- Email: [email protected]
Quantifying the distribution of paste-void spacing of hardened cement paste using X-ray computed tomography
M A TE RI A L S C HA RACT ER I ZA TI O N 73 ( 20 1 2 ) 1 3 7–1 4 3
Available online at www.sciencedirect.com
www.elsevier.com/locate/matchar
Quantifying the distribution of paste-void spacing of hardened cement paste using X-ray computed tomography Tae Sup Yuna , Kwang Yeom Kimb,⁎, Jinhyun Chooc, 1 , Dong Hun Kangd a
School of Civil and Environmental Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 120‐749, Republic of Korea Korea Institute of Construction Technology, 283 Goyangdae-ro, Ilsanseo-gu, Goyang, 411‐712, Republic of Korea c Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA d School of Civil and Environmental Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 120‐749, Republic of Korea b
AR TIC LE D ATA
ABSTR ACT
Article history:
The distribution of paste-void spacing in cement-based materials is an important feature
Received 6 April 2012
related to the freeze–thaw durability of these materials, but its reliable estimation remains
Received in revised form
an unresolved problem. Herein, we evaluate the capability of X-ray computed tomography
21 August 2012
(CT) for reliable quantification of the distribution of paste-void spacing. Using X-ray CT
Accepted 22 August 2012
images of three mortar specimens having different air-entrainment characteristics, we calculate the distributions of paste-void spacing of the specimens by applying previously
Keywords:
suggested methods for deriving the exact spacing of air-void systems. This methodology is
Cement
assessed by comparing the 95th percentile of the cumulative distribution function of the
Paste-void spacing
paste-void spacing with spacing factors computed by applying the linear-traverse method
Air voids
to 3D air-void system and reconstructing equivalent air-void distribution in 3D. Results
X-ray CT
show that the distributions of equivalent void diameter and paste-void spacing follow lognormal and normal distributions, respectively, and the ratios between the 95th percentile paste-void spacing value and the spacing factors reside within the ranges reported by previous numerical studies. This experimental finding indicates that the distribution of paste-void spacing quantified using X-ray CT has the potential to be the basis for a statistical assessment of the freeze–thaw durability of cement-based materials. © 2012 Elsevier Inc. All rights reserved.
1.
Introduction
Intrigued by the correlation between the freeze–thaw durability of cement-based materials and the microscopic configuration of entrained air [1–3], a number of studies have examined the air-void system of cement based materials in terms of the spacing factor suggested by Powers [4]. The spacing factor represents some undefined large percentile of the distribution of the paste fraction that lies within some distance of an air-void
(paste-void spacing) of an idealized air-void system. While the spacing factor has been widely used as a measure of acceptable freeze–thaw durability of concrete, the spacing factor indeed gives a single value for the entire distribution of paste-void spacing, and assumptions underlying the spacing factor result in unavoidable overestimation of the actual spacing [5]. Also, despite its original definition in three-dimensional (3D) air-void system, the spacing factor is for practical purposes estimated via two-dimensional (2D) stereological approaches: therefore, it
⁎ Corresponding author. Tel.: +82 10 3426 1321; fax: + 82 31 910 0211. E-mail addresses: [email protected] (T.S. Yun), [email protected] (K.Y. Kim), [email protected] (J. Choo), [email protected] (D.H. Kang). 1 Formerly Research Specialist, Korea Institute of Construction Technology, 283 Goyangdae-ro, Ilsanseo-gu, Goyang, 411‐712, Republic of Korea. 1044-5803/$ – see front matter © 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.matchar.2012.08.008
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does not take into account the 3D characteristics of the air-void system. To overcome these limitations, a few studies proposed alternative spacing equations for characterizing the distribution of paste-void spacing [6,7]. However, when the distribution of paste-void spacing of the numerically simulated air-void systems was compared using these alternative spacing equations, none of the equations was able to capture the exact distribution [8,9]. Moreover, in these numerical tests, the spacing factor significantly exceeded even the 95th percentile of the cumulative density function (CDF) of the spacing distribution unless the voids were mono-sized. In this regard, reliable estimation of the distribution of paste-void spacing and its representative value remains an unresolved problem. In this paper, we evaluate the capability of X-ray computed tomography (CT) for reliable characterization of the distribution of paste-void spacing in cement-based materials. We obtain X-ray CT images of the internal microstructure of mortar specimens composed of different air-void systems. The distributions of paste-void spacing in the specimens are then calculated by applying the method used for deriving the exact spacing of numerical air-void systems [8] to the reconstructed CT images. Referring to previously reported relationship between the 95th percentile values of the CDF for paste-void spacing and the spacing factors [8,9], we compute and compare the 95th percentile value of the CDF of paste-void spacing distribution with spacing factors obtained by the ASTM C457 [10]. Based on this comparison, we discuss the potential of X-ray CT based quantification of the pastevoid spacing distribution as a new measure of the freeze–thaw durability of cement-based materials.
2.
Materials, CT Imaging, and Image Processing
2.1.
Materials
of 3% and 8% of the cement weight, respectively. Sodium lauryl ether sulfate (SLES) was added (as synthetic anionic AEA) to the AE specimens. It was anticipated that the AEA would facilitate the formation of a more uniform air-void configuration compared with that in the Non-AE specimen in terms of air-void distribution, shape, and size. Each specimen was cast in a cylindrical container (diameter, 100 mm; height, 200 mm) for 7 days, after 24 h of moist conditioning. Specimens were then trimmed to a cylinder shape (diameter, 12 mm; height, 10 mm) prior to X-ray CT imaging.
