- Email: [email protected]
Investigation of the shape, size, angularity and surface texture properties of coarse aggregates
Construction and Building Materials 34 (2012) 330–336
Contents lists available at SciVerse ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Investigation of the shape, size, angularity and surface texture properties of coarse aggregates Dong Zhang ⇑, Xiaoming Huang 1, Yongli Zhao 2 School of Transportation, Southeast University, Nanjing, Jiangsu 210096, China
a r t i c l e
i n f o
Article history: Received 19 November 2011 Received in revised form 20 January 2012 Accepted 25 February 2012 Available online 5 April 2012 Keywords: Aggregates Shape Size Angularity Surface texture Image analysis
a b s t r a c t The shape, size, angularity and surface texture properties of coarse aggregates were studied in this paper. Aggregates with different shapes were separated manually and the percentage by number of each shape was computed. The three sizes (length, width and thickness) of aggregates were extracted using an image analysis approach and their statistical distributions were studied. An indicator called angularity and surface texture (AT) index was developed to characterize the combined effect of the coarse aggregate angularity and surface texture based on two-dimensional aggregate images. The statistical distributions of the AT indices of different sized limestone and basalt aggregates and their composite AT indices were studied. The void contents of different sized limestone and basalt aggregates in loose condition were tested to validate the AT index. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The morphology of coarse aggregates includes shape, size, angularity and surface texture. Many studies have demonstrated that the coarse aggregate morphology has a significant effect on the performances of aggregate based materials such as the field compaction of asphalt mixtures, the permanent deformation of asphalt mixtures and the shearing resistance of railway ballast [1–4]. In addition, the discrete element method (DEM) is now employed more and more to study the micromechanical behavior of asphalt mixtures. It is very important to model the three-dimensional (3D) morphology of coarse aggregates when the DEM is used to analysis the micromechanical behavior of asphalt mixtures. Laboratory investigation of the actual 3D morphology of coarse aggregates serves as a way to correlate the particles generated by DEM to real aggregates. Therefore, it is important to quantitatively characterize the aggregate shape, size, angularity and surface texture for the prediction of material performances and reconstruction of the coarse aggregates by DEM. In the last decades, the image analysis method has been used to characterize the morphology of coarse aggregates [5–9]. The 3D sizes of aggregates can be determined by taking two images of each ⇑ Corresponding author. Tel.: +86 13776693486; fax: +86 25 83795184. E-mail addresses: [email protected] (D. Zhang), [email protected] (X. Huang), [email protected] (Y. Zhao). 1 Tel./fax: +86 25 83795184. 2 Tel.: +86 25 83793096; fax: +86 25 83795184. 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.02.096
aggregate particle. The sizes of each particle are different even the particles are within the same sized aggregates. Studying the size distributions of coarse aggregates contributes to understanding the size properties of aggregates and to modeling the aggregates by DEM. The shape was usually characterized by the indicators such as sphericity and roundness in the image analysis method [6,9]. The shape indicators can then be correlated to the performance of the aggregate based materials. However, these shape indicators cannot be used to construct the 3D shapes by DEM. It is necessary to study the actual 3D shapes of coarse aggregates. In the image analysis method, two dimensional aggregate images were used to evaluate the angularity and surface texture of coarse aggregates [7,8]. The angularity index (AI) was developed by Rao et al. [10] to characterize the coarse aggregate angularity by tracing the change in slope of the outline of the two-dimensional aggregate image. Also, the surface texture (ST) index was proposed by Rao and Tutumluer [11] to characterize the coarse aggregate surface texture using the image analysis technique known as ‘‘erosion and dilation’’. Further study by Tutumluer et al. [12] shows that a definite relationship with a coefficient of determination R2 of 0.79 existed between the AI and ST index of the studied aggregates. This indicates that the AI and ST index are significantly related to each other. Therefore, the angularity and surface texture of aggregates may be characterized by one index since the two properties are both related with the outline of the two-dimensional aggregate image. The objective of this study is to investigate the shape, size, angularity and surface texture properties of coarse aggregates.
D. Zhang et al. / Construction and Building Materials 34 (2012) 330–336
331
The main work includes: (1) separate aggregates of different shapes manually and compute the percentage by number of each shape; (2) extract the length, width and thickness of aggregates using an image analysis method and study their statistical distributions; (3) develop an indicator to characterize the angularity and surface texture of coarse aggregates and analyze its statistical distributions; and (4) validate the proposed indicator.
2. Shape, size, angularity and surface texture characterization The 3D shapes of the coarse aggregates are approximated to be hexahedron, pentahedron and tetrahedron in this study. Flat and elongated aggregates are considered as an individual type since they are undesirable in the specifications of many countries. The flat and elongated aggregate herein is determined as the particle whose ratio of the maximum to minimum size is bigger than 3:1. Schematic drawings of the 3D aggregate shapes are illustrated in Fig. 1. The size property of coarse aggregates is characterized by length, width and thickness. Length is defined as the maximum size of the particle, width is the maximum size in the plane perpendicular to the length and thickness is the maximum size perpendicular to the length and width. The thickness is assumed to be the shortest size of the particle in this study. The two-dimensional image analysis method is now usually used to characterize the angularity and surface texture of coarse aggregates. As shown in Fig. 2, the angularity is defined as the convex part on the outline of a coarse aggregate image and the surface texture is considered as the tiny bumps on the outline. The main difference of the two morphological properties is that the angularity is a macro-property of the outline of the coarse aggregate image while the surface texture is a micro-property. Therefore, the angularity and surface texture reflected by a two-dimensional coarse aggregate image can be characterized by one indicator. As can be observed in Fig. 3, the coarse aggregate outline with more macroand micro-bumps has a longer perimeter. Based on this, an indicator called angularity and surface texture (AT) index is developed here to characterize the combined effect of the angularity and surface texture. The AT index is defined by the difference of the out-
Fig. 3. Schematic drawing of the outline and convex outline.
line perimeter and the convex outline perimeter of a twodimensional coarse aggregate image, as expressed by Eq. (1). As shown in Fig. 3, the outline perimeter is the total length of the image outline and the convex outline perimeter is the length of the image boundary lines that omit the concave part of the outline. The length of the concave lines is replaced by the length of straight lines in the computing of the convex outline perimeter.
