A Quantitative Evaluation of Size and Shape Characteristics for Desert Sand Particles

Abstract

In this paper, the size and shape characteristics of desert sand particles were quantitatively investigated via a combination of X-CT scanning and spherical harmonics functions. The size characteristics of the desert sand particles were evaluated via the Length (L), Width (W), Thickness (T), and Volume equivalent spherical diameter (VESD). The average value of the VESD for the desert sand particle is 118.2 μm, which is much smaller than that of commonly used fine aggregate, and more than 90% particles are smaller than 150 μm. The overall shape of the desert sand particles was assessed with two aspect ratios: elongation (EI) and flatness (FI). Desert sand particles were classified into four categories: spheroid-shaped, oblate-shaped, prolate-shaped, and blade-shaped. The sphericity (S) values of the desert sand particles were distributed in a wider range, with an average sphericity of 0.85, much larger than that of commonly used fine aggregates. Through a combination of aspect ratios and sphericity analysis, it can be roughly concluded that the desert sand particles appear in more irregular shapes, but with relatively smooth surface morphology and less convex or concave parts.

1. Introduction

Concrete is essentially a kind of composite material made by blending cement, coarse and fine aggregates, supplementary powders, etc. [1]. In this process, coarse and fine aggregate may account for 60–70% of the volume. The micro and macro performances of concrete at both fresh and hardened states, especially in terms of rheological and mechanical properties [2,3,4,5], are significantly affected by the particle morphology of the aggregate [6]. River sand, with its disputed advantages of pure mineral composition, higher stiffness, and good gradation, is the most commonly used fine aggregate [7]. However, to meet the demand for accelerated urbanization in China, natural river sand has been excessively quarried, which had led to a scarcity of river sand resources [8]. Moreover, the excessive extraction of river sand has caused serious environmental issues, including increased levels of dust, riverbank erosion, shifting of river course, suspended-solids contamination, and flooding, etc. [8,9,10]. To deal with these conditions, one of the current research trends is to find an alternative for river sand, and tremendous efforts have been applied towards this endeavor [11,12,13,14]. In northwest China, there is a wide desert area of approximately 1.28 million square kilometers, and these arid zones are rich in desert or dune sand resource. Dune sand has unparalleled advantages in terms of availability, cleanliness, hardness, cost of extraction and transport [15]. Given these advantages and considering aspects such as cost and ecology, it is supremely beneficial to produce concrete with desert sand [8].

In the past few decades, extensive efforts have been devoted to exploring the potential of adopting desert sand as a substitute for river sand in concrete preparation [16,17]. Generally, desert sand particles are relatively small and are distributed in a narrower size range, even with a considerable amount of very fine particles. Typically, the weight of 25% of grains in dune sand is smaller than 150 μm, while in river sand, this figure is generally less than 6%, and as specified in ASTM C33, for fine aggregate used in concrete [9], this further leads to the difference in fineness, water absorption, and porosity in river sand. Basically, poor gradation leads to inferior packing properties in desert sand particles, and desert sand is commonly considered as being not ideal for manufacturing concrete [18]. It was commonly accepted that a superior packing density of the aggregate can effectively reduce the volume of the voids between adjacent particles and increase the ability of the paste to sufficiently fill up these voids for an improved lubrication of the particles and result in the consequently higher workability and flowability of the mortar or concrete [19]. It has been shown that the packing conditions of sand particles are closely related to its size and shape characteristics. When considering desert sand, the poor gradation of the desert sand is adverse to achieving a superior packing density, as discussed above. However, Euibae Lee’s research indicates that desert sand particles are more spherical in shape and are beneficial to obtaining a higher packing density as well as the workability of the mix at fresh state [20]. Therefore, the precise characterization of the size and shape is of particular significance for predicating the macro and micro performances of desert sand concrete. However, there are currently a few research reports focusing on the quantitative description of the desert sand particle, based on the aspects of its size and shape morphology.

