Quantification of coarse aggregate shape in concrete

Abstract

The objective of this study is to choose indices for the characterization of aggregate form and angularity for large scale application. For this purpose, several parameters for aggregate form and angularity featured in previous research are presented. Then, based on these established parameters, 200 coarse quartzite aggregates are analyzed herein by using image processing technology. This paper also analyzes the statistical distributions of parameters for aggregate form and angularity as well as the correlation between form and angularity parameters. It was determined that the parameters for form or angularity of coarse aggregates could be fitted by either normal distribution or log-normal distribution at a 95% confidence level. Some of the form parameters were influenced by changes in angularity characteristics, while aspect ratio and angularity using outline slope, area ratio and radius angularity index, and aspect ratio and angularity index were independent of each other, respectively; and consequently, the independent parameters could be used to quantify the aggregate form and angularity for the purpose to study the influence of aggregate shape on the mechanical behavior of concrete. Furthermore, results from this study’s in-depth investigations showed that the aspect ratio and the angularity index can further understanding of the effects of coarse aggregates form and angularity on concrete mechanical properties, respectively. Finally, coarse aggregates with the same content, type and surfaces texture, but different aspect ratios and angularity indices were used to study the influence of coarse aggregate form and angularity on the behavior of concrete. It was revealed that the splitting tensile strength of concrete increased with increases in the aspect ratio or angularity index of coarse aggregates.

Keywords

coarse aggregate / form / angularity / digital image analysis / statistical distribution / splitting tensile strength

Introduction

Many studies have demonstrated that the shape and surface texture of fine and coarse aggregate have significant effects on the fracture and mechanical properties of concrete [1-5]. Therefore, characterization of coarse and fine aggregate shape and surface texture is important for control of aggregates and for understanding the influence of aggregate shape and surface texture on the behavior of concrete. Barrett [6] proposed that morphology (including shape and surface texture) of an aggregate can be described in terms of its form, angularity, and surface texture. Form describes the overall shape of an aggregate at macro-scale; angularity is defined as the measure of sharpness of aggregate corners at the meso-level, and surface texture is the measure of the smoothness of the aggregate surface at the micro-level.

Motivated by advancements in imaging techniques, digital image analysis technology has become an excellent tool to rapidly quantify aggregate shape and surface texture [7-9], and various parameters have been presented to quantify the form, angularity and surface texture of aggregates [10-13]. Obviously, these parameters, either for form or angularity or surface texture, should be distinguishable based on their individual characteristics without error. However, identification errors can easily occur, and the investigation needed to correct this problem has been limited except for Rousan et al. [13]. They studied the correlations between form parameters and visual numbers for form proposed by Rittenhouse [14], and the correlations between angularity parameters and the visual numbers for angularity proposed by Krumbiem [15]. The analysis results from Ref. [13] revealed that some of the form parameters can be used to describe form without being affected by angularity of an aggregate, such as aspect ratio, form index and flat and elongated ratio. Also, some of the angularity parameters can be used to describe angularity without being affected by form, such as angularity using outline slope. However, they did not study the correlations between aggregates’ form and angularity parameters, which is essential for understanding their uniqueness and potential applications to the industries they are used in.

Furthermore, Pan et al. [17] quantitated the aggregate shape in terms of three indices and studied the effects of aggregate shape on the interfacial transition zone and the early age cracking behavior of concrete. They found that the aggregate surface texture had a greater influence on early concrete fracture than angularity did. However, research defining the quantitative impact of aggregate shapes on the mechanical properties of concrete are still very limited.

In this paper, Section 2 contains a literature survey discussing previous research on several parameters for aggregate form and angularity. As Section 3 then shows how these parameters can be used to analyze 200 coarse quartzite aggregates via image processing technology. This section also shows the statistical distribution of form and angularity parameters as well as the correlation between form and angularity parameters. Section 4 shows how concrete specimens made from coarse aggregates with the same content, type and surface texture, but different form and angularity characteristics, were tested to investigate the quantitative effect of the aggregate form and angularity on the mechanical properties of concrete. Finally, Section 5 offers the major conclusions and summarizes the contribution this paper makes to the advancement of coarse aggregate studies.

Parameters for characterizing aggregate shape

In this section, a brief description is provided on some of the parameters for characterizing form and angularity of the aggregate particles. All of these parameters were obtained by using image analysis techniques.

