantification and classification

a b s t r a c t Angularity and surface texture of aggregates are important morphological characteristics, which have significant effects on the micromechanical responses of asphalt composites. A novel approach to quantify and classify the complexity of aggregate angularity and surface texture is proposed from a statistical perspective in this study. The methodology consists of three main steps, as follows: 1) the aggregate is threedimensional (3D) reconstructed, and the model surface is triangulated into facets to conduct clustering for aggregate angles evaluation; 2) consequently, a reference plane is determined for each facet cluster to quantify the surface texture of a surface area which overlaps the cluster, and thus the surface texture is quantified; and 3) aggregates are classified by using the distribution characteristics of the angularity and surface texture respectively. Based on the quantification with the presented approach, 275 grains were classified by the angularity and surface texture. Results indicate the benefit of the proposed method in accurate quantification and classification of aggregate angularity and surface texture, which facilitate the bridging of the gap between aggregate morphology and micromechanical performance of asphalt composites. Ó 2020 Published by Elsevier Ltd.

1. Introduction Aggregates constitute most of the asphalt composite, which determine the composite skeleton and thus have a significant influence on micromechanical responses of the pavement [1–3]. As two important morphological characteristics, the angularity and surface texture are used to describe the detail of the aggregate shape and have great effect on the pavement performance, which ⇑ Corresponding author at: School of Highway, Chang’an University, Xi’an 710064, China. E-mail addresses: [email protected] (C. Jin), [email protected] (F. Zou), xu. [email protected] (X. Yang), [email protected] (K. Liu), [email protected] (P. Liu), [email protected] (M. Oeser). https://doi.org/10.1016/j.conbuildmat.2020.118120 0950-0618/Ó 2020 Published by Elsevier Ltd.

has been reported by many previous studies [4,5]. Specifically, angular particles facilitate the interlocking effect; and rough particles can increase the friction among aggregates and reinforce the aggregate-asphalt interface. Thus, particles with a large quantity of surface angles and rough surface may facilitate the stability of aggregate skeleton, which is useful to pavement durability and rutting resistance. As a method which captures the micromechanical responses of the internal structure of a composite, micromechanical simulations are superior to laboratory tests in solution complexity and economy [4,6–9]. Since realistic particles are widely preferred in simulations for more reliable outputs, the angularity and surface texture of realistic aggregates need to be quantified and classified

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accurately to study the exact relationship between the two morphological properties and the micromechanical responses of the composite [10]. Based on that, a premium configuration of aggregate angularity and surface texture can be obtained to improve mechanical properties of the composite significantly. In other words, the classifications of angularity and surface texture are used to configurate the fractions of aggregates with different angularity and surface texture to reach an optimized composition of aggregates in the asphalt composite. During the last decades, the quantification approaches for angularity and surface texture of realistic particles have been studied both in two-dimensional (2D) and three-dimensional (3D) schemes. The quantification for aggregate angularity mainly falls into three categories: the radius based approach which evaluates the angularity by the difference between the 2D outline and its equivalent ellipse [11], the gradient based approach which evaluates the angularity by the gradient variation degree of the sampled points on 2D outline or 3D surface [12–14], and the Fast Fourier Transform (FFT) based approach which calculates the angularity by FFT representation of 2D outline or 3D surface [15–17]. To study the aggregate morphology, AIMS (Aggregate Image System) [18], AIMS 2 [19,20] and laser scanning equipment [21– 23] were used to obtain 2D or 3D outlines of aggregates. AIMS and AIMS2 capture the 2D projection of each aggregate as a binary image to extract 2D outlines of aggregates using the edge detection techniques. The laser equipment captures the point cloud on aggregate surface to reconstruct the 3D geometry of the aggregate surface with surface triangles using computer graphics techniques. Based on 2D or 3D outline of the aggregate, the shape descriptors including form factors, circularity measures and sphericity were calculated. The quantification for aggregate surface texture mainly falls into three categories, too: the surface departure based approach which evaluates surface texture by the mean and standard deviation of the sampled surface heights measured by using optical interferometry technique [23]; image morphology based approach which calculates the surface texture by the volume loss after erosion and expansion of 3D aggregate image [14,24]; and FFTbased approach which calculates the surface texture by FFT representation of 2D outline or 3D surface [25,26]. 2D aggregate outlines highly depend on the projection direction of the particle, and it is difficult to determine a representative outline for morphology characterization. In comparison with 2D outlines, 3D solid models can capture the complexity of aggregate shape more accurately to extract angularity and surface texture [27]. Previous works contributed a lot to the quantification of aggregate morphology. However, in existing literature, most determined indices of angularity and surface texture are of a simple value with self-defined dimensions which are difficult to understand. It suggests that the two morphological properties need more comprehensive indices in metric units to represent the distribution of angles and surface texture on aggregate surface clearly from a statistical perspective for further applications. Conventional categories of aggregates are mainly flat, elongated, round, angular and fractured types [28,29]. Flat and elongated types refer to aggregate form, and round, angular and fractured types refer to aggregate angularity. But for surface texture, the criteria for roughness is not well identified. Obviously, both the angularity and surface texture need more consideration to evaluate the complexity of the two properties adequately. Furthermore, comprehensive classifications of aggregate angularity and surface texture are the basis to construct design parameters of aggregate content for virtual specimens. Consequently, the correlations between the aggregate morphology and the mechanical properties of the asphalt composite can be further investigated through numerical simulations.