AT ¼
Outline Perimeter—Convex Outline Perimeter Convex Outline Perimeter
ð1Þ
The AT index of an aggregate particle is established by averaging the AT index values of its two-dimensional images weighted by their areas, as shown in following equation:
AT ¼
Pn 1 Ai ATi Pn 1 Ai
ð2Þ
where n is the number of images used in the calculation, Ai is the area of the ith image of the particle and ATi is the AT index of the ith image of the particle. The AT index of the whole aggregate sample (composite AT index) is determined by averaging the AT index values of aggregate particles weighted by their areas used in computing their own AT index. The composite AT index of the aggregates mixed by different aggregate samples can be determined by averaging the composite AT index values of different aggregate samples weighted by their weights. 3. Materials and experimental methods
(a)
(c)
(b)
(d)
3.1. Materials The 4.75–9.5 mm, 9.5–13.2 mm, 13.2–16 mm, 16–19 mm and 19–26.5 mm limestone aggregates and the 4.75–9.5 mm, 9.5–13.2 mm and 13.2–16 mm basalt aggregates were used in this study. The 4.75–9.5 mm aggregates are the particles that pass the 9.5 mm sieve but retain on the 4.75 mm sieve. Other sized aggregates have a similar meaning. The 4.75–9.5 mm aggregates are simply called 4.75 mm aggregates in the following discussion and so are other sized aggregates. 3.2. Experimental methods
Fig. 1. Schematic drawings of the 3D aggregate shapes: (a) hexahedron; (b) pentahedron; (c) tetrahedron; and (d) flat and elongated particles.
Fig. 2. Schematic drawing of a two-dimensional aggregate image.
Different shaped aggregates in an aggregate sample were separated first manually and then the percentages by number of hexahedron, pentahedron, tetrahedron and the flat and elongated aggregates were computed. In determining the aggregate shape, the face with a relatively small area was not counted and Fig. 1 was used as a reference. Fig. 4 shows the manually separated aggregates in which they are tetrahedron, pentahedron and hexahedron aggregates from the left to right. Fig. 5 shows the typical 3D aggregate shapes in which they are hexahedron, pentahedron and tetrahedron aggregates from up to down. The sample sizes (by number) of different sized aggregates used in the shape statistical analysis are shown in Table 1. Three sizes (length, width and thickness) of the aggregates were extracted using an image analysis approach. Two sizes of each aggregate particle can be extracted from an image of the aggregates. In order to obtain the third size of each aggregate particle, all particles were set upright and the other picture was taken. The outline perimeter and the convex outline perimeter of each coarse aggregate image were also extracted using these images. The sample sizes (by number) of different sized aggregates used in the size, angularity and surface texture analysis are shown in Table 2. Detailed procedures are described as follows:
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D. Zhang et al. / Construction and Building Materials 34 (2012) 330–336
Fig. 6. Percentages by number of different shaped aggregates in limestone aggregates.
Fig. 4. Manually separated aggregates (tetrahedron, pentahedron and hexahedron aggregates from the left to right).
Fig. 7. Percentages by number of different shaped aggregates in basalt aggregates.
4. Results and discussion 4.1. Aggregate shapes
Fig. 5. Typical 3D aggregate shapes (hexahedron, pentahedron and tetrahedron aggregates from up to down).
Table 1 Sample sizes of different sized aggregates used in the shape statistical analysis (by number). Sieve size (mm) Limestone Basalt
4.75 475 525
9.5 542 507
13.2 479 363
16 330 –
19 385 –
Table 2 Sample sizes of different sized aggregates used in the size, angularity and surface texture analysis (by number). Sieve size (mm) Limestone Basalt
4.75 344 391
9.5 487 405
13.2 431 299
16 317 –
19 361 –
1. Dye aggregates black using very thin ink (mixed with water) and then dry them. 2. Place the aggregates on a white background and then take a picture from above. 3. Set the aggregates upright manually and then take the other picture from above. 4. Analyze the two pictures to extract the three sizes of each aggregate particle. 5. Analyze the two pictures to extract the outline perimeter and the convex outline perimeter of each aggregate image.
Figs. 6 and 7 show the percentages by number of different shaped aggregates in limestone aggregates and basalt aggregates, respectively. As shown in Fig. 6, the percentage of hexahedron is the highest, the percentage of pentahedron is the second highest, the percentage of tetrahedron is the third highest and the percentage of the flat and elongated particles is the lowest in different sized limestone aggregates. As shown in Fig. 7, the percentages of hexahedron, pentahedron, tetrahedron and the flat and elongated aggregates in different sized basalt aggregates have the same law as those of limestone aggregates except that the percentages of tetrahedron and the flat and elongated aggregates in 4.75 mm and 9.5 mm basalt aggregates are nearly the same. In general, the percentage of hexahedron is about 50–70%, the percentage of pentahedron is about 20–30%, the percentage of tetrahedron is about 10–20% and the percentage of the flat and elongated particles is about 0–10% in different-sized limestone and basalt aggregates. 4.2. Aggregate sizes The three sizes of each particle were extracted from the two pictures of each aggregate sample. Statistical features of the length, width and thickness of all particles in one sample were analyzed. Table 3 shows the statistical results of the three sizes of the 9.5 mm limestone aggregates. Figs. 8–10 show the histogram and normal P–P plot of the length, width and thickness of the 9.5 mm limestone aggregates, respectively. The normal P–P plot is used to test if the data obey the normal distribution. If the points on the P–P plot are all located on the diagonal shown in Fig. 8b, the tested data obey the normal distribution. As shown in Figs. 8–10, the length, width and
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D. Zhang et al. / Construction and Building Materials 34 (2012) 330–336 Table 3 Statistical results of the three sizes of the 9.5 mm limestone aggregates. Statistical parameters
Minimum (mm)
Maximum (mm)
Mean (mm)
Standard deviation (mm)
Length Width Thickness
11.38 7.18 5.78
27.47 17.54 16.99
17.87 12.97 11.25
3.10 1.68 2.05
Fig. 9. Histogram and normal P–P plot of the width of the 9.5 mm limestone aggregates: (a) histogram; (b) normal P–P plot.