2.2.
The X-ray CT images of the specimens were obtained using an X-EYE CT System (SEC Corporation, Korea) equipped with a microfocus X-ray tube capable of attaining high spatial resolution up to 6.18 μm3. The voltage and current used in this study were 150 kV and 100 μA, respectively (the maximum values of the system are 225 kV and 3.0 mA, respectively). As a flat-panel detector, a CCD camera collected X-ray attenuation information upon irradiation. The detector measured 409.6 × 409.6 mm with a pixel pitch of 200 μm and 2.5 lp/mm (line pairs per millimeter) of limiting resolution. The maximum wobbling allowance of the manipulator was set to be 5 μm to ensure the correct rotational mode. The image had a pixel size of 0.0108× 0.0108 mm (dx= dy) with 1024 × 1024 pixels. A total of 1024 section images (1024 × 1024 pixels for each image) were obtained at intervals of 0.00868 mm (dz).
2.3.
Image Processing
Fig. 1a shows a raw CT image in which dark color denotes air voids and the gray region denotes cement matrix (i.e., mixture of paste and sands). Segmentation of air voids from the cement matrix is performed by image thresholding (i.e., binarization). Given the varied distribution of pixel values in each 2D image, the Otsu's method [11] was adopted to determine the threshold value in each image. In addition to thresholding, we eliminated various degrading artifacts embedded in the raw CT images that inevitably occur during the image acquisition and reconstruction processes [12,13]. In particular, ring artifacts were
Three mortar specimens, named Non-AE, AE-1, and AE-2, were each prepared by mixing 510 g of cement, 247.4 g of water, and 1250 g of fine sand (water-to-cement ratio, 0.485). The Non-AE (air-entrained) specimen was mixed without any air-entrained agent (AEA), whereas AE-1 and AE-2 specimens contained AEA
(a)
(b)
0
250
200
2.76
Length [mm]
Devices
150 5.52 100 8.28
11.04
50
0 0
2.76
5.52
8.28
Length [mm]
11.04
9.44 mm
Fig. 1 – X-ray CT images. (a) Raw section image (dark color: air voids; gray color: cement matrix; dashed line: region of interest (ROI) with the diameter of 9.44 mm). (b) Binary image after noise reduction.
M A TE RI A L S C HA RACT ER I ZA TI O N 73 ( 20 1 2 ) 1 3 7–1 4 3
(a) Non-AE
(b) AE-1
139
(c) AE-2
8.89 mm
9.44 mm
9.44 mm
Fig. 2 – 3D configuration of the specimens, Non-AE, AE-1, and AE-2. The upper images show the internal configuration of original specimens. The air voids illustrated in the lower section exist within 9.44 mm diameter and 8.89 mm height.
calibrated using a series of noise reduction techniques, including coordinate transformation, low-frequency filter, and Fourier transformation, as described in [14]. Fig. 1b shows the binary CT image after noise reduction. Following the segmentation of the air-void pixels via these image-processing techniques, the 3D voxel structure of each specimen was constructed by stacking the set of 1024 2D sectional images along its height. In Fig. 2, 3D views of the specimens and their air-void configurations show clear differences in the amounts of entrained air voids within three specimens. The connectivity among air-void pixels by considering 26 neighboring pixels was evaluated and the connected air-void pixels were regarded as individual air-void objects. This approach enabled quantification of the total number of air-void objects, the number of pixels comprising each object (i.e., the volume of each air-void), and the distribution of equivalently sized air voids. Table 1 summarizes the number of air-void objects and the arithmetic mean values of air-void volume and equivalent air-void diameter.
3. Characterization of Paste-void Spacing Distribution 3.1.
Calculation of Paste-void Spacing
In this study, the distribution of paste-void spacing is obtained by applying the method for calculating the exact spacing of a numerical air-void system [8] to the 3D air-void system imaged by X-ray CT (Fig. 2). A large number of points (i.e., pixels) are randomly selected within an area outside the voids and the distance from each point to its nearest air-void surface is
Table 1 – Air-void characteristics of the specimens. Non‐AE
AE‐1
AE‐2
Number of air 1422 8145 12,768 void object 0.0131013 0.0046396 0.0036598 Average air void volume [mm3] Average of 0.1358501 0.0992645 0.0931464 equivalent air void diameter [mm]
Fig. 3 – Evolution of the 95th percentile of the distribution of paste-void spacing for three tested specimens with increasing number of randomly selected points.