Therefore, the objective of this paper was to quantify and classify aggregate angularity and surface texture from a statistical perspective. To achieve this goal, the aggregate is 3D reconstructed using X-ray computed tomography (CT) imaging accurately. Subsequently, the aggregate surface was triangulated into facets to be clustered for angularity and surface texture quantification by innovative indices. At last, aggregates are classified by the distribution characteristics of angularity and surface texture in microscopic view respectively. 2. Methodology and roadmap The entire procedure to quantify and classify the angularity and surface texture is constituted of three main steps (Fig. 1), as follows: 1) aggregate reconstruction and surface triangulation; 2) angularity and surface texture quantification; and 3) adaptive classification of angularity and surface texture. Table 1 defines the key variables in this paper. 2.1. Aggregate reconstruction and surface triangulation 3D solid reconstruction of the aggregate provides intact geometry and topology of aggregate profile, which is the prerequisite step to quantify angularity and surface texture. The reconstruction is conducted from X-ray CT imaging using functions in the 3D modeling toolkit ACIS (the assembly of the first characters of the three developers: AlanGray, CharlesLang, and IanBraid, plus Solid). Specifically, the 3D reconstruction of aggregates from X-ray CT imaging consists of two main steps: 1) two-dimensional (2D) enclosed outlines in each CT image are detected with shape features of outlines and grayscale threshold to identify aggregate pixels from non-aggregate pixels, as shown in Fig. 2b–d; and 2) the mapping between each aggregate and its outlines on various layers is established, so that 3D models of aggregates were constructed by using the skinning operation in ACIS, the 3D modeling toolkit, as shown in Fig. 2e–f. The details were described in the previous studies of the authors [30–33]. The surface angle of the model is usually determined by approximately flat surface pieces. Thus, the model surface should be triangulated into tiny facets to locate flat regions. ACIS provides a function for surface triangulation which is controlled by the parameter: surface tolerance, as shown in Fig. 3. The surface tolerance controls the surface deviation which is caused by the facet representation. It is believed that the accuracy of surface fitting is inversely related to the surface tolerance. The parameter needs proper assignment to reach the balance between representation accuracy and facet quantity. The model needs a trial triangulation to locate flat areas on model surface roughly before the further clustering of formal triangulation. The trial triangulation uses a very large surface tolerance and obtains trial facets which are sorted by the area in descending sequence. The centroids of trial facets are considered as centers of flat areas on model surface and used as center positions with a sequence number. After that, the model surface is then triangulated by using proper surface tolerance to obtain formal facets. 2.2. Angularity and surface texture quantification In this paper, a surface angle is defined based on the dihedral angle between two large and approximately flat areas on aggregate surface, and the surface texture is defined based on the tiny undulation on aggregate surface. In other words, the surface angle and texture are in the scope of macro- and micro-level, respectively. Therefore, the angularity and surface texture should be quantified in sequence.

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Fig. 1. The roadmap of quantification and classification of the angularity and surface texture.

Table 1 Description of key variables. Item

Related parameter

Description

Application

The facet clustering method

T Norm

The threshold for the angle between the two normal vectors of the last extension and the facet to be extended. The threshold for the thickness of the candidate cluster. The comprehensive normal vector of the facets involved in an extension. The area of the facet. The normal vector of the facet. The comprehensive normal vector of the facet constituting the cluster. The distance from a sample point on a cluster to the reference plane. The quantity of sampled points for the cluster. The depth of the surface texture of the cluster. ^ angle ; rangle Þ or The distance threshold to identify if Angularityðl ^ depth ; rdepth Þ of two particles are close. Textureðl

Used to identify approximately flat region on the aggregate surface for surface angle calculation.

T Thick Normextension Areafacet Normfacet Normculster The surface texture quantification method The preliminary classification algorithm

d qcluster Depthcluster TD Angularity ^ angle ; rangle Þ ðl Texture ^ depth ; rdepth Þ ðl

The formal classification algorithm

Diff 1;2 subi Areasubi Areaov erlap q1i ; q2i Q 1; Q 2 T Diff Labelangle   ðlangle ; langle

Used to obtain the preliminary classification of the angularity and surface texture.

Used to obtain the formal classification of the angularity and surface texture.

AR Þ

Labeltexture ðldepth ; ldepth AR Þ 

The weighted mean value and standard deviation of surface angles of a particle. The weighted mean value and standard deviation of texture depths of a particle. The difference between the angularity or surface texture charts of two aggregates. The subarea of the difference between two charts. The area of subi The overlap area of two charts. The quantity of points involved in subi in two charts. The quantity of points of two charts. The threshold for Diff 1;2 . The tuple to identify aggregate classes by the angularity.

Used to evaluate the surface texture of the aggregate.

The tuple to identify aggregate classes by the surface texture.