stone and basalt aggregates all obey the normal distribution approximately. The means and standard deviations of the length, width and thickness of different-sized limestone and basalt aggregates are summarized in Table 4. Fig. 8. Histogram and normal P–P plot of the length of the 9.5 mm limestone aggregates: (a) histogram; (b) normal P–P plot.
thickness of the 9.5 mm limestone aggregates all obey the normal distribution approximately. The three sizes of other sized limestone and basalt aggregates were analyzed using the same method. The results of the analysis show that the length, width and thickness of different-sized lime-
4.3. Angularity and surface texture The AT index of each aggregate particle among different sized aggregates was calculated according to Eq. (2). The composite AT index of each aggregate sample was also computed. 4.3.1. Statistical distribution of the AT index Fig. 11 shows the histogram and normal P–P plot of the AT indices of the 9.5 mm limestone aggregates. As shown in Fig. 11, the AT
Table 4 Means and standard deviations of the length, width and thickness of different-sized limestone and basalt aggregates. Aggregate type
Sieve size (mm)
Length Mean (mm)
Standard deviation (mm)
Mean (mm)
Width Standard deviation (mm)
Thickness Mean (mm)
Standard deviation (mm)
Limestone
4.75 9.5 13.2 16 19
10.43 17.87 22.74 29.71 37
2.43 3.1 3.63 4.94 5.54
7.6 12.97 16.67 21.01 26.84
1.64 1.68 1.6 1.85 3.24
6.78 11.25 14.32 18.25 22.56
1.65 2.05 2.23 2.91 4.03
Basalt
4.75 9.5 13.2
9.15 19.07 22.46
1.79 3.03 3.28
6.76 13.7 17.02
1.3 1.71 1.39
6.02 11.58 14.43
1.33 2.22 2.16
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D. Zhang et al. / Construction and Building Materials 34 (2012) 330–336
Fig. 10. Histogram and normal P–P plot of the thickness of the 9.5 mm limestone aggregates: (a) histogram; (b) normal P–P plot.
Fig. 11. Histogram and normal P–P plot of the AT indices of the 9.5 mm limestone aggregates: (a) histogram; (b) normal P–P plot.
indices of the 9.5 mm limestone aggregates obey the normal distribution approximately. Fig. 12 shows the histogram and normal P–P plot of the AT indices of the 13.2 mm limestone aggregates. Obviously, the AT indices of the 13.2 mm limestone aggregates don’t obey the normal distribution. The Laplace, Logistic, Lognormal, Pareto, Student t, Weibull and Uniform distribution P–P plots were used to further study the AT index distribution of the 13.2 mm limestone aggregates. The results indicate that the AT indices of the 13.2 mm limestone aggregates obey the lognormal distribution approximately, as shown in Fig. 13. The statistical distributions of the AT indices of other sized aggregates were also analyzed using the same method. The results of the analysis show that the AT indices of the 13.2 mm limestone aggregates, 16 mm limestone aggregates and 9.5 mm basalt aggregates obey the lognormal distribution approximately and the AT indices of other sized limestone and basalt aggregates all obey the normal distribution approximately. It is worth noting that the aggregate morphological properties are affected by its source stone (by which the aggregates are produced) properties and the production technology. Therefore, the morphological index distributions of aggregates produced by different stones and technology may be different.
gate sample has the greatest composite AT index and the 13.2 mm basalt aggregate sample has the smallest composite AT index among the different sized basalt aggregate samples. The composite AT indices of the 4.75 mm and 9.5 mm basalt aggregate samples are larger than those of the 4.75 mm and 9.5 mm limestone aggregate samples by 9.4% and 18.1%, respectively. However, the composite AT index of the 13.2 mm basalt aggregate sample is smaller than that of 13.2 mm limestone aggregate sample by 27.3%.
4.3.2. Composite AT index of each aggregate sample Fig. 14 shows the composite AT indices of different sized limestone and basalt aggregate samples. As shown in Fig. 14, the 13.2 mm limestone aggregate sample has the greatest composite AT index among the different sized limestone aggregate samples and the composite AT indices of other sized limestone aggregate samples do not have a major difference. The 9.5 mm basalt aggre-
4.3.3. Summary of the results The means, standard deviations, and statistical distributions of the AT indices and the composite AT indices of different sized limestone and basalt aggregates are summarized in Table 5. 5. T-test of the repeatability of the image analysis method and sample representativeness 5.1. Repeatability of the image analysis method The 9.5 mm limestone aggregates were used to test the repeatability of the image analysis method used in this study. The testing steps are as follows: (1) take the two pictures of the aggregate sample first according to the procedures described in Section 3.2; and (2) collect the aggregates together and do the same experiment again. Four pairs of data of the length, width, thickness and AT index were extracted from the pictures. A paired samples t-test was then conducted. The significance level was set to be 0.05. Table 6 shows the t-test results. As shown in Table 6, the P-values are all significantly greater than 0.05, which indicates that the mean of
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D. Zhang et al. / Construction and Building Materials 34 (2012) 330–336
Fig. 14. Composite AT indices of different sized limestone and basalt aggregate samples.
each pair of data is equal. Therefore, the image analysis method used in this study has good repeatability in collecting the three sizes and AT indices of aggregates. 5.2. Sample representativeness
Fig. 12. Histogram and normal P–P plot of the AT indices of the 13.2 mm limestone aggregates: (a) histogram; (b) normal P–P plot.