There has been increased awareness of the effect of particle shape on the properties of composites in the sand gravel industry. Traditionally, a two-dimensional (2D) method, called Aggregate Imaging System (AIMS), which consists of laser scanning and digital images of aggregate particles being spread over a surface, was applied to the characterization of particle morphology [21,22]. Particle shape analysis was subsequently performed on the obtained 2D images, and some mathematical indexes were defined to describe its sphericity, angularity, and convexity [22,23,24,25,26,27,28]. For instance, a surface texture (ST) index was defined by Pan and Tutumluer [29] to quantify the surface irregularities of coarse aggregates at the pixel level. Additionally, a Fourier series method was introduced to quantitatively describe the 2D surface (perimeter) roughness and to study its effect on the bond strength of aggregate/mortar interfaces in model concretes. However, despite its convenience and relatively low cost, the 2D method can only yield limited useful information of a 3D particle and the derived shape indexes from 2D projects are highly dependent on the chosen observing directions, which may result in a non-unique shape description for a certain individual particle [7,30]. In recent years, with the development of X-ray computed tomography (X-CT), researchers are able to visualize the three-dimensional (3D) morphological characteristics of sand particles through a stack of CT slices. Following this, spherical harmonics function (SH) analysis can be derived for star-shaped particles, not only for the shape descriptors including aspect ratio, angularity, convexity, etc., but also for statistical reconstruction of the studied particle with numerical procedures [3,31,32,33]. With the combination of X-CT technique and SH function, the shape morphology of the crushed fine aggregate, cement clinker, LBS particles, and Ottawa sand particles has been quantitatively determined [7,34,35]. Inspired by the previous research, the combination of X-CT and SH function was considered and applied for the quantitative characterization of desert sand particles.

In this paper, the size and shape characteristics of desert sand particles were quantitatively investigated via X-CT scanning and reconstruction based on SH functions. In total, three samples were scanned and 2218 particles were analyzed to make sure the obtained results had statistical meaning. The results obtained indicated that desert sand particles are much smaller than commonly used fine aggregates and the particles are in more irregular shape, while the surface of desert sand particles is relatively smoother than that of other commonly used fine aggregates. The results will help to reconstruct the 3D microstructure of the concrete/mortar prepared with desert sand and lay a foundation for the predication of the macro properties of the composites.

2. Materials and Methods

2.1. Sample Preparation

The sample preparation for CT examination can be subdivided into 2 steps:

(1)

Adding a considerable amount of sand powder into the epoxy and stirring the mixture with a wooden stick for about 30 s to make sure the sand powder is well dispersed within the epoxy;

(2)

Using a vacuum pump to squeeze the mixture into a straw (1 cm in diameter) and to keep rotating the straw for 15 min to avoid the particles settling down within the epoxy.

After the epoxy has hardened, the straw was cut and used for CT examination. To make sure sufficient particles were scanned, three samples were prepared, usually on orders of 1000.

2.2. Image Acquisition and Processing

A Y.CT Precision S X-ray scanner (YXLON, Hamburg, Germany) was used for the sample scan. All three samples were scanned via X-CT without using a filter for X-ray source, since the X-ray transmission was sufficient. During the examination, the source voltage and current were set to be 50 kV and 280 µA and the sample platform could rotate for 360°. Considering the relatively smaller size of the desert sand when compared with natural river sand, the voxel size was set to be around 3 µm, and a cylindrical volume of interest (VOI) was chosen randomly within each sample for imaging. An original CT slice with a size of 1920 pixel × 1920 pixel is shown in Figure 1a, within which the brighter particles represent the desert sands. For each sample, 1120 CT slices were obtained. Thus, the imaged zone is about 6 mm in diameter and 3 mm in height, within 700–800 sand particles included in each sample. When the VOI was captured, there existed scanned particles just located on the boundary of the chosen VOI. However, via a digital image processing method, this section of the particles was assigned to the boundary pixel and was ignored for analysis. Then, the raw CT slice was segmented using the OSTU method after a series pretreatment functions including best fit function and three times 3 × 3 median filter operation to eliminate the noises and to enhance the boundary between phases for better segmentation [36,37]. Subsequently, the binary image, shown in Figure 1b, was obtained, and all CT slices were stacked together to obtain a 3D microstructure for further analysis.