To quantify the aggregate angularity accurately, the facets need to be clustered properly to identify approximately flat areas with a threshold of thickness. However, adjacent facets within a single threshold of thickness may contribute to the transition region of a surface angle, which is not preferred to be recognized as a single cluster. Therefore, large and flat areas on aggregate surface should be detected as facet clusters in prior to transition areas for an accu-

rate angle quantification. The clustering can be conducted by using the extension from a center facet to its vertex-shared neighbors, and the extension continues until the termination condition is reached, as shown in Fig. 4. Thus, the identification of center facets is important to generate proper clusters. Center facets can be identified by center positions in sequence. Because the clustering with center facets may not cover all facets, the facets which do not

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Fig. 2. The 3D reconstruction of aggregates based on X-ray CT imaging.

Fig. 3. Illustration of surface deviation in surface triangulation of aggregates.

Fig. 4. Facet clustering process: a) facet extension; and b) thickness constraint for clustering.

C. Jin et al. / Construction and Building Materials 246 (2020) 118120

belong to any cluster need to be dealt with. The entire procedure of facet clustering is as follows: 1. According to their sequence numbers, center positions are traversed one by one, as follows: the nearest facet of the current position is used as a center facet; if the facet does not belong to a cluster, the extension from the facet is conducted under the normal and thickness constraints which are denoted T Norm and T Thick , respectively. 2. Facets not belonging to any cluster are traversed, as follows: if the current facet does not belong to a cluster, the facet is used as a center facet to conduct the extension from the facet under T Norm and T Thick . 3. All clusters are traversed, as follows: a cluster and its edgeshared neighbors are assembled under T Thick , in which an assembly with a lower thickness is prior to conduct. In above steps, the normal constraint refers to the threshold for the angle between the two normal vectors of the last extension and the facet to be extended, as shown in Fig. 4b. The normal vector of the extension is calculated based on Eq. (1). The thickness constraint refers to the threshold for the thickness of the candidate cluster, namely the maximum distance of any two vertices in the cluster on the direction described as Eq. (2). Facets are properly clustered after the entire procedure of facet clustering is accomplished.

Normextensioni ¼

Xni

Areafacetj Pni Normfacetj j¼1 j¼1 Areafacetj

ð1Þ

where Normextensioni is the comprehensive normal vector of the ni facets involved in the i th extension, Areafacetj and Normfacetj are the

where cluster a and clusterb are two edge-shared clusters. In this paper, the aggregate surface texture is defined based on the tiny undulation on the aggregate surface. Since the surface texture consists of convex and concave areas, an amplitude that is based on a reference plane is necessary to quantify the depth of the surface texture comprehensively. Because the obtained clusters are of approximately flat shape, the surface texture of each cluster is quantified to evaluate the surface texture of aggregate surface. To reach this goal, the reference plane of each cluster is supposed to locate near the position where the distances from the plane to points on the cluster are approximately equal. Thus, the reference plane is identified based on Eqs. (4) and (5) according to least square method, as shown in Fig. 5. Therefore, the obtained clusters are traversed as follows: points on each cluster is uniformly sampled; a reference plane is identified based on the sample points using the least square method; the mean value of the distances from each sampled point to the reference plane is calculated as the texture depth of the cluster, as shown in Eq. (6).

a0 x þ a1 y þ a2 z þ a3 ¼ 0   P ja0 xi þa1 yi þa2 zi þa3 j 2 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi di ¼ min a20 þa21 þa22 P  ) min ða0 xi þ a1 yi þ a2 zi þ a3 Þ2 P P 32 3T 2 P 2 P a0 xi y i xi zi xi xi P P P P 7 6 xy 6 2 y zi y i yi 76 a1 7 i 7 6 ) 6P i P i P 2 P 76 7 ¼ 0 4 xi zi zi y i zi zi 54 a2 5 P P P a3 xi yi zi qcluster min

Normcluster ¼

Areafacetk Pm Normfacetk k¼1 k¼1 Areafacetk

ð2Þ

where Normcluster is the comprehensive normal vector of the m facets constituting the cluster, Areafacetk and Normfacetk are the area and normal vector of the k th facet. According to Eqs. (1) and (2), the comprehensive normal vector of a facet set is the weighted mean of normal vectors of facets in the set, where the weight of each facet is its area ratio. Based on the dot product of normal vectors of two edge-shared clusters, the dihedral angle between the two clusters are calculated using Eq. (3). Meanwhile, the ratio of the area sum of the two clusters which constitute an angle to the area sum of all clusters (called area ratio of the angle for short) is also an important factor in angle quantification. Thus, the distributions of the angle and area ratio of the angle are both used to represent the aggregate angularity from a statistical perspective.

Angle ¼

!  Normclustera  Normclusterb 180    p  arccos p jNormcluster jNormcluster  a

b

ð3Þ

ð4Þ

P

area and normal vector of the j th facet, as shown in Fig. 4b.