Two 9.5 mm limestone aggregate samples were chosen independently. The three sizes and AT indices of the aggregates in the two samples were obtained using the procedures described in Section 3.2. The three sizes and AT indices of 287 particles in each sample were used to do the t-test considering that the minimum sample size in Table 2 is 299. A two samples t-test was then done. The significance level was set to be 0.05. Table 7 shows the ttest results. As shown in Table 7, the P-values are all significantly greater than 0.05, which indicates that each indicator of the two samples has the same mean. Therefore, the sample sizes used in this study are large enough to represent the actual size and AT index distributions of the aggregates. 6. Validation of the AT index
Fig. 13. Lognormal P–P plot of the AT indices of the 13.2 mm limestone aggregates.
ASTM C1252-98 and AASHTO TP56 (uncompacted void content test) are used to evaluate the combined angularity and surface texture properties of coarse aggregates in an indirect manner. In loose condition, angular and rough-textured aggregates are generally expected to have a larger void content than rounded and smooth-surfaced aggregates. Based on this, the void contents of different sized limestone and basalt aggregates in loose condition were tested according to AASHTO T19 to validate the AT index. In the testing, the 4.75 mm and 9.5 mm aggregates were tested using a 3 L cylindrical metal measure and the aggregates larger than 13.2 mm were tested using a 10 L cylindrical metal measure. Fig. 15 shows the void contents of different sized limestone and basalt aggregates in loose condition. As shown in Fig. 15, the 13.2 mm limestone aggregate sample has the greatest void content among the different sized limestone aggregate samples and the
Table 5 Summary of the AT indices and composite AT indices of different sized limestone and basalt aggregates. Aggregate type
Sieve size (mm)
AT index
Composite AT index
Mean
Standard deviation
Distribution
Limestone
4.75 9.5 13.2 16 19
0.0118 0.011 0.0147 0.0115 0.0113
0.0053 0.0037 0.019 0.0053 0.0033
Normal Normal Lognormal Lognormal Normal
0.01163 0.01118 0.01515 0.0115 0.01133
Basalt
4.75 9.5 13.2
0.0129 0.0132 0.0109
0.0063 0.0098 0.0042
Normal Lognormal Normal
0.01272 0.0132 0.01102
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D. Zhang et al. / Construction and Building Materials 34 (2012) 330–336 Table 6 T-test of the repeatability of the image analysis method. Testing parameters
P (two-tailed)
Length Width Thickness AT index
0.926 0.890 0.112 0.521
AT indices corresponds to a larger difference of void contents. And with the increase of the sieve size, the void content and composite AT index of the limestone aggregates have almost the same variation trend, and so do the void content and composite AT index of the basalt aggregates. Therefore, the AT index developed in this study is effective to characterize the combined effect of the coarse aggregate angularity and surface texture.
7. Conclusions Table 7 T-test of the sample representativeness. Testing parameters
P (two-tailed)
Length Width Thickness AT index
0.870 0.369 0.881 0.554
Fig. 15. Void contents of different sized limestone and basalt aggregates in loose condition.
The shape, size, angularity and surface texture properties of coarse aggregates were studied in this paper. The following conclusions can be drawn: 1. In both limestone and basalt aggregates used in this study, the percentage of hexahedron is about 50–70%, the percentage of pentahedron is about 20–30%, the percentage of tetrahedron is about 10–20% and the percentage of the flat and elongated particles is about 0–10%. 2. The length, width and thickness of different-sized limestone and basalt aggregates used in this study all obey the normal distribution approximately. 3. The AT indices of the 13.2 mm limestone aggregates, 16 mm limestone aggregates and 9.5 mm basalt aggregates used in this study obey the lognormal distribution approximately. The AT indices of other sized limestone and basalt aggregates used in this study all obey the normal distribution approximately. 4. The t-test results demonstrate that the image analysis method used in this study has good repeatability in collecting the sizes and AT indices of aggregates and the sample sizes used in this study are large enough to represent the actual size and AT index distributions of aggregates. 5. The void contents of different sized limestone and basalt aggregates in loose condition were tested to validate the AT index. The results indicate that the AT index is effective for characterizing the combined effect of the coarse aggregate angularity and surface texture.
References
Fig. 16. Relation between the composite AT indices and void contents of different sized limestone and basalt aggregates.