Type of parameters for form

Aspect ratio

Aspect ratio (AR), which was proposed by Kuo and Freeman [10] and always used to describe the form of aggregates in 2-dimensions, can be expressed by Eq. (1):

(1)AR=L/W,

in which, L and W represents the length and the width of an aggregate image, respectively.

By examining Eq. (1), it will be noted that, for circle and equilateral polygon images of aggregates, aspect ratios were equal to 1.0. But for other shapes of aggregates, aspect ratios were greater than 1.0.

Form index

Form index (FI) was proposed by Masad et al. to describe the form of aggregate in 2 dimensions [18]. It is based on the change of the aggregate’s radius, which is the distance between the center of the aggregate and its boundary. Form index is given by Eq. (2),

(2)FI={\displaystyle \sum _{\theta =\mathrm{0}}^{\theta =\mathrm{360}-\mathrm{\Delta }\theta }{\displaystyle \frac{\left|R_{\theta +\mathrm{\Delta }\theta }\right|}{R_{\theta }}}},

where θ and R represent the directional angle and the radius in corresponding direction, respectively.

It can be found that for a circle image of aggregate, the form index is equal to 0. The higher the form index is, the less circular the shape of the particle will be.

Roundness

Roundness (R) [13] is a widely used measure of form in 2-dimensional studies, and expressed by Eq. (3), in which l and A is the perimeter and area of an aggregate image in 2-dimensional projection, respectively.

(3)R=l^{\mathrm{2}}/\mathrm{4}\mathrm{\pi }A.

Obviously, the value of roundness is always equal to or greater than 1.0.

Area ratio

Area ratio was proposed by Bangaru and Das [16] to describe the form of aggregates in 2-dimensional studies, and it can be calculated by the following equation:

(4)Arearatio=A_{ce}/A,

in which, A is the area of an aggregate image in two dimensions; A_ce is the area of an circumscribing ellipse, as shown in Fig. 1.

Sphericity

Sphericity [13] measuring the form in terms of 3 dimensions is given by Eq. (5), in which d₁, d₂, and d₃ represent the longest, intermediate, and shortest dimension, respectively.

(5)Sphericity={\left({\displaystyle \frac{d_{\mathrm{2}}\times d_{\mathrm{3}}}{d_{\mathrm{1}}^{\mathrm{2}}}}\right)}^{\mathrm{1}/\mathrm{3}}.

Flat and elongated ratio

Flat and elongated ratio (FER) [13] is defined as the ratio of flatness and elongation used to describe the aggregate form in 3-dimensions, in which flatness is measured by the ratio of the intermediate dimension d₂ to the shortest dimension d₃, and elongation is measured by the ratio of the longest dimension d₁ to the intermediate dimension d₂. Therefore, flat and elongated ratio (FER) is give by:

(6)FER=d_{\mathrm{1}}/d_{\mathrm{3}}.

It can be found that aspect ratio is similar to flat and elongated ratio, but it is usually used for 2-dimensional projections [13].

Type of parameters for angularity

Angularity using outline slope

Based on the change of slope of an aggregate boundary, Rao et al. [20-21] proposed a quantitative angularity index (AI) to describe the angularity of aggregates in two or three dimensions. In order to determine AI, three orthogonal views (top, front and side) of the aggregate image should be first extracted. Next, for each image, the outline was approximated by an n side polygon as shown in Fig. 2, and the angle subtended at each vertex of the polygon was then computed. Thirdly, the changes in angle α at each vertex with respect to the angle in the preceding vertex were determined subsequently, and the probability that these changes have a value in the range e to (e+10) is calculated. Finally, the angularity index for each view (AI_i) was thus obtained by Eq. (6), and then AI was calculated by Eq. (7) according to the weighted average of the three angularities

(7)A{I}_i={\displaystyle \sum _{e=\mathrm{0}}^{\mathrm{170}}e\times P(e),}

(8)AI={\displaystyle \frac{{\displaystyle \sum _{i=\mathrm{1}}^{\mathrm{3}}(A{I}_i\times Are{a}_i)}}{{\displaystyle \sum _{i=\mathrm{1}}^{\mathrm{3}}Are{a}_i}}},

where e is the starting angle value, increasing by increment of 10°; P(e) is the probability that change in angle α has a value in the range e to (e+10); Area_i is the area of image for the top, front and side view, respectively. The fact that a polygon with 24 sides is used to approximate an aggregate limits the change between two successive angles to a maximum of 180°.

It can be found that the angularity index will be zero for a circle or spherical image of aggregate, and larger than zero for other shapes of aggregates.