Xm

5

Depthcluster ¼

1 X 2 di qcluster

ð5Þ

ð6Þ

where a0 ; a1 ; a2 ; a3 are coefficients of the equation of the reference plane, ðxi ; yi ; zi Þ is the coordinate of the i th sampled point, di is the distance from the i th sampled point to the plane, qcluster is the quantity of sampled points for the cluster, and Depthcluster is the texture depth. In addition to the texture depth, the ratio of the area of the cluster to the sum area of all clusters (called area ratio of the piece of surface texture for short) is also important in surface texture quantification. Thus, the distributions of texture depth and area ratio of the surface texture are both used to represent the aggregate surface texture from a statistical perspective. 2.3. Adaptive classification of angularity and surface texture Since aggregate angularity and surface texture have been quantified from the statistical perspective, which can be plotted as line charts. Thus, the classification of the two morphological properties is based on the comparison of the line charts.

Fig. 5. The cluster texture in isometric and side view.

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As described above, the aggregate angularity is represented by the distribution of the angle and the area ratio of the angle. The aggregate surface texture is represented by the distribution of the texture depth and the area ratio of the piece of surface texture. To classify the two morphological properties effectively, the weighted mean value as well as standard deviation of angles and surface texture of an aggregate are adopted and represented

^ angle ; rangle Þ Angularityðl

^ depth ; rdepth Þ, respectively, and Textureðl ^ angle is the area ratio of each angle while where the weight of l ^ depth is the area ratio of each piece of the surface texthe weight of l ^ angle ; rangle Þ or ture. However, the simple comparison of Angularityðl ^ depth ; rdepth Þ for aggregates is not adequate to obtain the Textureðl accurate classification of aggregate morphology. In microscopic perspective, two aggregates are considered similar in angularity or surface texture when two charts of the morphological property contain similar data points (value and quantity). It can be observed in a line chart that an area is covered by the line segments in vertical direction. The area difference which is identified by Boolean subtractions can be used to evaluate the shape difference of the two charts, which consists of several subareas as shown in Fig. 6. Evidently, the similarity of the two charts increases as the area difference decreases. In addition, two charts with similar shape but different point quantity should also be properly considered to evaluate the difference between two charts accurately. Thus, the difference between the two charts is quantified by using Eq. (7).

  jq1i q2i j 1 þ maxðQ ;Q Þ 1 2  P Areaov erlap þ Areasubi

P Diff 1;2 ¼ Fig. 6. Illustration of difference between two charts in microscopic view.

subi Areasubi

Fig. 7. X-ray CT imaging and 3D reconstruction of aggregates.

ð7Þ

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Fig. 8. The quantification of angularity and surface texture for eight selected aggregates: a) 3D solid model of aggregates; b) Results of surface triangulation for aggregates; c) Results of facet clustering for aggregates; d) line charts of the angularity of aggregates; and e) line charts of the surface texture of aggregates.

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where Diff 1;2 is the difference between the two charts, subi is the i th subarea, Areasubi is the area of subi , Areaov erlap is the overlap area of chart 1 and chart 2, q1i and q2i are the quantity of points involved in subi in chart 1 and chart 2, and Q 1 and Q 2 are the quantity of points in chart 1 and chart 2, respectively. According to Eq. (7), Diff 1;2 equals to zero if the two charts are

3. Each point in the class is identified whether Diff 1;2 between the point and any point in current subclass is less than T Diff : if so, the point is removed from the class and added in the current subclass. If no point can be added in the current subclass, step1-2 are kept running until the class becomes empty.

jq1i q2i j approxtotally identical. Evidently, the maximum value of maxðQ 1 ;Q 2 Þ

For the aggregate angularity, the horizontal and vertical axes are the area ratio of the angle and the angle itself, respectively; for the aggregate surface texture, the horizontal and vertical axes are the area ratio of the piece of surface texture and the texture depth, respectively. Formal classification is obtained after the conduction of the above algorithm. ^ angle and l ^ depth , the mean values of area ratio of In addition to l angles and pieces of surface texture of a particle, denoted langle AR and ldepth AR , respectively, are also used to describe the morphological characteristics of a particle. Thus, the two tuples

imates 1 when a chart is totally contained in the other and large difference exists between Q 1 and Q 2 , which makes Areaov erlap approximates zero and thus Diff 1;2 reaches its maximum value 2. In other words, Diff 1;2 2 ½0; 2. ^ angle ; rangle Þ or Textureðl ^ depth ; rdepth Þ of Therefore, Angularityðl aggregates is used to obtain a preliminary classification of the two morphological properties, based on which the formal classifications are determined by Diff 1;2 . The preliminary classification is conducted with the scatter dia^ angle ; rangle Þ and Textureðl ^ depth ; rdepth Þ of aggregrams of Angularityðl gates: the spatially close points are grouped into one class in the diagram. The algorithm for preliminary classification is as follows: 1. The mean area per point occupies, namely the ratio of the area of the rectangle which exactly bounds the points to the quantity of the points in the diagram, is calculated to obtain the positive square root as the distance threshold, denoted T D , to identify whether two points are close. 2. An initial set containing all points in the diagram is constructed, and the points are traversed in sequence, as follows: a point is removed from the initial set and 1) placed into the current subset when the distance between the point and any point in the subset is less than T D ; or otherwise, 2) used to construct a new subset which turns to the current subset. 3. The algorithm ends when the initial set becomes empty. In the above algorithm, T D is adaptively assigned according to the spatial distribution of points. T D becomes higher when the points distribute dispersedly to group relative-concentrated points; otherwise, T D becomes lower to group points which are close to each other enough. Based on the preliminary classification, points belonging to a class are conducted a further comparison with Diff 1;2 to obtain the formal classification. As for points in each class, the algorithm for formal classification is as follows: 1. If the class only contains a single point, the point constitutes a subclass and the algorithms ends. 2. Diff 1;2 between any two points in the class is calculated to identify whether the minimum value exceeds the predefined threshold which is denoted T Diff : if so, every point constitutes a class and the algorithm ends; otherwise, the two points with minimum Diff 1;2 are removed from the class and used to construct a new subclass which is set as the current one.