void content first increases and then decreases with the increase of the aggregate size. The 9.5 mm basalt aggregate sample has the greatest void content and the 13.2 mm basalt aggregate sample has the smallest void content among the different sized basalt aggregate samples. The void contents of the 4.75 mm and 9.5 mm basalt aggregate samples are larger than those of the 4.75 mm and 9.5 mm limestone aggregate samples by 2.9% and 3.3%, respectively. However, the void content of the 13.2 mm basalt aggregate sample is smaller than that of 13.2 mm limestone aggregate sample by 10.8%. Fig. 16 shows the relation between the composite AT indices and void contents of different sized limestone and basalt aggregates. As shown in Fig. 16, for the same sized limestone and basalt aggregates, a greater composite AT index corresponds to a larger void content and a greater difference between the two composite
[1] Aho BD, Vavrik WR, Carpenter SH. Effect of flat and elongated coarse aggregate on field compaction of hot-mix asphalt. Transport Res Rec 2001;1761:26–31. [2] Pan T, Tutumluer E, Carpenter SH. Effect of coarse aggregate morphology on permanent deformation behavior of hot mix asphalt. J Transport Eng 2006;132(7):580–9. [3] Huang H. Discrete element modeling of railroad ballast using imaging based aggregate morphology characterization. Ph.D. Dissertation, University of Illinois at Urbana-Champaign; 2010. [4] Fletcher T, Chandan C, Masad E, Sivakumar K. Aggregate imaging system for characterizing the shape of fine and coarse aggregates. Transport Res Rec 2003;1832:67–77. [5] Rao C, Tutumluer E, Stefanski JA. Coarse aggregate shape and size properties using a new image analyzer. J Test Eval 2001;29(5):461–71. [6] Mora CF, Kwan AKH. Sphericity, shape factor, and convexity measurement of coarse aggregate for concrete using digital image processing. Cem Concr Res 2000;30(3):351–8. [7] Wang LB, Wang XR, Mohammad L, Abadie C. Unified method to quantify aggregate shape, angularity and texture using Fourier analysis. J Mater Civil Eng 2005;17(5):498–504. [8] Masad E, Button JW. Unified imaging approach for measuring aggregate angularity and texture. Comput-Aided Civil Infrastruct Eng 2000;15:273–80. [9] Al-Rousan T, Masad E, Tutumluer E, Pan T. Evaluation of image analysis techniques for quantifying aggregate shape characteristics. Constr Build Mater 2007;21(5):978–90. [10] Rao C, Tutumluer E, Kim IT. Quantification of coarse aggregate angularity based on image analysis. Transport Res Rec 2002;1787:117–24. [11] Rao C, Tutumluer E. Determination of coarse aggregate surface texture using imaging analysis. In: Proceedings of the 16th ASCE engineering mechanics conference. Seattle: University of Washington; 2003. [12] Tutumluer E, Pan T, Carpenter SH. Investigation of aggregate shape effects on hot mix performance using an image analysis approach. Pooled fund study
Contents lists available at SciVerse ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Investigation of the shape, size, angularity and surface texture properties of coarse aggregates Dong Zhang ⇑, Xiaoming Huang 1, Yongli Zhao 2 School of Transportation, Southeast University, Nanjing, Jiangsu 210096, China
a r t i c l e
i n f o
Article history: Received 19 November 2011 Received in revised form 20 January 2012 Accepted 25 February 2012 Available online 5 April 2012 Keywords: Aggregates Shape Size Angularity Surface texture Image analysis
a b s t r a c t The shape, size, angularity and surface texture properties of coarse aggregates were studied in this paper. Aggregates with different shapes were separated manually and the percentage by number of each shape was computed. The three sizes (length, width and thickness) of aggregates were extracted using an image analysis approach and their statistical distributions were studied. An indicator called angularity and surface texture (AT) index was developed to characterize the combined effect of the coarse aggregate angularity and surface texture based on two-dimensional aggregate images. The statistical distributions of the AT indices of different sized limestone and basalt aggregates and their composite AT indices were studied. The void contents of different sized limestone and basalt aggregates in loose condition were tested to validate the AT index. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The morphology of coarse aggregates includes shape, size, angularity and surface texture. Many studies have demonstrated that the coarse aggregate morphology has a significant effect on the performances of aggregate based materials such as the field compaction of asphalt mixtures, the permanent deformation of asphalt mixtures and the shearing resistance of railway ballast [1–4]. In addition, the discrete element method (DEM) is now employed more and more to study the micromechanical behavior of asphalt mixtures. It is very important to model the three-dimensional (3D) morphology of coarse aggregates when the DEM is used to analysis the micromechanical behavior of asphalt mixtures. Laboratory investigation of the actual 3D morphology of coarse aggregates serves as a way to correlate the particles generated by DEM to real aggregates. Therefore, it is important to quantitatively characterize the aggregate shape, size, angularity and surface texture for the prediction of material performances and reconstruction of the coarse aggregates by DEM. In the last decades, the image analysis method has been used to characterize the morphology of coarse aggregates [5–9]. The 3D sizes of aggregates can be determined by taking two images of each ⇑ Corresponding author. Tel.: +86 13776693486; fax: +86 25 83795184. E-mail addresses: [email protected] (D. Zhang), [email protected] (X. Huang), [email protected] (Y. Zhao). 1 Tel./fax: +86 25 83795184. 2 Tel.: +86 25 83793096; fax: +86 25 83795184. 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.02.096
aggregate particle. The sizes of each particle are different even the particles are within the same sized aggregates. Studying the size distributions of coarse aggregates contributes to understanding the size properties of aggregates and to modeling the aggregates by DEM. The shape was usually characterized by the indicators such as sphericity and roundness in the image analysis method [6,9]. The shape indicators can then be correlated to the performance of the aggregate based materials. However, these shape indicators cannot be used to construct the 3D shapes by DEM. It is necessary to study the actual 3D shapes of coarse aggregates. In the image analysis method, two dimensional aggregate images were used to evaluate the angularity and surface texture of coarse aggregates [7,8]. The angularity index (AI) was developed by Rao et al. [10] to characterize the coarse aggregate angularity by tracing the change in slope of the outline of the two-dimensional aggregate image. Also, the surface texture (ST) index was proposed by Rao and Tutumluer [11] to characterize the coarse aggregate surface texture using the image analysis technique known as ‘‘erosion and dilation’’. Further study by Tutumluer et al. [12] shows that a definite relationship with a coefficient of determination R2 of 0.79 existed between the AI and ST index of the studied aggregates. This indicates that the AI and ST index are significantly related to each other. Therefore, the angularity and surface texture of aggregates may be characterized by one index since the two properties are both related with the outline of the two-dimensional aggregate image. The objective of this study is to investigate the shape, size, angularity and surface texture properties of coarse aggregates.
D. Zhang et al. / Construction and Building Materials 34 (2012) 330–336
331
The main work includes: (1) separate aggregates of different shapes manually and compute the percentage by number of each shape; (2) extract the length, width and thickness of aggregates using an image analysis method and study their statistical distributions; (3) develop an indicator to characterize the angularity and surface texture of coarse aggregates and analyze its statistical distributions; and (4) validate the proposed indicator.