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measured. When calculating the paste-void spacing in binary images like Fig. 1b, the length of paste should not include distances passed through aggregate (i.e., sands should be excluded). For this purpose, we consider the volume fraction of mortar specimen based on mix design, following the conventional practice to determine the spacing factor. The calculation of the volume fraction of each constituent leads that the paste comprises 46.5% of the paste plus aggregate (i.e., sands in this study) volume: thus, the paste-void spacing value is obtained by multiplying the distance between the randomly selected paste pixel and nearest air-void surface by 0.465. While the previous numerical study used 1000 points for this method [8], this study compares the distributions obtained from various
numbers of points to optimize the number of random points. The evolution of the distribution for an increasing number of points is examined in terms of the 95th percentile of the CDF of paste-void spacing distribution in which the probability function can be regarded as flat. It is noted that when the 95th percentile was used in previous studies as a representative value of the distribution, the value coincided to the spacing factor in a numerical air-void system composed of mono-sized air voids [8,9]. The 95th percentile value tends to converge to the asymptotic value as the number of selected points increases for tested specimens (Fig. 3). Therefore, we present and discuss the distribution of paste-void spacing for 10,000 points randomly distributed in the paste of each specimen. Note that
(a) Non-AE
(b) AE-1
(c) AE-2
Fig. 4 – Probability density distribution (bar plot) and cumulative distribution function (open circles) of equivalent void diameter and paste-void spacing. Statistically fitted distribution curves are shown as solid lines. The paste-void spacing was obtained from 10,000 random points selected within the paste.
M A TE RI A L S C HA RACT ER I ZA TI O N 73 ( 20 1 2 ) 1 3 7–1 4 3
Table 2 – Statistical properties of the 95th percentile value of CDF from 20 realizations.
4.
Unit: [mm]
Mean Maximum Minimum Standard deviation
Non‐AE
AE‐1
0.166 0.171 0.163 1.83 × 10−3
0.133 0.135 0.131 1.02 × 10−3
0.324 0.329 0.319 2.08 × 10−3
4.1. Estimation of Spacing Factor by the Linear-traverse Method in 3D
Statistical Evaluation of Paste-void Distributions
Fig. 4 shows the probability density functions (PDFs) (columns) and corresponding CDFs (open circles) of the equivalent void diameter and paste-void spacing of each specimen. The distribution of equivalent void diameter is examined because the ratio of the spacing factor to the 95th percentile of the CDF of paste-void spacing depends on the type of void-size distribution [9]. The solid lines in Fig. 4 indicate that the equivalent void diameter follows a log-normal distribution, and hence the spacing factor may be more than 1.5 times the 95th percentile, according to [9]. Reasonable consideration of the distribution type of paste-void spacing is also important because the value at a specific percentile of the CDF (e.g., the 95th percentile) is significantly affected by the type of PDF for fitting the distribution. For the sake of simplicity, a range of widely known PDFs are considered rather than introducing a new PDF. We find that a normal distribution can properly represent the distribution of paste-void spacing, compared to other PDFs, as shown in Fig. 4. Based on these statistical characterizations, we extract the 95th percentile of the CDF of paste-void spacing distribution; this distribution is then compared with values obtained using the Powers spacing factor, as employed in previous studies [8,9]. Table 2 summarizes the statistical properties of the 95th percentile values obtained by 20 realizations of the procedure described in Section 3.1. Note that the variations in the 95th percentile values can be regarded very small.
(a)
Comparison with Powers Spacing Factors
In this section, we compare the 95th percentile of the CDF of paste-void spacing obtained by X-ray CT with the Powers spacing factors.
AE‐2
10,000 points correspond to ~1.62⋅ 10−3% of total volume of the specimens.
3.2.
141
The linear-traverse method for determining spacing factor, described in the ASTM C457 [10], is directly applied to the 3D air-void system of the same specimens imaged by X-ray CT whereas the current application is limited to 2D polished section. Randomly oriented lines are drawn through the 3D stacked image voxel structure, as shown in Fig. 5a, and the number and length of air voids intersected are computed along each line, as illustrated in Fig. 5b. The air-void pixels are determined by interpolating eight neighboring pixels in 3D. Then, the total length of traverse line Tt, the number of air voids intersected, the length of air voids Ta, and the length of paste Tp considering the mixture ratio as described in Section 3.1 (e.g., Tp = (Tt − Ta)⋅0.465) are obtained to compute the spacing factor. This procedure is iterated 1000 times, and variations in the spacing factor are calculated with respect to increasing total traversed length. Fig. 6 shows that for all specimens, the estimated spacing factors approach specific asymptotic values as the total length of traverse lines increases. The performance of 20 realizations of the lineartraverse method reveals that sampling effect on the spacing factor is marginal.
4.2.
Estimation of Spacing Factor by Idealizing Air Voids
As the number of individual air-void objects and the volume of air-void are known in 3D, it is feasible that the mono-dispersed spherical air voids equally spaced in a cubic assembly of the same volume are reconstructed to estimate the spacing factor as the ratio of the paste volume fraction to the air-void fraction is larger than 4.342. The calculation of the spacing factor by idealizing the air-void system is straightforward using CT images of the 3D microstructural configuration of specimens.
(b)
Fig. 5 – Implementation of the linear-traverse method for the 3D air-void system shown in Fig. 2. (a) Schematic illustration of randomly oriented linear traverse lines crossing the air voids. (b) Determination of the length and number of air voids intersected by the traverse line.