Radius angularity index

The radius angularity index (RAI) [18] compares the radius of the aggregate outline to the radius of the equivalent ellipse which has the same area and aspect ratio as the aggregate image, as shown in Fig. 3. The calculations are done following the equation below:

(9)RAI={\displaystyle \sum _{\theta =\mathrm{0}}^{\theta =\mathrm{360}-\mathrm{\Delta }\theta }{\displaystyle \frac{\left|R_{p\theta }-R_{EE\theta }\right|}{R_{EE\theta }}}},

where R_pθ is the radius of the aggregate outline at a directional angle θ, and R_EEθ is the radius of the equivalent ellipse at the same θ.

Convexity ratio

Convexity ratio is evaluated from the 2 dimensions of an aggregate [19], as illustrated in Fig. 4. It is measured by Eq. (9).

(9)CR=A/A_c,

where, A is the area of an aggregate image; A_e is the convex area, which is the area of the minimum convex boundary circumscribing the aggregate, as shown in Fig. 4.

By definition, the value of the convexity ratio for a circular, an elliptical or an equilateral polygon image of aggregates will be 1.0. According to the definition of the angularity, however, an equilateral polygon is obviously more angular than a circle or an ellipse, which means convexity ratio fails to reflect the angularity of the aggregate correctly.

Angularity index

In two dimensions, angularity index (AN) was proposed by Kuo and Freeman [10] and defined as shown in Eq. (10), in which, P_c is the perimeter of the minimum convex boundary circumscribing an aggregate outline; and P_e is the perimeter of an equivalent ellipse.

(10)AN={(P_{\mathrm{c}}/P_{\mathrm{e}})}^{\mathrm{2}}.

It is easy to find that the angularity index for either a circle or an ellipse will be 1.0, but for angular aggregates, it will be larger than 1.0.

Experimental procedure and analysis method

Experimental procedure

The previous section has introduced some of the parameters for aggregate form and angularity. The next task is to quantify these parameters by digital image processing techniques. Digital image processing consists of converting video pictures into digital form and applying various mathematical procedures to extract significant information from an image. The device showed in Fig. 5 was designed to capture aggregate images. It was found in the test that some shadows of aggregates will be produced if the images were obtained under natural light. To avoid the effect of natural light on the image, four filament lamps (5 watts) were placed neatly in a box with each aggregate sample’s surface placed away from the light except on the top. In addition, it should be noted that the influences of the surface texture of coarse aggregate on the test results were not considered due to the following reasons:

1) Surface textures of quartzite coarse aggregates, which were also used in this study were investigated in Ref. [22], and the average value of surface textures for 50 coarse aggregates was 446.7 μm, which was much smaller than the axis length, perimeter, or area of a coarse aggregate.

2) The digital camera showed in Fig. 5 could not acquire the texture of an aggregate surface accurately, which was always obtained by a microscope.

After the transparent glass were fixed on the top of the box, the aggregates were first placed in an orderly arrangement on a white paper (297 mm × 420 mm) which lay flat on the glass, and double-sided adhesive tape was used to secure the position of coarse aggregates. Then the acquisition of images was done thanks to the digital camera placed above. After acquisition, three orthogonal images (top, side and front) of aggregates were obtained as shown in Fig. 6(a), in which the reference is a cylinder with a two-centimeter diameter. The aggregates are shown in black as the light is behind them. Thus, their shape was more accurate and the image processing was easier.

Analysis methods

To evaluate the parameters (except convexity ratio, which can not reflect the angularity of aggregates correctly) mentioned in Section 2, Image-pro Plus image analysis software and MATLAB were adopted. Image-pro Plus image analysis software was developed by Media Cybernetics and could be used to acquire images, count, measure and classify objects.

Simple dimensions such as area, perimeter or axis of an aggregate were directly obtained by using the Image-pro Plus image analysis software; therefore, some parameters, including aspect ratio, roundness, sphericity, flat and elongated ratio and angularity were calculated using the data measured from the Image-pro Plus image analysis software. Otherwise, MATLAB programs were developed to compute the parameters left, i.e., form index, area ratio, radius angularity index and angularity using outline slope in this paper. In this analysis, the same views were used for all analyses of form and angularity parameters. Relevant views were used according to the analysis: all three views were used for three-dimensional analyses, but only the top view was used for two-dimensional analyses.

The dimensions of aggregates obtained by the software were in pixels, and the reference was used for determining actual dimensions of aggregates. As the reference is a cylinder with a diameter of 20 millimeters, the actual dimensions, such as length, perimeters and areas in millimeters can be calculated by Eqs. (11), (12) and (13), respectively.