2.3. Particle Characterization

Based on the obtained 3D microstructure, the spherical harmonics (SH) functions were applied for the reconstruction of the 3D particle surface. Subsequently, the 3D size parameters (i.e., volume, surface, principal dimensions) and shape descriptors (i.e., aspect ratios and sphericity) of the desert sand particles can be derived for the evaluation of 3D particle [34]. For each particle, the principal dimensions including the length L, width W, and thickness T, where L is the longest length within the particle, W is the longest length within the particle that is perpendicular to L, and T is the longest length within the particle that is perpendicular to both L and W. The exact definitions of the L, W, and T parameters for a sample desert sand particle are illustrated in Figure 2 in detail. In addition, the volume equivalent spherical diameter (VESD) of each sand particle was calculated for each particle to identify its size features. Based on the three principal dimensions, two widely used aspect ratios, i.e., the elongation index (EI = W/L) and flatness index (FI = T/W) were calculated and adopted to classify the particle shape to be spheroid, oblate, prolate, or blade [29]. Moreover, the sphericity index S was introduced to evaluate how close the particle was to spherical. According to Wadell’s research, the sphericity index S was defined as the ratio of the surface area of an equivalent sphere (with the same volume as the analyzed particle) to the measured surface area of the particle [38].

3. Results and Discussions

In this research, three samples were prepared for CT examination, and in total, 2218 desert sand particles were detected and analyzed to make sure the obtained shape and size characteristics were of statistical meaning. For all three samples, the particle counts, average values of the particle volume, surface area, and other related size and shape metrics in each sample were summarized and compared in the

Table 1. Average values of the derived size and shape metrics of the desert sand particles from three CT scans.

	Counts	V/µm3	Sp/µm2	VESD/µm	L/µm	W/µm	T/µm	W/L	T/W	S
Sample 1	798	953,561.6	50,648.7	112.5	168.8	126.2	87.3	0.75	0.70	0.85
Sample 2	800	924,851.3	49,634.4	111.2	167.2	124.8	86.3	0.75	0.70	0.85
Sample 3	620	904,093.3	49,327.8	111.6	166.7	124.6	84.9	0.76	0.70	0.86
All	2218	929,378.2	49,913.6	111.8	167.7	125.3	86.3	0.75	0.70	0.85

. It can be clearly seen that though less particles were included in Sample 3, the average values of the discussed parameters were extremely close to the other two samples. Thus, in the following section, all desert sand particles in three samples were combined and viewed as a whole for size and shape analysis. It can be seen from the Table 1 that the average volume and surface area of the desert sand particle are 929,378.2 µm³ and 49,913.6 µm², respectively. In previous research, the commonly used standard sand (Pingtan Sand, PTS) was also quantitatively evaluated via X-CT, in which the average volume and surface area of the PTS are 2.17 mm³ and 9.32 mm² [34]. Generally speaking, the desert sand particles are much smaller than the PTS, with their size being closer to the cement or SCM particles. In the following section, the size and shape characteristics are detailed and described from the aspects of other listed parameters in Table 1.

3.1. Size Information

The distributions of the parameters L, W, and T via histograms are shown in Figure 3, Figure 4 and Figure 5, respectively for all of the desert sand particles, with weighting by volume. As expected, the distribution of W is shifted towards smaller values than the L distribution, and the T distribution shifted towards smaller values than the W distribution. The distribution of all three parameters appear to be in Gaussian distribution, each with peak being around 150 μm, 110 μm, and 70 μm for L, W, and T, respectively. As listed in Table 1, the average values of L, W, and T are 167.7 μm, 125.2 μm, and 86.3 μm, respectively, which are all about 15 μm larger than that of peak values obtained from Figure 3, Figure 4 and Figure 5. This is a result of the non-symmetric nature of the L, W, and T distributions.