2. Shape, size, angularity and surface texture characterization The 3D shapes of the coarse aggregates are approximated to be hexahedron, pentahedron and tetrahedron in this study. Flat and elongated aggregates are considered as an individual type since they are undesirable in the specifications of many countries. The flat and elongated aggregate herein is determined as the particle whose ratio of the maximum to minimum size is bigger than 3:1. Schematic drawings of the 3D aggregate shapes are illustrated in Fig. 1. The size property of coarse aggregates is characterized by length, width and thickness. Length is defined as the maximum size of the particle, width is the maximum size in the plane perpendicular to the length and thickness is the maximum size perpendicular to the length and width. The thickness is assumed to be the shortest size of the particle in this study. The two-dimensional image analysis method is now usually used to characterize the angularity and surface texture of coarse aggregates. As shown in Fig. 2, the angularity is defined as the convex part on the outline of a coarse aggregate image and the surface texture is considered as the tiny bumps on the outline. The main difference of the two morphological properties is that the angularity is a macro-property of the outline of the coarse aggregate image while the surface texture is a micro-property. Therefore, the angularity and surface texture reflected by a two-dimensional coarse aggregate image can be characterized by one indicator. As can be observed in Fig. 3, the coarse aggregate outline with more macroand micro-bumps has a longer perimeter. Based on this, an indicator called angularity and surface texture (AT) index is developed here to characterize the combined effect of the angularity and surface texture. The AT index is defined by the difference of the out-
Fig. 3. Schematic drawing of the outline and convex outline.
line perimeter and the convex outline perimeter of a twodimensional coarse aggregate image, as expressed by Eq. (1). As shown in Fig. 3, the outline perimeter is the total length of the image outline and the convex outline perimeter is the length of the image boundary lines that omit the concave part of the outline. The length of the concave lines is replaced by the length of straight lines in the computing of the convex outline perimeter.
AT ¼
Outline Perimeter—Convex Outline Perimeter Convex Outline Perimeter
ð1Þ
The AT index of an aggregate particle is established by averaging the AT index values of its two-dimensional images weighted by their areas, as shown in following equation:
AT ¼
Pn 1 Ai ATi Pn 1 Ai
ð2Þ
where n is the number of images used in the calculation, Ai is the area of the ith image of the particle and ATi is the AT index of the ith image of the particle. The AT index of the whole aggregate sample (composite AT index) is determined by averaging the AT index values of aggregate particles weighted by their areas used in computing their own AT index. The composite AT index of the aggregates mixed by different aggregate samples can be determined by averaging the composite AT index values of different aggregate samples weighted by their weights. 3. Materials and experimental methods
(a)
(c)
(b)
(d)
3.1. Materials The 4.75–9.5 mm, 9.5–13.2 mm, 13.2–16 mm, 16–19 mm and 19–26.5 mm limestone aggregates and the 4.75–9.5 mm, 9.5–13.2 mm and 13.2–16 mm basalt aggregates were used in this study. The 4.75–9.5 mm aggregates are the particles that pass the 9.5 mm sieve but retain on the 4.75 mm sieve. Other sized aggregates have a similar meaning. The 4.75–9.5 mm aggregates are simply called 4.75 mm aggregates in the following discussion and so are other sized aggregates. 3.2. Experimental methods
Fig. 1. Schematic drawings of the 3D aggregate shapes: (a) hexahedron; (b) pentahedron; (c) tetrahedron; and (d) flat and elongated particles.
Fig. 2. Schematic drawing of a two-dimensional aggregate image.
Different shaped aggregates in an aggregate sample were separated first manually and then the percentages by number of hexahedron, pentahedron, tetrahedron and the flat and elongated aggregates were computed. In determining the aggregate shape, the face with a relatively small area was not counted and Fig. 1 was used as a reference. Fig. 4 shows the manually separated aggregates in which they are tetrahedron, pentahedron and hexahedron aggregates from the left to right. Fig. 5 shows the typical 3D aggregate shapes in which they are hexahedron, pentahedron and tetrahedron aggregates from up to down. The sample sizes (by number) of different sized aggregates used in the shape statistical analysis are shown in Table 1. Three sizes (length, width and thickness) of the aggregates were extracted using an image analysis approach. Two sizes of each aggregate particle can be extracted from an image of the aggregates. In order to obtain the third size of each aggregate particle, all particles were set upright and the other picture was taken. The outline perimeter and the convex outline perimeter of each coarse aggregate image were also extracted using these images. The sample sizes (by number) of different sized aggregates used in the size, angularity and surface texture analysis are shown in Table 2. Detailed procedures are described as follows:
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Fig. 6. Percentages by number of different shaped aggregates in limestone aggregates.
Fig. 4. Manually separated aggregates (tetrahedron, pentahedron and hexahedron aggregates from the left to right).
Fig. 7. Percentages by number of different shaped aggregates in basalt aggregates.
4. Results and discussion 4.1. Aggregate shapes
Fig. 5. Typical 3D aggregate shapes (hexahedron, pentahedron and tetrahedron aggregates from up to down).
Table 1 Sample sizes of different sized aggregates used in the shape statistical analysis (by number). Sieve size (mm) Limestone Basalt
4.75 475 525
9.5 542 507
13.2 479 363
16 330 –
19 385 –
Table 2 Sample sizes of different sized aggregates used in the size, angularity and surface texture analysis (by number). Sieve size (mm) Limestone Basalt
4.75 344 391
9.5 487 405
13.2 431 299
16 317 –
19 361 –
1. Dye aggregates black using very thin ink (mixed with water) and then dry them. 2. Place the aggregates on a white background and then take a picture from above. 3. Set the aggregates upright manually and then take the other picture from above. 4. Analyze the two pictures to extract the three sizes of each aggregate particle. 5. Analyze the two pictures to extract the outline perimeter and the convex outline perimeter of each aggregate image.