(11)d_a=\mathrm{20}\cdot d_{ap}/d_{rp},

(12)P_a=\mathrm{\pi }\cdot \mathrm{20}\cdot P_{ap}/P_{rp},

(13)A_a={\displaystyle \frac{\mathrm{\pi }\cdot {\mathrm{20}}^{\mathrm{2}}\cdot A_{ap}}{\mathrm{4}\cdot A_{rp}}},

where d_a, P_a and A_a represent the aggregate’s actual length, perimeter and area in mm, mm and mm², respectively; d_ap, P_ap and A_ap represent the aggregate length, perimeter and area on the image in pixels, respectively; and d_rp, P_rp and A_rp represent the reference length, perimeter and area on the image in pixels, respectively.

Analysis results

Statistical distribution of form and angularity parameters

Two hundred quartzite coarse aggregates with diameters between 16 mm and 20 mm were investigated, and the statistical distribution for each parameter was analyzed. Statistical parameters were calculated, particularly the mean values including μ of form and angularity parameters, standard deviations σ and coefficient of variations δ for all 200 coarse aggregates using simulated results. This work is summarized in Tables 1 and 2, respectively. It can be noted in Table 1 that the coefficient of variation of each form parameter ranged from 7.4% to 18.3%, which means that the effect of the coarse aggregates shape on form parameters is obvious. Moreover Table 2 shows that the maximum of coefficient of variation for each angularity parameter equals 38.6%, which also means that the coarse aggregates shape has significant influence on the angularity of coarse aggregates.

The distribution of the analyzed results for form and angularity parameters of coarse aggregates are illustrated by the histograms shown in Figs. 7 and 8, respectively. From the histograms, it is reasonable to assume a normal or log-normal distribution to fit the data for all 200 coarse aggregates investigated.

In order to verify the normal or log-normal distribution for form or angularity parameters of coarse aggregates, a Pearson’s χ² test [23] was performed. Normal distribution H₀ and log-normal distribution H₁ is assumed in Eqs. (14) and (15), respectively.

(14)X~N(\mu ,{\sigma }^{\mathrm{2}}),

(15)X~LN(\mu ,{\sigma }^{\mathrm{2}}),

where X represents one of the form or angularity parameters.

The results of the χ² test for the distribution of form or angularity parameters for all the coarse aggregates are presented in Tables 3 and 4, respectively. These Tables indicate that the area ratio, the sphericity and angularity using outline slope of coarse aggregates can be fitted by both H₀ for the normal distribution and H₁ for the log-normal distribution; moreover, the roundness and the angularity index can be fitted by normal distribution, while the aspect ratio, the form index, the flat and elongated ratio as well as the radius angularity index can be fitted by log-normal distribution.

Finally, the probability density function f(x) for form or angularity parameters of all the coarse aggregate samples, are shown in Figs. 7 and 8, which illustrate how well normal or log-normal distribution performs for these parameters.

Correlation between form and angularity parameters

Moreover, to choose indices that are capable of separating form from angularity, correlations between parameters for form and angularity were examined, as shown in Figs. 9-11.

Figures 9-11 show a linear regression on every pair of form parameter/angularity parameter, and the Pearson correlation coefficient was calculated by Eq. (16).

(16)r={\displaystyle \frac{{\displaystyle \sum _{i=1}^n\left(x_i-\overline{x}\right)\left(y_i-\overline{y}\right)}}{\sqrt{{\displaystyle \sum _{i=1}^n\left(x_i-\overline{x}\right)}}\cdot \sqrt{{\displaystyle \sum _{i=1}^n\left(y_i-\overline{y}\right)}}}},

where x_i and y_i are the two-dimensional random variables for the i-th observation of X = [x₁, x₂,…, x_n] and Y = [y₁, y₂,…, y_n], respectively; X and Y represent the values for form and angularity parameters, respectively; n is the sample size; and \overline{x}and \overline{y}represent the average value for X and Y, respectively.

For a two-tailed significance level of α = 0.01 for all aggregates, the critical value of correlation coefficient was 0.182. That is to say, when the absolute value of the Pearson correlation coefficient is smaller than the critical value, the hypothesis of the existing correlation is rejected. The test results are shown in Tables 5 to 7.

Tables 5 to 7 show that aspect ratio and angularity using outline slope, area ratio and radius angularity index, and aspect ratio or flat and elongated ratio and angularity index are independent of each other, respectively. That is to say, these three groups of parameters can be used to describe both the form and angularity of aggregates without being affected by each other.