Labelangle ðlangle ; langle AR Þ, Labeltexture ðldepth ; ldepth AR Þ are used to identify classes by the angularity and surface texture, respectively, 







where langle , ldepth , langle AR and ldepth AR are the mean values of l^ angle , l^ depth , langle AR and ldepth AR of particles which belong to one class. 3. Case study This section reconstructed 275 aggregate solid models based on X-ray CT imaging to evaluate the aggregate angularity and surface texture and in perspective view. Consequently, the adaptive classification of the two morphological properties is conducted according to the distribution of the angle and surface texture. 3.1. Aggregate reconstruction environment A pack of aggregates are randomly selected from the library and put in a 100-mm-diameter cylinder container for scanning with Zeiss Xradia 520 Versa X-ray CT microscope (Fig. 7a). With a 0.5mm scanning interval, 100 images were acquired (Fig. 7c). Each pixel in an image was approximately 0.049 mm. The detection and mapping of 2D enclosed outlines of aggregates in CT images was developed with GDI+ class in Visual C++, based on which the 3D reconstruction of aggregates is accomplished with modeling toolkit ACIS 7.0, as shown in Fig. 7d. 275 individual aggregate particles were identified from CT images, and the distribution of sieve sizes of 275 grains is as shown in Fig. 7b. Obviously, the accuracy of the quantified angularity and surface texture is strongly influenced by the scanning resolution of X-ray computed tomography (CT). As explained above, the 3D modeling procedure for aggregates consists of two main steps: 1) two-dimensional (2D) enclosed outlines in each CT image are detected; and 2) the mapping between each aggregate and its outlines on various layers is established to construct 3D models of aggregates.

Table 2 Quantification parameters for angularity and surface texture of eight selected aggregates. Aggregate identifier

Lengths of long, medium, and short axes (mm), L  M  S

Quantity of facets

Quantity of facet clusters

Quantity of angles

Angle statistics, ^ angle ; rangle Þ ðl

Surface texture statistics, ^ depth ; rdepth Þ ðl

Aggregate#1 Aggregate #2 Aggregate #3 Aggregate #4 Aggregate #5 Aggregate #6 Aggregate #7 Aggregate #8

12.77  9.44  5.49 15.87  13.12  6.52 12.02  4.32  4.15 17.86  10.02  6.28 14.12  12.29  10.03 15.49  13.97  13.07 7.5  7.28  6.77 14.08  11.56  11.23

1918 2472 1332 2508 2260 2722 2226 3496

20 21 15 22 18 17 22 29

52 57 38 59 46 44 60 80

(125, (133, (117, (126, (125, (119, (131, (131,

(0.19, (0.18, (0.15, (0.28, (0.19, (0.21, (0.14, (0.22,

31) 31) 31) 31) 32) 34) 23) 21)

0.10) 0.08) 0.12) 0.26) 0.06) 0.15) 0.08) 0.08)

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In this procedure, on one hand, the accuracy of outline detection is evidently influenced by image resolution; on the other hand, the scanning interval determines the quantity of outlines of an aggregate, which affect the precision of 3D modeling. Thus, it is believed that high image resolution and low scanning interval facilitate the accuracy of morphology characterization. However, too high resolution and too low interval will make the modeling a very heavy computational task and unnecessary. After tentative computations,

9

the modeling parameters turn out to be reasonable according to the authors’ previous works [30–33]. 3.2. Quantification of aggregate angularity and surface texture It is necessary to select aggregates of representative shape out of 275 particles to demonstrate the effectiveness of the proposed methodology.

Fig. 9. The comparison of angularity and surface texture aggregates of two groups: a) Two groups of solid models; b) surface triangulation of the two groups of models; c) line charts of the angularity of the two groups; and d) line charts of the surface texture of the two groups.