Figs. 6 and 7 show the percentages by number of different shaped aggregates in limestone aggregates and basalt aggregates, respectively. As shown in Fig. 6, the percentage of hexahedron is the highest, the percentage of pentahedron is the second highest, the percentage of tetrahedron is the third highest and the percentage of the flat and elongated particles is the lowest in different sized limestone aggregates. As shown in Fig. 7, the percentages of hexahedron, pentahedron, tetrahedron and the flat and elongated aggregates in different sized basalt aggregates have the same law as those of limestone aggregates except that the percentages of tetrahedron and the flat and elongated aggregates in 4.75 mm and 9.5 mm basalt aggregates are nearly the same. In general, the percentage of hexahedron is about 50–70%, the percentage of pentahedron is about 20–30%, the percentage of tetrahedron is about 10–20% and the percentage of the flat and elongated particles is about 0–10% in different-sized limestone and basalt aggregates. 4.2. Aggregate sizes The three sizes of each particle were extracted from the two pictures of each aggregate sample. Statistical features of the length, width and thickness of all particles in one sample were analyzed. Table 3 shows the statistical results of the three sizes of the 9.5 mm limestone aggregates. Figs. 8–10 show the histogram and normal P–P plot of the length, width and thickness of the 9.5 mm limestone aggregates, respectively. The normal P–P plot is used to test if the data obey the normal distribution. If the points on the P–P plot are all located on the diagonal shown in Fig. 8b, the tested data obey the normal distribution. As shown in Figs. 8–10, the length, width and
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D. Zhang et al. / Construction and Building Materials 34 (2012) 330–336 Table 3 Statistical results of the three sizes of the 9.5 mm limestone aggregates. Statistical parameters
Minimum (mm)
Maximum (mm)
Mean (mm)
Standard deviation (mm)
Length Width Thickness
11.38 7.18 5.78
27.47 17.54 16.99
17.87 12.97 11.25
3.10 1.68 2.05
Fig. 9. Histogram and normal P–P plot of the width of the 9.5 mm limestone aggregates: (a) histogram; (b) normal P–P plot.
stone and basalt aggregates all obey the normal distribution approximately. The means and standard deviations of the length, width and thickness of different-sized limestone and basalt aggregates are summarized in Table 4. Fig. 8. Histogram and normal P–P plot of the length of the 9.5 mm limestone aggregates: (a) histogram; (b) normal P–P plot.
thickness of the 9.5 mm limestone aggregates all obey the normal distribution approximately. The three sizes of other sized limestone and basalt aggregates were analyzed using the same method. The results of the analysis show that the length, width and thickness of different-sized lime-
4.3. Angularity and surface texture The AT index of each aggregate particle among different sized aggregates was calculated according to Eq. (2). The composite AT index of each aggregate sample was also computed. 4.3.1. Statistical distribution of the AT index Fig. 11 shows the histogram and normal P–P plot of the AT indices of the 9.5 mm limestone aggregates. As shown in Fig. 11, the AT
Table 4 Means and standard deviations of the length, width and thickness of different-sized limestone and basalt aggregates. Aggregate type
Sieve size (mm)
Length Mean (mm)
Standard deviation (mm)
Mean (mm)
Width Standard deviation (mm)
Thickness Mean (mm)
Standard deviation (mm)
Limestone
4.75 9.5 13.2 16 19
10.43 17.87 22.74 29.71 37
2.43 3.1 3.63 4.94 5.54
7.6 12.97 16.67 21.01 26.84
1.64 1.68 1.6 1.85 3.24
6.78 11.25 14.32 18.25 22.56
1.65 2.05 2.23 2.91 4.03
Basalt
4.75 9.5 13.2
9.15 19.07 22.46
1.79 3.03 3.28
6.76 13.7 17.02
1.3 1.71 1.39
6.02 11.58 14.43
1.33 2.22 2.16
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Fig. 10. Histogram and normal P–P plot of the thickness of the 9.5 mm limestone aggregates: (a) histogram; (b) normal P–P plot.
Fig. 11. Histogram and normal P–P plot of the AT indices of the 9.5 mm limestone aggregates: (a) histogram; (b) normal P–P plot.
indices of the 9.5 mm limestone aggregates obey the normal distribution approximately. Fig. 12 shows the histogram and normal P–P plot of the AT indices of the 13.2 mm limestone aggregates. Obviously, the AT indices of the 13.2 mm limestone aggregates don’t obey the normal distribution. The Laplace, Logistic, Lognormal, Pareto, Student t, Weibull and Uniform distribution P–P plots were used to further study the AT index distribution of the 13.2 mm limestone aggregates. The results indicate that the AT indices of the 13.2 mm limestone aggregates obey the lognormal distribution approximately, as shown in Fig. 13. The statistical distributions of the AT indices of other sized aggregates were also analyzed using the same method. The results of the analysis show that the AT indices of the 13.2 mm limestone aggregates, 16 mm limestone aggregates and 9.5 mm basalt aggregates obey the lognormal distribution approximately and the AT indices of other sized limestone and basalt aggregates all obey the normal distribution approximately. It is worth noting that the aggregate morphological properties are affected by its source stone (by which the aggregates are produced) properties and the production technology. Therefore, the morphological index distributions of aggregates produced by different stones and technology may be different.
gate sample has the greatest composite AT index and the 13.2 mm basalt aggregate sample has the smallest composite AT index among the different sized basalt aggregate samples. The composite AT indices of the 4.75 mm and 9.5 mm basalt aggregate samples are larger than those of the 4.75 mm and 9.5 mm limestone aggregate samples by 9.4% and 18.1%, respectively. However, the composite AT index of the 13.2 mm basalt aggregate sample is smaller than that of 13.2 mm limestone aggregate sample by 27.3%.