To understand the influence of aggregate shape on the behavior of concrete, the form and angularity parameters should also change with the changes of aggregate shape. Fig. 12 shows that with the increase of the axis ratio (maximum axis/minimum axis) of ellipse, aspect ratio or flat and elongated ratio increases, while area ratio remains the same. However, the test results of concrete, to be discussed in Section 4, showed that the axis ratio of elliptical aggregates influences concrete strength. Therefore, area ratio cannot be used to study the influence of aggregate form on concrete mechanical properties.

Moreover, Fig. 13 shows that angularity index decreases as the side of the equilateral polygon increases, while the change of angularity using the outline slope had no obvious trend. Obviously, angularity index is more useful for investigating the effect of aggregate angularity on concrete mechanical properties.

Experimental results of concrete

It can be concluded from the above that aspect ratio and angularity index can be used for quantifying the form and the angularity of coarse aggregates independently and for studying the effect of aggregate shape on concrete mechanical properties. Therefore, in order to investigate the influence of aspect ratio and angularity index on concrete mechanical properties, ellipsoidal coarse aggregates with axial ratios of 1.25:1:1 and 1.5:1:1 were made of high borosilicate glass (HBG). HGB was used because it is easy to process and economical. Hence, the AR for these two ellipsoid coarse aggregates was 1.25 and 1.5, respectively. Moreover, spherical, cubic, and dodecahedron coarse aggregates were also made, of which the AN was 1.0, 1.11 and 1.23, respectively. The size (the length of the shortest axial) of all coarse aggregates was 18 mm, which had the same surface roughness as shown in Fig. 14.

For each kind of coarse aggregates, six 100 mm cubic concrete specimens were made and used to obtain the mechanical properties of concrete subjected to splitting tension. Local Portland cement (42.5R) was used in these tests. The water/cement ratio, the cement/sand ratio and the sand/HGB coarse aggregate ratio of concrete was 0.65, 0.49 and 0.45 (by weight), respectively.

All the specimens were cured in a room maintained at approximately 25°C with a nominal relative humidity of 100%, which was maintained for 28 days whereupon specimens were removed for testing. The splitting tensile strengths of the specimens were evaluated by the WE-30 Pressure tester.

The test results (average results for six specimens) of concrete with different aspect ratios, and angularity indices under splitting tension are shown in Fig.15. It was determined that the splitting tensile strength decreased with increases in aspect ratio (AR) or angularity index (AN) of coarse aggregates. This may be mainly attributed to the following reasons. Firstly, the interface length in concrete with a larger aspect ratio of coarse aggregates was longer, which resulted in more and longer microcracks forming along the interface. Secondly, the outline of coarse aggregate became gentler when the angularity index was smaller, which distributed the force more evenly on the aggregate and improved its ability to resist the deformation. Hence, concrete with circle/spherical aggregates provided the highest splitting tensile strength.

However, Fig. 15 shows that the splitting tensile strength for concrete with cubic aggregates where AN was equal 1.23, which was slightly higher than that for concrete with dodecahedral aggregates where AN was equal to 1.11. This may have been caused by the crushing of some cubic aggregates in concrete (Fig. 16(e)).

Finally, the macroscopic failure modes of some specimens from these tests are shown in Fig. 16. It can be observed that under splitting tension, the cracks in concrete were somewhat consistent with cracks at the interface and mortar: All of the aggregates in the specimens were intact except for some cubic aggregates where the AN was equal to1.23 (Fig. 16(e)).

Conclusions

To choose indices which can describe the aggregate form and angularity without being affected by each other and which can be used to investigate the effects of coarse aggregate shape on concrete mechanical behavior, the statistical distribution of form and angularity parameters for 200 quartzite coarse aggregates were studied. The correlations between form and angularity parameters were analyzed with results showing how these parameters can be fitted by normal or log-normal distribution at a 95% confidence level. Moreover, most parameters of form were influenced by parameters of angularity, while aspect ratio and angularity index can independently describe the form and angularity of aggregates without being influenced by each other. This study furthered the understanding of how aggregate form and angularity influences concrete mechanical properties. Finally, the influences of aspect ratio and angularity index of coarse aggregates on concrete splitting tensile strength were studied, revealing that the splitting tensile strength of concrete increased as aspect ratio or angularity index of coarse aggregates increased.

More studies are planned to determine the effect of shape and surface texture of coarse aggregates on mechanical properties of concrete materials and will be investigated in-depth.

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