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Conventionally, the aggregate falls into four categories: flat (aggregate #1, #2), elongated (aggregate #3, #4), angular (aggregate #5, #6), and round (aggregate #7, #8). Thus, the eight particles belonging to the four categories are selected out to illustrate the applicability of the proposed method to quantify the aggregate angularity and surface texture. Meanwhile, the round and angular aggregates can also be used to prove the effectiveness of the quantified angularity. The 3D models of the selected particles are as shown in Fig. 8a. The length of long, medium and short axes of the eight particles are virtually measured and listed in Table 2, and details were elaborated in the authors’ previous works (Jin et al. [32,33]). The surface triangulation of aggregate #1-#8 are conducted with the surface tolerance set 0.049 mm, as shown in Fig. 8b. Consequently, the clustering for the obtained facets is conducted with the T Norm and T Thick being assigned 10° and 5% of the short axis length of the particle, as shown in Fig. 8c. It can be observed that adjacent facets which approximate a planar surface are used to generate the same cluster. As for the surface texture, it indicates that the roughness degree of the aggregate surface increases as the mean value of surface texture increases and the standard deviation of surface texture decreases according to Table 2. Therefore, Aggregate #3 has the smoothest surface while Aggregate #6 has the roughest surface. Moreover, the range of texture depth is fairly narrow, which implies the roughness distribution on the aggregate surface doesn’t vary dramatically, as shown in Fig. 8e. To validate the effectiveness of the proposed method, two groups of quantifications are also conducted: 1) three particles with the same shape but diverse sizes, and 2) three particles with close size and shapes. Another particle is taken as the example to conduct the quantifications, as shown in Fig. 9a and b. After that, the dihedral angle between each pair of adjacent clusters is recognized as a surface angle, and the texture depth of each cluster is calculated. The quantification parameters for angularity and surface texture of eight selected aggregates are as shown in Table 2. Moreover, the distribution of the angularity and surface texture of the eight aggregates are plotted using line charts, as shown in Fig. 8d and e. As for the angularity, it indicates that the uneven degree of the aggregate surface increases as the mean value of surface angles decreases and the standard deviation of the angles increases from Table 2. For instance, Aggregate #1, #4, #5, and #6 are believed more complicated in geometry than the other particles. Mean^ angle than round particles. while, angular particles have smaller l Aggregate #3, #5, #6 have more sharp edges on the surface than

Diff 1;2 between aggregate of original and 0.75 times size Diff 1;2 between aggregate of original and 0.5 times size Diff 1;2 between aggregate of 0.75 times and 0.5 times size

Group 2

Diff 1;2 between the original aggregate and its one-time cutting result Diff 1;2 between the original aggregate and its two-times cutting result Diff 1;2 between the aggregate after one-time cutting and two-times cutting results

3.3. Classification of aggregate angularity and surface texture In this section, 275 particles are preliminarily and formally classified by the angularity and surface texture, respectively. ^ angle ; rangle Þ In this procedure, T D is calculated based on Angularityðl ^ depth ; rdepth Þ distribution of the particles, and conseor Textureðl

0 1.07

quently preliminary classes are obtained using the algorithm for the preliminary classification. Based on the specific distribution of angles or surface texture, particles in each preliminary class are further divided into subclasses according to the predefined T Diff using the algorithm for the formal classification. Especially, T Diff has been assigned with different values to study the effect of T Diff on the obtained classes. The parameters of formal classes of the particles by the angularity and surface texture are as shown in Fig. 10 and Table 4. It can be observed that the quantity of classes decreases as T Diff increases both for the angularity and surface texture. It indicates that finer classification of particles can be obtained with a smaller T Diff . ^ depth , langle AR , and ldepth AR of each particle are ^ angle , l After that, l

0 0.81

calculated to obtain Labelangle ðlangle ; langle AR Þ and Labeltexture ðldepth ; ldepth AR Þ for each class, the four components of which are then

Table 3 The comparison of the angularity and the surface texture among two groups of particles. Group 1

the others, and meanwhile, Aggregate # 7 and #8 have evener surfaces than the others. The reason is that angles between the normal vectors of two adjacent facets are smaller for round particles than ^ angle and smaller rangle . other particles, which thus results in larger l Besides, the data points of round particles are more concentrated than that of other particles, as shown in Fig. 8d. As for group 1, the particle of original size, 0.75- and 0.5-times sizes are used as the objects to be quantified. The line charts of the angularity and the surface texture of group 1 are as shown in Fig. 9c and d, and Diff 1;2 for the angularity and the surface texture among particles of group 1 is as shown in Table 3. It can be observed there is no angularity difference among the three charts, and Diff 1;2 for any two charts out of the three equals to zero. Meanwhile, the three charts of surface texture have similar shapes but different Diff 1;2 . The reason is that the texture depth decreases as the particle size decreases. Thus, particles of the same shape but diverse sizes are with the same charts and equal Diff 1;2 for angularity, and charts are of the same shape but different Diff 1;2 for surface texture. As for group 2, two tiny parts of the particle are cut off successively to obtain two new models of similar shape and surface texture. The line charts of the angularity and the surface texture of group 2 are as shown in Fig. 9c and d, and Diff 1;2 for the angularity and the surface texture among particles of group 2 is as shown in Table 3. Because a few surface angles and texture are lost in the cutting operation, the differences of the angularity and surface texture among the three charts are a little larger than group 1. It also can be observed that Diff 1;2 between the original aggregate and the aggregate after cutting increases as the shape difference becomes more. Thus, the obtained Diff 1;2 for angularity and surface texture of particles of similar shape and size is reasonable. The accuracy and applicability of the proposed methodology to particles of diverse sizes and shapes are validated.