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M A TE RI A L S CH A RACT ER IZ A TI O N 73 (2 0 1 2 ) 1 3 7–1 4 3
(a) Non-AE
Table 3 – Comparison of the 95th percentile value of CDF with Powers spacing factors. Unit: [mm]
Paste-void spacing at the 95th percentile Spacing factor Linear‐traverse in 3D Idealized air void
(b) AE-1
(c) AE-2
Non‐AE
AE‐1
AE‐2
0.331
0.168
0.134
0.418 0.483
0.233 0.265
0.162 0.226
plotted in Fig. 7. Regardless of air-entrainment characteristics, two spacing factors estimated by the ASTM C457 (e.g., direct application of 3D linear traverse method and idealized air void) are larger than the paste-void spacing of the 95th percentile. The ratio of paste-void spacing at the 95th percentile ranged from 1.20 to 1.67, which is analogous to previous results obtained from a numerical air-void system in which void diameter followed a lognormal distribution [9]. This comparison indicates that X-ray CT possesses a sufficient capability for reliable extraction of the paste-void spacing distribution from real hardened cement paste, and can therefore be considered as an alternative tool for evaluating the freeze–thaw durability of cement-based materials. In addition, as shown in Fig. 7, the 95th percentile values and the spacing factors appear to have linear relationships. This linearity implies that the spacing factor may provide a consistent result for representing the paste-void spacing distribution of cement-based materials. The slight underestimated paste-void spacing values compared with spacing factors in this study may be attributed to the fact that we simply multiplied 0.465, considering mixture ratio, with computed paste-void spacing. As the shortest path traveled from the randomly selected point to the edge of the nearest air-void does not necessarily pass through aggregates, this approximation may tend to underestimate the true distance. Yet, the
Fig. 6 – Variation in the spacing factor according to the total length of traverse lines.
The linear traverse method shares the same concept of 3D idealized air void system proposed by Powers [4]. Yet, the implementation of 3D linear traverse method in Section 4.1 and idealizing air void system in 3D are doable using 3D X-ray CT images to assess spacing factors. Note that well-known equations for stereological determination of the spacing factor are based on this idealized system [4,5,8].
4.3.
Discussion
Table 3 shows the 95th percentile values of the CDF for paste-void spacing and the spacing factors determined by 3D linear traverse approach and idealized air void system, as
Fig. 7 – Comparison between the 95th percentile of the distribution of paste-void spacing and the spacing factors obtained by the linear traverse method and idealizing air voids.
M A TE RI A L S C HA RACT ER I ZA TI O N 73 ( 20 1 2 ) 1 3 7–1 4 3
effect of assumed simplification originated from mixture ratio multiplication prevails in the computation of both paste-void spacing and spacing factors. Nevertheless, it is postulated that the 95th percentile values can be considered as more reliable parameters than the spacing factors because the spacing factors, which are 3D measures, have been estimated by 2D stereological methods. Also, the results of this study show the evidence that the spacing factor inherently exceeds even a very large percentile of the distribution, as stated previously based on numerical tests [8,9]. Therefore, the capability of X-ray CT for quantifying the distribution of paste-void spacing provides an opportunity to develop a statistical approach for the assessment of freeze–thaw durability of cement-based materials.
5.
Conclusions
This paper has described an experimental evaluation of X-ray CT as a tool for quantifying the distribution of paste-void spacing in cement-based materials. The internal microstructure of three mortar specimens prepared with different airentrainments was imaged by 3D X-ray CT, and distributions of paste-void spacing of the specimens were obtained by calculating the distance from randomly distributed points outside air voids to their nearest void surfaces. We show that stable results can be achieved when the number of points exceeds ~10,000 (1.63⋅ 10−3% of total volume of the specimens) in this study, and the distributions of equivalent void diameter and paste-void spacing follow lognormal and normal distributions, respectively. We validate the X-ray CT based methodology by comparing the 95th percentile of the CDF of the paste-void spacing distribution with the Powers spacing factors. Results show that the spacing factors estimated by the ASTM C457 and Powers [4] are 1.20 to 1.67 times larger than the 95th percentile paste-void spacing value, similarly corroborated by previous numerical studies. The experimental finding presented herein indicates that the distribution of paste-void spacing quantified using X-ray CT has the potential to be the basis for developing a statistical assessment of the freeze–thaw durability of cementbased materials based on 3D air-void configuration, despite simplification imposed during computation. Due to the imaging capability of the X-ray CT device available for this study, relatively small specimens containing sands were used. Since the spatial resolution of CT image depends on the specimen size, it might be challenging to characterize specimens with coarse aggregates by this methodology. Nevertheless, the potential applications by high resolution CT images are wide open for quantifying the paste-void spacing truly as 3D measures to overcome current methods.
Acknowledgments Financial support for this work was provided by grants from the Basic Science Research Program of the National Research
143
Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (Nos. 2011‐0022883 and 2011‐0005593), and a grant from the New & Renewable Energy program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), funded by the Korean Government Ministry of Knowledge Economy (No. 2010T100200494).