Figure 6 shows a similar distribution function but for the volume-equivalent spherical diameter (VESD), which is the diameter of a sphere with equivalent volume to the particle. Similar characteristics can be found in the Figure 5, as apparent in Figure 3, Figure 4 and Figure 5. It can be derived from the Figure 6 that more than 90% of desert sand particles are smaller than 150 μm. However, when we perform the sieve size test for the PTS particle, the sieve opening sizes are generally set to be >2.36 mm, 2.36–1.18 mm, 1.18–0.6 mm, 0.6–0.3 mm, 0.3–0.15 mm, and 0.15–0.075 mm, and less than 5% of the PTS particles are smaller than 150 μm. Thus, it can be concluded that desert sand particles are significantly smaller than PTS particles or river sand particles and the size of desert sand is comparable to cement or supplementary cementitious materials, i.e., fly ash and GGBS, rather than commonly used fine aggregates. The distribution of four size indexes via histogram are compared and shown in Figure 7 and it appears that the distribution of W is closest to the VESD.

3.2. Shape Characteristics

In this section, the shape characteristics evaluated based on the descriptors, i.e., FI, EI, and S, generated from SH function are presented and clarified. Moreover, the correlations between these parameters, which are considered able to describe the morphological features of desert sand particles, are explored.

3.2.1. Sphericity (S)

In this section, sphericity (S) is a shape descriptor based on volume and surface area that evaluates how a particle becomes a sphere (S = 1 for a sphere). Figure 8 presents a log–log plot of the surface area versus the volume of the desert sand particle. Figure 8 illustrates that all of the data points distribute between the lines of S = 0.60 and 0.95. Compared with the S values of the PTS particles (0.70 < S < 0.95) [34] and LBS particles (0.80 < S < 1) [7], the sphericity of desert sand particles is distributed in a wider range.

Furthermore, the volume-based distribution histogram of the S was plotted and shown in Figure 9, with (a) being the differential and (b) being the cumulative distribution curve. As the graph indicates, only 0.67% desert sand particles had sphericity smaller than 0.70, and 13.34% particles had sphericity smaller than 0.80. The average sphericity of desert sand is 0.85, slightly higher than that of Ottawa sand and PTS (0.83), obviously larger that of crushed fine aggregate (0.81) [39]. The distribution of the sphericity index indicated that desert sand particles are in a regular shape when compared with PTS particles or Ottawa sand particles.

3.2.2. Elongation (EI) and Flatness (FI)

Aspect ratios, i.e., elongation index (EI) and flatness index (FI), are parameters commonly used to describe the shape morphology of particles. Figure 10 and Figure 11 show the distribution functions for the EI and FI. The average values of EI and FI are 0.75 and 0.70, respectively. However, as presented in Su’s research, for PTS particles, the average values of EI and FI are 0.78 and 0.83 [34], respectively. It is clear that the average values of both EI and FI for desert sand particles are smaller than those of PTS particles. Moreover, for desert sand particles, the average value of EI is larger than that of FI index, suggesting that the intermediate principal size (W) is closer to the primary principle size (L) rather than the minor principle size (T), which is also different from PTS particles. Therefore, roughly speaking, desert sand particles possess a more irregular shape morphology.

Furthermore, a classification system proposed by Zingg was adopted in this study, in which the particles can be subdivided into four categories according to the values of EI and FI, i.e., spheroid (EI > 2/3 and FI > 2/3), oblate (EI > 2/3 and FI < 2/3), prolate (EI < 2/3 and FI > 2/3), and blade (EI < 2/3 and FI < 2/3) [40]. In this research, 2218 sand particles were analyzed and the results are shown in Figure 12. It can be seen that nearly half of the desert sand particles can be defined as “spheroid” (approximately 45%). Approximately 33% of the particles can be classified as “oblate”, 15% can be classified as “prolate”, and 6.31% can be classified as “blade”, while for both PTS particles and Leighton Buzzard sand particles, more than 2/3 particles were defined to be spheroid and nearly no particles belonged to the blade group [7,34].

Figure 13a–d represent the three-dimensional view of the reconstructed desert sand particles belonging to four shape categories. These are all screen shots of 3D images of the VRML file for each particle. The magnification of these images varies with each image, in order to ensure that all images appear to be about the same size on paper. For each particle, the EI, FI, and VESD values are also listed. Qualitatively, a clear difference can be seen between the different shapes. When comparing the third particle in spheroid group and the second particle in blade group, they have similar VESD values (109.71 μm vs. 108.12 μm) and totally different shapes. For these irregular sand particles, a single index, such as VSED, cannot represent a particle, and a lot of morphology information would be missed, particularly for how these particles affect fresh mortar and concrete rheology at early age.