Angularity Surface texture Angularity Surface texture Angularity Surface texture

0 0.7

Angularity Surface texture Angularity Surface texture Angularity Surface texture

0.36 0.64



0.38 0.67 0.14 0.12





sorted ascendingly, as shown in Fig. 10c–d. It can be observed that the value difference between classes is of good discrimination and becomes larger as T Diff increases for 







langle , langle AR , ldepth and

ldepth AR . The classification results of aggregates with T Diff ¼ 0:6 by the angularity and surface texture are taken as an example, as shown in Fig. 11. It indicates that a smaller T Diff results in closer angularity or surface texture of particles in a same class, lower difference

C. Jin et al. / Construction and Building Materials 246 (2020) 118120

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Fig. 10. Illustration of classification of particles by the angularity and surface texture: a) the distribution of aggregate quantities in classes for angularity; b) the distribution of aggregate quantities in classes for surface texture; c) the distribution of average angles of classes for angularity; d) the distribution of average area ratios of classes for angularity; e) the distribution of average depths of classes for surface texture; and f) the distribution of average area ratios of classes for surface texture.

between classes, and larger quantity of classes. Practically, the classification of aggregates aims to study the relationship between morphological characteristics and mechanical properties, and thus it is believed that classes containing too few particles are not preferred in classifying massive particles. Therefore, T Diff should not be assigned an excessive small value. A value between 0.5 and 1 is recommended.

4. Summary and conclusions The Aggregate morphology greatly affects the skeleton of asphalt mixture to resist external loads. Accurate quantification and adaptive classification of morphological indices of particles are the foundation of the study on the relationship between aggregate morphology and micromechanical behavior of composite

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C. Jin et al. / Construction and Building Materials 246 (2020) 118120

Table 4 Formal classification parameters of aggregates by angularity and surface texture. Morphological features

Angularity

The distance threshold for preliminary classification,T D The difference threshold for formal classification,T Diff Quantity of the classes

37 0.6 82

Surface texture 0.9 45

1.2 38

21 0.6 106

0.9 38



1.2 24



Fig. 11. The illustration of classification of particles with T Diff ¼ 0:6 by angularity and surface texture: a) ten representative classes with Labelangle ðlangle ; langle   representative classes with Labeltexture ðldepth ; ldepth AR Þ.

AR Þ;

and b) ten

C. Jin et al. / Construction and Building Materials 246 (2020) 118120

skeleton, which is important to deformation resistance of the composite. This paper proposed a novel approach to quantify and classify the angularity and surface texture of realistic aggregates from a statistical perspective using 3D solid reconstruction techniques. Based on the constructed aggregate model, the model surface was discretized into triangle facets with an adaptive surface tolerance using functions in ACIS. To quantify the aggregate angularity accurately, adjacent facets which approximate a flat area were used to form a cluster. In this procedure, a concept of center position was adopted in facet clustering algorithm to make sure that large and flat areas on aggregate surface be detected as facet clusters in prior to transition areas, which is important to the accuracy of surface angle detection. Based on obtained clusters, dihedral angles between each two normal vectors of edge-shared clusters are calculated as the surface angles to quantify the angularity in a statistical perspective. Since each cluster approximates a planar surface, a concept of texture depth referred to a plane which is identified using least square method for the cluster was presented and calculated to quantify the surface texture of the corresponding part of the aggregate surface. Thus, the comprehensive surface texture of the particle is quantified by the obtained texture depths. Based on the quantification of aggregate angularity and surface texture, an adaptive classification of the two morphological properties for particles was conducted by two steps: preliminary and formal classification. The first step classifies the particles macroscopically into groups by mean and standard deviation of angularity or surface texture, based on which the second step further classifies each group of aggregates microscopically into subgroups using comparison between any two charts of angularity or surface texture of particles in the group. 275 aggregates were reconstructed, surface triangulated, and facet clustered before the quantification of the angularity and surface texture. Results indicate that the uneven degree of the aggregate surface increases as the mean value of surface angles decreases and the standard deviation of the angles increases, and the roughness degree of the aggregate surface increases as the mean value of surface texture increases and the standard deviation of surface texture decreases. The particles were consequently classified by the angularity and surface texture with adaptive parameters, respectively. It indicates that a smaller T Diff results in closer angularity or surface texture of particles in a same class and larger quantity of classes. Compared to conventional categories, the proposed method quantifies and classifies the angularity and surface texture of aggregates more comprehensively in a statistical and microscopic perspective. Thus, the two morphological properties of aggregates become intuitive and easy for understanding. Moreover, the obtained classification of the two properties facilitates the virtual design of composite microstructure, which can be used to investigate the premium composition of aggregates of different angularity and surface texture. Specifically, virtual composite specimens can be customized through the configuration parameters of the angularity and surface texture. Based on that, the correlation between the two morphological properties and the mechanical performance of the asphalt composite can be further studied with numerical simulations.