REFERENCES [1] Gonnermann HF. Tests of concretes containing air-entraining Portland cements or air-entraining materials added to batch at mixer. J Am Concr Inst 1944;15:477-507. [2] Klieger P. Effect of entrained air on the strength and durability of concretes made with various maximum sizes of aggregate. Proc Highw Res Board 1952;31:1952. [3] Cordon WA, Merrill D. Requirements for freezing and thawing durability for concrete; 1963. [4] Powers TC. The air requirement of frost-resistant concrete. Proc Highw Res Board 1949;29:184-211. [5] Pleau R, Pigeon M, Laurencot J-L. Some findings on the usefulness of image analysis for determining the characteristics of the air-void system on hardened concrete. Cem Concr Compos 2001;23:237-46. [6] Philleo RE. A method for analyzing void distribution in air-entrained concrete. Cem Concr Aggregates 1983;5:128-30. [7] Pleau R, Pigeon M. The use of the flow length concept to assess the efficiency of air entrainment with regards to frost durability: Part I—description of the test method. Cem Concr Aggregates 1996;18:19-29. [8] Snyder KA. A numerical test of air void spacing equations. Adv Cem Based Mater 1998;8:28-44. [9] Snyder KA. Estimating the 95th percentile of the paste-void spacing distribution in hardened cement paste containing air entrainment. International RILEM Workshop on Frost Damage in Concrete (PRO 25); 1999. [10] American Society of Testing and Materials (ASTM). ASTM C457: standard test method for microscopical determination of parameters of the air-void system in hardened concrete; 2010. [11] Otsu N. A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern 1979;9:62-6. [12] Hiriyannaiah HP. X-ray computed tomography for medical imaging. IEEE Signal Process Mag 1997;14:42-59. [13] Bernard D, Chirazi A. Numerically enhanced microtomographic imaging method using a novel ring artifact filter. In: Desrues J, Viggiani G, Besuelle P, editors. Advances in X-ray tomography for geomaterials; 2006. [14] Kim KY, Yun TS, Choo J, Kang DH, Shin HS. Determination of air-void parameters of hardened cement-based materials using X-ray computed tomography. Construction and Building Materials 2012;37:93–101.
Available online at www.sciencedirect.com
www.elsevier.com/locate/matchar
Quantifying the distribution of paste-void spacing of hardened cement paste using X-ray computed tomography Tae Sup Yuna , Kwang Yeom Kimb,⁎, Jinhyun Chooc, 1 , Dong Hun Kangd a
School of Civil and Environmental Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 120‐749, Republic of Korea Korea Institute of Construction Technology, 283 Goyangdae-ro, Ilsanseo-gu, Goyang, 411‐712, Republic of Korea c Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA d School of Civil and Environmental Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 120‐749, Republic of Korea b
AR TIC LE D ATA
ABSTR ACT
Article history:
The distribution of paste-void spacing in cement-based materials is an important feature
Received 6 April 2012
related to the freeze–thaw durability of these materials, but its reliable estimation remains
Received in revised form
an unresolved problem. Herein, we evaluate the capability of X-ray computed tomography
21 August 2012
(CT) for reliable quantification of the distribution of paste-void spacing. Using X-ray CT
Accepted 22 August 2012
images of three mortar specimens having different air-entrainment characteristics, we calculate the distributions of paste-void spacing of the specimens by applying previously
Keywords:
suggested methods for deriving the exact spacing of air-void systems. This methodology is
Cement
assessed by comparing the 95th percentile of the cumulative distribution function of the
Paste-void spacing
paste-void spacing with spacing factors computed by applying the linear-traverse method
Air voids
to 3D air-void system and reconstructing equivalent air-void distribution in 3D. Results
X-ray CT
show that the distributions of equivalent void diameter and paste-void spacing follow lognormal and normal distributions, respectively, and the ratios between the 95th percentile paste-void spacing value and the spacing factors reside within the ranges reported by previous numerical studies. This experimental finding indicates that the distribution of paste-void spacing quantified using X-ray CT has the potential to be the basis for a statistical assessment of the freeze–thaw durability of cement-based materials. © 2012 Elsevier Inc. All rights reserved.
1.
Introduction
Intrigued by the correlation between the freeze–thaw durability of cement-based materials and the microscopic configuration of entrained air [1–3], a number of studies have examined the air-void system of cement based materials in terms of the spacing factor suggested by Powers [4]. The spacing factor represents some undefined large percentile of the distribution of the paste fraction that lies within some distance of an air-void
(paste-void spacing) of an idealized air-void system. While the spacing factor has been widely used as a measure of acceptable freeze–thaw durability of concrete, the spacing factor indeed gives a single value for the entire distribution of paste-void spacing, and assumptions underlying the spacing factor result in unavoidable overestimation of the actual spacing [5]. Also, despite its original definition in three-dimensional (3D) air-void system, the spacing factor is for practical purposes estimated via two-dimensional (2D) stereological approaches: therefore, it
⁎ Corresponding author. Tel.: +82 10 3426 1321; fax: + 82 31 910 0211. E-mail addresses: [email protected] (T.S. Yun), [email protected] (K.Y. Kim), [email protected] (J. Choo), [email protected] (D.H. Kang). 1 Formerly Research Specialist, Korea Institute of Construction Technology, 283 Goyangdae-ro, Ilsanseo-gu, Goyang, 411‐712, Republic of Korea. 1044-5803/$ – see front matter © 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.matchar.2012.08.008
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M A TE RI A L S CH A RACT ER IZ A TI O N 73 (2 0 1 2 ) 1 3 7–1 4 3
does not take into account the 3D characteristics of the air-void system. To overcome these limitations, a few studies proposed alternative spacing equations for characterizing the distribution of paste-void spacing [6,7]. However, when the distribution of paste-void spacing of the numerically simulated air-void systems was compared using these alternative spacing equations, none of the equations was able to capture the exact distribution [8,9]. Moreover, in these numerical tests, the spacing factor significantly exceeded even the 95th percentile of the cumulative density function (CDF) of the spacing distribution unless the voids were mono-sized. In this regard, reliable estimation of the distribution of paste-void spacing and its representative value remains an unresolved problem. In this paper, we evaluate the capability of X-ray computed tomography (CT) for reliable characterization of the distribution of paste-void spacing in cement-based materials. We obtain X-ray CT images of the internal microstructure of mortar specimens composed of different air-void systems. The distributions of paste-void spacing in the specimens are then calculated by applying the method used for deriving the exact spacing of numerical air-void systems [8] to the reconstructed CT images. Referring to previously reported relationship between the 95th percentile values of the CDF for paste-void spacing and the spacing factors [8,9], we compute and compare the 95th percentile value of the CDF of paste-void spacing distribution with spacing factors obtained by the ASTM C457 [10]. Based on this comparison, we discuss the potential of X-ray CT based quantification of the pastevoid spacing distribution as a new measure of the freeze–thaw durability of cement-based materials.