4.3.2. Composite AT index of each aggregate sample Fig. 14 shows the composite AT indices of different sized limestone and basalt aggregate samples. As shown in Fig. 14, the 13.2 mm limestone aggregate sample has the greatest composite AT index among the different sized limestone aggregate samples and the composite AT indices of other sized limestone aggregate samples do not have a major difference. The 9.5 mm basalt aggre-
4.3.3. Summary of the results The means, standard deviations, and statistical distributions of the AT indices and the composite AT indices of different sized limestone and basalt aggregates are summarized in Table 5. 5. T-test of the repeatability of the image analysis method and sample representativeness 5.1. Repeatability of the image analysis method The 9.5 mm limestone aggregates were used to test the repeatability of the image analysis method used in this study. The testing steps are as follows: (1) take the two pictures of the aggregate sample first according to the procedures described in Section 3.2; and (2) collect the aggregates together and do the same experiment again. Four pairs of data of the length, width, thickness and AT index were extracted from the pictures. A paired samples t-test was then conducted. The significance level was set to be 0.05. Table 6 shows the t-test results. As shown in Table 6, the P-values are all significantly greater than 0.05, which indicates that the mean of
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Fig. 14. Composite AT indices of different sized limestone and basalt aggregate samples.
each pair of data is equal. Therefore, the image analysis method used in this study has good repeatability in collecting the three sizes and AT indices of aggregates. 5.2. Sample representativeness
Fig. 12. Histogram and normal P–P plot of the AT indices of the 13.2 mm limestone aggregates: (a) histogram; (b) normal P–P plot.
Two 9.5 mm limestone aggregate samples were chosen independently. The three sizes and AT indices of the aggregates in the two samples were obtained using the procedures described in Section 3.2. The three sizes and AT indices of 287 particles in each sample were used to do the t-test considering that the minimum sample size in Table 2 is 299. A two samples t-test was then done. The significance level was set to be 0.05. Table 7 shows the ttest results. As shown in Table 7, the P-values are all significantly greater than 0.05, which indicates that each indicator of the two samples has the same mean. Therefore, the sample sizes used in this study are large enough to represent the actual size and AT index distributions of the aggregates. 6. Validation of the AT index
Fig. 13. Lognormal P–P plot of the AT indices of the 13.2 mm limestone aggregates.
ASTM C1252-98 and AASHTO TP56 (uncompacted void content test) are used to evaluate the combined angularity and surface texture properties of coarse aggregates in an indirect manner. In loose condition, angular and rough-textured aggregates are generally expected to have a larger void content than rounded and smooth-surfaced aggregates. Based on this, the void contents of different sized limestone and basalt aggregates in loose condition were tested according to AASHTO T19 to validate the AT index. In the testing, the 4.75 mm and 9.5 mm aggregates were tested using a 3 L cylindrical metal measure and the aggregates larger than 13.2 mm were tested using a 10 L cylindrical metal measure. Fig. 15 shows the void contents of different sized limestone and basalt aggregates in loose condition. As shown in Fig. 15, the 13.2 mm limestone aggregate sample has the greatest void content among the different sized limestone aggregate samples and the
Table 5 Summary of the AT indices and composite AT indices of different sized limestone and basalt aggregates. Aggregate type
Sieve size (mm)
AT index
Composite AT index
Mean
Standard deviation
Distribution
Limestone
4.75 9.5 13.2 16 19
0.0118 0.011 0.0147 0.0115 0.0113
0.0053 0.0037 0.019 0.0053 0.0033
Normal Normal Lognormal Lognormal Normal
0.01163 0.01118 0.01515 0.0115 0.01133
Basalt
4.75 9.5 13.2
0.0129 0.0132 0.0109
0.0063 0.0098 0.0042
Normal Lognormal Normal
0.01272 0.0132 0.01102
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D. Zhang et al. / Construction and Building Materials 34 (2012) 330–336 Table 6 T-test of the repeatability of the image analysis method. Testing parameters
P (two-tailed)
Length Width Thickness AT index
0.926 0.890 0.112 0.521
AT indices corresponds to a larger difference of void contents. And with the increase of the sieve size, the void content and composite AT index of the limestone aggregates have almost the same variation trend, and so do the void content and composite AT index of the basalt aggregates. Therefore, the AT index developed in this study is effective to characterize the combined effect of the coarse aggregate angularity and surface texture.
7. Conclusions Table 7 T-test of the sample representativeness. Testing parameters
P (two-tailed)
Length Width Thickness AT index
0.870 0.369 0.881 0.554
Fig. 15. Void contents of different sized limestone and basalt aggregates in loose condition.
The shape, size, angularity and surface texture properties of coarse aggregates were studied in this paper. The following conclusions can be drawn: 1. In both limestone and basalt aggregates used in this study, the percentage of hexahedron is about 50–70%, the percentage of pentahedron is about 20–30%, the percentage of tetrahedron is about 10–20% and the percentage of the flat and elongated particles is about 0–10%. 2. The length, width and thickness of different-sized limestone and basalt aggregates used in this study all obey the normal distribution approximately. 3. The AT indices of the 13.2 mm limestone aggregates, 16 mm limestone aggregates and 9.5 mm basalt aggregates used in this study obey the lognormal distribution approximately. The AT indices of other sized limestone and basalt aggregates used in this study all obey the normal distribution approximately. 4. The t-test results demonstrate that the image analysis method used in this study has good repeatability in collecting the sizes and AT indices of aggregates and the sample sizes used in this study are large enough to represent the actual size and AT index distributions of aggregates. 5. The void contents of different sized limestone and basalt aggregates in loose condition were tested to validate the AT index. The results indicate that the AT index is effective for characterizing the combined effect of the coarse aggregate angularity and surface texture.
References
Fig. 16. Relation between the composite AT indices and void contents of different sized limestone and basalt aggregates.
void content first increases and then decreases with the increase of the aggregate size. The 9.5 mm basalt aggregate sample has the greatest void content and the 13.2 mm basalt aggregate sample has the smallest void content among the different sized basalt aggregate samples. The void contents of the 4.75 mm and 9.5 mm basalt aggregate samples are larger than those of the 4.75 mm and 9.5 mm limestone aggregate samples by 2.9% and 3.3%, respectively. However, the void content of the 13.2 mm basalt aggregate sample is smaller than that of 13.2 mm limestone aggregate sample by 10.8%. Fig. 16 shows the relation between the composite AT indices and void contents of different sized limestone and basalt aggregates. As shown in Fig. 16, for the same sized limestone and basalt aggregates, a greater composite AT index corresponds to a larger void content and a greater difference between the two composite
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