3.2.3. Relationship between Sphericity and Aspect Ratios

As discussed in Section 3.2.2, desert sand particles can be classified into four categories according to their aspect ratios. Subsequently, the distribution of the S index for four kinds of particles (spheroid, prolate, oblate, and blade) was plotted and compared in Figure 14. The average values of the sphericity of spheroid-shaped, prolate-shaped, oblate-shaped, and blade-shaped particles are 0.89, 0.84, 0.83, and 0.77, respectively. As expected, the sphericity values of spheroid-shaped particles are much larger than those of the other three types of particles. However, it is interesting to find that the prolate-shaped and oblate-shaped particles possess close sphericity values and similar distributions, which means that the S index cannot be used to distinguish prolate-shaped and oblate-shaped particles.

In summary, the shape morphology of desert sand particles was evaluated via two different descriptors: the aspect ratios and sphericity. For S index, the average value for desert sand particle is 0.85, larger than that of PTS particles, Ottawa sand particles, and crushed fine aggregates particles, which indicates that desert sand particles are in more regular shapes. However, when comparing the aspect ratios, the average values of EI and FI of desert sand particles are both smaller than those of PTS particles, which leads to the fraction of spheroid-shaped particles being much less than that of PTS particles. Ostensibly, the descriptions of shape morphology for desert sand particles derived from aspect ratios and sphericity contradict each other.

To illustrate this problem, two pairs (group 1 and group 2) of particles with similar aspect ratio values and different sphericity values were selected and compared in Figure 14. It can be seen clearly in Figure 15a,b that the particle with a lower sphericity value appears to have a rougher surface, with many convex and concave parts. Given this, it can be roughly concluded that the aspect ratios focus more on the overall particle shape, while S is an index that tends to describe particle surface morphology.

3.3. Relationship between Size and Shape Characteristics

In this section, the desert sand particles were subdivided into five groups (<50 μm, 50–100 μm, 100–150 μm, 150–200 μm, and >200 μm) according to VESD values. The average aspect ratio values and sphericity values in each group were summarized in

Table 2. Average values of size indexes and shape descriptors of desert sand particles with different sizes.

	VESD/µm	L/µm	W/µm	T/µm	W/L	T/W	S	Fraction/%
<50 µm	45.18	68.36	49.72	34.75	0.74	0.71	0.82	2.12
50–100 µm	85.48	127.25	95.28	65.71	0.76	0.70	0.86	34.45
100–150 µm	166.12	250.97	187.63	127.85	0.76	0.69	0.85	53.88
150–200 µm	119.68	180.06	133.99	92.48	0.77	0.70	0.86	8.03

to explore the relationship between the size and shape morphology. It can be seen from Table 2 that the sphericity of particles with a VESD smaller than 50 µm are obviously smaller than particles larger than 50 µm, which indicates that particles (<50 µm) are in a more irregular shape.

4. Conclusions

In this paper, the size and shape characteristics of desert sand particles were quantitatively investigated via X-CT scanning and reconstruction based on SH functions. In total, three samples were scanned and 2218 particles were analyzed to make sure the obtained results had statistical meaning. The following conclusions can be drawn:

(1)

The size characteristics of the desert sand particles were quantitatively evaluated via the Length (L), Width (W), Thickness (T), and Volume equivalent spherical diameter (VESD). The average value of the VESD for the desert sand particle is 118.2 μm, which is much smaller than that of commonly used fine aggregate, and more than 90% particles are smaller than 150 μm.

(2)

The overall shape of the desert sand particles was assessed based on two aspect ratios: elongation (EI) and flatness (FI) and the desert sand particles were classified into four categories: spheroid-shaped, oblate-shaped, prolate-shaped, and blade-shaped, with fractions of 44.99%, 33.32%, 15.37%, and 6.31%, respectively. The average sphericity (S) of the desert sand particles is 0.85, much larger than that of PTS, Ottawa sand, or crushed fine aggregate. Based on a combination of aspect ratios and sphericity, desert sand particles appear in more of an irregular shape, but with relatively smooth surface morphology and less convex or concave parts.