2.
Materials, CT Imaging, and Image Processing
2.1.
Materials
of 3% and 8% of the cement weight, respectively. Sodium lauryl ether sulfate (SLES) was added (as synthetic anionic AEA) to the AE specimens. It was anticipated that the AEA would facilitate the formation of a more uniform air-void configuration compared with that in the Non-AE specimen in terms of air-void distribution, shape, and size. Each specimen was cast in a cylindrical container (diameter, 100 mm; height, 200 mm) for 7 days, after 24 h of moist conditioning. Specimens were then trimmed to a cylinder shape (diameter, 12 mm; height, 10 mm) prior to X-ray CT imaging.
2.2.
The X-ray CT images of the specimens were obtained using an X-EYE CT System (SEC Corporation, Korea) equipped with a microfocus X-ray tube capable of attaining high spatial resolution up to 6.18 μm3. The voltage and current used in this study were 150 kV and 100 μA, respectively (the maximum values of the system are 225 kV and 3.0 mA, respectively). As a flat-panel detector, a CCD camera collected X-ray attenuation information upon irradiation. The detector measured 409.6 × 409.6 mm with a pixel pitch of 200 μm and 2.5 lp/mm (line pairs per millimeter) of limiting resolution. The maximum wobbling allowance of the manipulator was set to be 5 μm to ensure the correct rotational mode. The image had a pixel size of 0.0108× 0.0108 mm (dx= dy) with 1024 × 1024 pixels. A total of 1024 section images (1024 × 1024 pixels for each image) were obtained at intervals of 0.00868 mm (dz).
2.3.
Image Processing
Fig. 1a shows a raw CT image in which dark color denotes air voids and the gray region denotes cement matrix (i.e., mixture of paste and sands). Segmentation of air voids from the cement matrix is performed by image thresholding (i.e., binarization). Given the varied distribution of pixel values in each 2D image, the Otsu's method [11] was adopted to determine the threshold value in each image. In addition to thresholding, we eliminated various degrading artifacts embedded in the raw CT images that inevitably occur during the image acquisition and reconstruction processes [12,13]. In particular, ring artifacts were
Three mortar specimens, named Non-AE, AE-1, and AE-2, were each prepared by mixing 510 g of cement, 247.4 g of water, and 1250 g of fine sand (water-to-cement ratio, 0.485). The Non-AE (air-entrained) specimen was mixed without any air-entrained agent (AEA), whereas AE-1 and AE-2 specimens contained AEA
(a)
(b)
0
250
200
2.76
Length [mm]
Devices
150 5.52 100 8.28
11.04
50
0 0
2.76
5.52
8.28
Length [mm]
11.04
9.44 mm
Fig. 1 – X-ray CT images. (a) Raw section image (dark color: air voids; gray color: cement matrix; dashed line: region of interest (ROI) with the diameter of 9.44 mm). (b) Binary image after noise reduction.
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(a) Non-AE
(b) AE-1
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(c) AE-2
8.89 mm
9.44 mm
9.44 mm
Fig. 2 – 3D configuration of the specimens, Non-AE, AE-1, and AE-2. The upper images show the internal configuration of original specimens. The air voids illustrated in the lower section exist within 9.44 mm diameter and 8.89 mm height.
calibrated using a series of noise reduction techniques, including coordinate transformation, low-frequency filter, and Fourier transformation, as described in [14]. Fig. 1b shows the binary CT image after noise reduction. Following the segmentation of the air-void pixels via these image-processing techniques, the 3D voxel structure of each specimen was constructed by stacking the set of 1024 2D sectional images along its height. In Fig. 2, 3D views of the specimens and their air-void configurations show clear differences in the amounts of entrained air voids within three specimens. The connectivity among air-void pixels by considering 26 neighboring pixels was evaluated and the connected air-void pixels were regarded as individual air-void objects. This approach enabled quantification of the total number of air-void objects, the number of pixels comprising each object (i.e., the volume of each air-void), and the distribution of equivalently sized air voids. Table 1 summarizes the number of air-void objects and the arithmetic mean values of air-void volume and equivalent air-void diameter.