CRediT authorship contribution statement Can Jin: Methodology, Writing - original draft. Feilong Zou: Investigation. Xu Yang: Methodology, Resources. Kai Liu: Methodology, Writing - review & editing. Pengfei Liu: Methodology, Writ-

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ing - review & editing. Markus Oeser: Methodology, Writing review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The research reported in this paper was supported by the National Natural Science Foundation of China (Grant No. 51978228, 51508147 and 51708114) and Australia-Germany Joint Research Co-operation Scheme (Grant No. 57446137); the support is greatly appreciated. References [1] R. Ghabchi, M. Zaman, H. Kazmee, D. Singh, Effect of shape parameters and gradation on laboratory-measured permeability of aggregate bases, Int. J. Geomech. (2015). 10.1061/(ASCE)GM. 1943-5622.0000397. [2] H. Wang, Y. Bu, Y. Wang, X. Yang, Z. You, The effect of morphological characteristic of coarse aggregates measured with fractal dimension on asphalt mixture’s high-temperature performance, Adv. Mater. Sci. Eng. (2016) 1–9. [3] B. Zhao, J. Wang, 3D quantitative shape analysis on form, roundness, and compactness with lCT, Powder Technol. 291 (2016) 262–275. [4] X. Cai, K.H. Wu, W.K. Huang, C. Wan, Study on the correlation between aggregate skeleton characteristics and rutting performance of asphalt mixture, Constr. Build. Mater. 179 (2018) 294–301. [5] M. Pasetto, N. Baldo, Influence of the aggregate skeleton design method on the permanent deformation resistance of stone mastic asphalt, Mater. Res. Innov. 18 (2014). S3–96-S3-101. [6] Y. Liu, Q.L. Dai, Z.P. You, Viscoelastic model for discrete element simulation of asphalt mixtures, J. Eng. Mech. ASCE 135 (2009) 324–333. [7] Y. Peng, J.-X. Bao, Comparative study of 2D and 3D micromechanical discrete element modeling of indirect tensile tests for asphalt mixtures, Int. J. Geomech. 18 (6) (2018) 04018046. [8] H. Ying, M.A. Elseifi, L.N. Mohammad, M.M. Hassan, Heterogeneous finite element modeling of the dynamic complex modulus test of asphalt mixture using X-ray computed tomography, J. Mater. Civ. Eng. 26 (9) (2014) 04014052. [9] Z.P. You, S. Adhikari, M.E. Kutay, Dynamic modulus simulation of the asphalt concrete using the X-ray computed tomography images, Mater. Struct. 42 (2009) 617–630. [10] X. Yang, Z.P. You, C. Jin, H.N. Wang, Aggregate representation for mesostructure of stone based materials using a sphere growth model based on realistic aggregate shapes, Mater. Struct. 49 (2016) 2493–2508. [11] E. Masad, D. Olcott, T. White, T. Tashman, Correlation of fine aggregate imaging shape indices with asphalt mixture performance, J. Transp. Res. Board 1757 (1) (2001) 148–156. [12] S. Chen, X. Yang, Z. You, M. Wang, Innovation of aggregate angularity characterization using gradient approach based upon the traditional and modified Sobel operation, Constr. Build. Mater. 120 (2016) 442–449. [13] X. Ding, T. Ma, W. Gao, Morphological characterization and mechanical analysis for coarse aggregate skeleton of asphalt mixture based on discreteelement modeling, Constr. Build. Mater. 154 (2017) 1048–1061. [14] X. Yang, S.Y. Chen, Z.P. You, 3D voxel-based approach to quantify aggregate angularity and surface texture, J. Mater. Civ. Eng. 29 (7) (2017). 10.1061/ (ASCE)MT.1943-5533.0001872. [15] Y. Liu, W. Sun, H. Nair, D.S. Lane, L. Wang, Quantification of aggregate morphologic characteristics with the correlation to uncompacted void content of coarse aggregates in Virginia, Constr. Build. Mater. 124 (2016) 645–655. [16] D. Su, W.M. Yan, Quantification of angularity of general-shape particles by using Fourier series and a gradient-based approach, Constr. Build. Mater. 161 (2018) 547–554. [17] W.J. Sun, L.B. Wang, E. Tutumluer, image analysis technique for aggregate morphology analysis with two-dimensional fourier transform method, Transp. Res. Rec. (2012) 3–13. [18] R. Ghabchi, M. Zaman, H. Kazmee, D. Singh, Effect of shape parameters and gradation on laboratory-measured permeability of aggregate bases, Int. J. Geomech. 15 (4) (2015) 04014070. [19] J.Q. Chen, H. Wang, H.C. Dan, Y.J. Xie, Random modeling of three-dimensional heterogeneous microstructure of asphalt concrete for mechanical analysis, J. Eng. Mech. 144 (9) (2018) 04018083. [20] T.S.A. Francisco, D.A. Hartmann, A.R.G. Pazos, Y.R. Kim, Virtual fabrication and computational simulation of asphalt concrete microstructure, Int. J. Pavement Eng. (2015) 1–12. [21] J.R.J. Lee, M.L. Smith, L.N. Smith, A new approach to the three-dimensional quantification of angularity using image analysis of the size and form of coarse aggregates, Eng. Geol. 91 (2–4) (2007) 254–264.

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