3. Characterization of Paste-void Spacing Distribution 3.1.
Calculation of Paste-void Spacing
In this study, the distribution of paste-void spacing is obtained by applying the method for calculating the exact spacing of a numerical air-void system [8] to the 3D air-void system imaged by X-ray CT (Fig. 2). A large number of points (i.e., pixels) are randomly selected within an area outside the voids and the distance from each point to its nearest air-void surface is
Table 1 – Air-void characteristics of the specimens. Non‐AE
AE‐1
AE‐2
Number of air 1422 8145 12,768 void object 0.0131013 0.0046396 0.0036598 Average air void volume [mm3] Average of 0.1358501 0.0992645 0.0931464 equivalent air void diameter [mm]
Fig. 3 – Evolution of the 95th percentile of the distribution of paste-void spacing for three tested specimens with increasing number of randomly selected points.
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measured. When calculating the paste-void spacing in binary images like Fig. 1b, the length of paste should not include distances passed through aggregate (i.e., sands should be excluded). For this purpose, we consider the volume fraction of mortar specimen based on mix design, following the conventional practice to determine the spacing factor. The calculation of the volume fraction of each constituent leads that the paste comprises 46.5% of the paste plus aggregate (i.e., sands in this study) volume: thus, the paste-void spacing value is obtained by multiplying the distance between the randomly selected paste pixel and nearest air-void surface by 0.465. While the previous numerical study used 1000 points for this method [8], this study compares the distributions obtained from various
numbers of points to optimize the number of random points. The evolution of the distribution for an increasing number of points is examined in terms of the 95th percentile of the CDF of paste-void spacing distribution in which the probability function can be regarded as flat. It is noted that when the 95th percentile was used in previous studies as a representative value of the distribution, the value coincided to the spacing factor in a numerical air-void system composed of mono-sized air voids [8,9]. The 95th percentile value tends to converge to the asymptotic value as the number of selected points increases for tested specimens (Fig. 3). Therefore, we present and discuss the distribution of paste-void spacing for 10,000 points randomly distributed in the paste of each specimen. Note that
(a) Non-AE
(b) AE-1
(c) AE-2
Fig. 4 – Probability density distribution (bar plot) and cumulative distribution function (open circles) of equivalent void diameter and paste-void spacing. Statistically fitted distribution curves are shown as solid lines. The paste-void spacing was obtained from 10,000 random points selected within the paste.
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Table 2 – Statistical properties of the 95th percentile value of CDF from 20 realizations.
4.
Unit: [mm]
Mean Maximum Minimum Standard deviation
Non‐AE
AE‐1
0.166 0.171 0.163 1.83 × 10−3
0.133 0.135 0.131 1.02 × 10−3
0.324 0.329 0.319 2.08 × 10−3
4.1. Estimation of Spacing Factor by the Linear-traverse Method in 3D
Statistical Evaluation of Paste-void Distributions
Fig. 4 shows the probability density functions (PDFs) (columns) and corresponding CDFs (open circles) of the equivalent void diameter and paste-void spacing of each specimen. The distribution of equivalent void diameter is examined because the ratio of the spacing factor to the 95th percentile of the CDF of paste-void spacing depends on the type of void-size distribution [9]. The solid lines in Fig. 4 indicate that the equivalent void diameter follows a log-normal distribution, and hence the spacing factor may be more than 1.5 times the 95th percentile, according to [9]. Reasonable consideration of the distribution type of paste-void spacing is also important because the value at a specific percentile of the CDF (e.g., the 95th percentile) is significantly affected by the type of PDF for fitting the distribution. For the sake of simplicity, a range of widely known PDFs are considered rather than introducing a new PDF. We find that a normal distribution can properly represent the distribution of paste-void spacing, compared to other PDFs, as shown in Fig. 4. Based on these statistical characterizations, we extract the 95th percentile of the CDF of paste-void spacing distribution; this distribution is then compared with values obtained using the Powers spacing factor, as employed in previous studies [8,9]. Table 2 summarizes the statistical properties of the 95th percentile values obtained by 20 realizations of the procedure described in Section 3.1. Note that the variations in the 95th percentile values can be regarded very small.
(a)
Comparison with Powers Spacing Factors
In this section, we compare the 95th percentile of the CDF of paste-void spacing obtained by X-ray CT with the Powers spacing factors.
AE‐2
10,000 points correspond to ~1.62⋅ 10−3% of total volume of the specimens.
3.2.
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The linear-traverse method for determining spacing factor, described in the ASTM C457 [10], is directly applied to the 3D air-void system of the same specimens imaged by X-ray CT whereas the current application is limited to 2D polished section. Randomly oriented lines are drawn through the 3D stacked image voxel structure, as shown in Fig. 5a, and the number and length of air voids intersected are computed along each line, as illustrated in Fig. 5b. The air-void pixels are determined by interpolating eight neighboring pixels in 3D. Then, the total length of traverse line Tt, the number of air voids intersected, the length of air voids Ta, and the length of paste Tp considering the mixture ratio as described in Section 3.1 (e.g., Tp = (Tt − Ta)⋅0.465) are obtained to compute the spacing factor. This procedure is iterated 1000 times, and variations in the spacing factor are calculated with respect to increasing total traversed length. Fig. 6 shows that for all specimens, the estimated spacing factors approach specific asymptotic values as the total length of traverse lines increases. The performance of 20 realizations of the lineartraverse method reveals that sampling effect on the spacing factor is marginal.
4.2.
Estimation of Spacing Factor by Idealizing Air Voids
As the number of individual air-void objects and the volume of air-void are known in 3D, it is feasible that the mono-dispersed spherical air voids equally spaced in a cubic assembly of the same volume are reconstructed to estimate the spacing factor as the ratio of the paste volume fraction to the air-void fraction is larger than 4.342. The calculation of the spacing factor by idealizing the air-void system is straightforward using CT images of the 3D microstructural configuration of specimens.
(b)
Fig. 5 – Implementation of the linear-traverse method for the 3D air-void system shown in Fig. 2. (a) Schematic illustration of randomly oriented linear traverse lines crossing the air voids. (b) Determination of the length and number of air voids intersected by the traverse line.
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(a) Non-AE
Table 3 – Comparison of the 95th percentile value of CDF with Powers spacing factors. Unit: [mm]
Paste-void spacing at the 95th percentile Spacing factor Linear‐traverse in 3D Idealized air void
(b) AE-1
(c) AE-2
Non‐AE
AE‐1
AE‐2
0.331
0.168
0.134
0.418 0.483
0.233 0.265
0.162 0.226
plotted in Fig. 7. Regardless of air-entrainment characteristics, two spacing factors estimated by the ASTM C457 (e.g., direct application of 3D linear traverse method and idealized air void) are larger than the paste-void spacing of the 95th percentile. The ratio of paste-void spacing at the 95th percentile ranged from 1.20 to 1.67, which is analogous to previous results obtained from a numerical air-void system in which void diameter followed a lognormal distribution [9]. This comparison indicates that X-ray CT possesses a sufficient capability for reliable extraction of the paste-void spacing distribution from real hardened cement paste, and can therefore be considered as an alternative tool for evaluating the freeze–thaw durability of cement-based materials. In addition, as shown in Fig. 7, the 95th percentile values and the spacing factors appear to have linear relationships. This linearity implies that the spacing factor may provide a consistent result for representing the paste-void spacing distribution of cement-based materials. The slight underestimated paste-void spacing values compared with spacing factors in this study may be attributed to the fact that we simply multiplied 0.465, considering mixture ratio, with computed paste-void spacing. As the shortest path traveled from the randomly selected point to the edge of the nearest air-void does not necessarily pass through aggregates, this approximation may tend to underestimate the true distance. Yet, the
Fig. 6 – Variation in the spacing factor according to the total length of traverse lines.
The linear traverse method shares the same concept of 3D idealized air void system proposed by Powers [4]. Yet, the implementation of 3D linear traverse method in Section 4.1 and idealizing air void system in 3D are doable using 3D X-ray CT images to assess spacing factors. Note that well-known equations for stereological determination of the spacing factor are based on this idealized system [4,5,8].
4.3.
Discussion
Table 3 shows the 95th percentile values of the CDF for paste-void spacing and the spacing factors determined by 3D linear traverse approach and idealized air void system, as
Fig. 7 – Comparison between the 95th percentile of the distribution of paste-void spacing and the spacing factors obtained by the linear traverse method and idealizing air voids.
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effect of assumed simplification originated from mixture ratio multiplication prevails in the computation of both paste-void spacing and spacing factors. Nevertheless, it is postulated that the 95th percentile values can be considered as more reliable parameters than the spacing factors because the spacing factors, which are 3D measures, have been estimated by 2D stereological methods. Also, the results of this study show the evidence that the spacing factor inherently exceeds even a very large percentile of the distribution, as stated previously based on numerical tests [8,9]. Therefore, the capability of X-ray CT for quantifying the distribution of paste-void spacing provides an opportunity to develop a statistical approach for the assessment of freeze–thaw durability of cement-based materials.
5.
Conclusions
This paper has described an experimental evaluation of X-ray CT as a tool for quantifying the distribution of paste-void spacing in cement-based materials. The internal microstructure of three mortar specimens prepared with different airentrainments was imaged by 3D X-ray CT, and distributions of paste-void spacing of the specimens were obtained by calculating the distance from randomly distributed points outside air voids to their nearest void surfaces. We show that stable results can be achieved when the number of points exceeds ~10,000 (1.63⋅ 10−3% of total volume of the specimens) in this study, and the distributions of equivalent void diameter and paste-void spacing follow lognormal and normal distributions, respectively. We validate the X-ray CT based methodology by comparing the 95th percentile of the CDF of the paste-void spacing distribution with the Powers spacing factors. Results show that the spacing factors estimated by the ASTM C457 and Powers [4] are 1.20 to 1.67 times larger than the 95th percentile paste-void spacing value, similarly corroborated by previous numerical studies. The experimental finding presented herein indicates that the distribution of paste-void spacing quantified using X-ray CT has the potential to be the basis for developing a statistical assessment of the freeze–thaw durability of cementbased materials based on 3D air-void configuration, despite simplification imposed during computation. Due to the imaging capability of the X-ray CT device available for this study, relatively small specimens containing sands were used. Since the spatial resolution of CT image depends on the specimen size, it might be challenging to characterize specimens with coarse aggregates by this methodology. Nevertheless, the potential applications by high resolution CT images are wide open for quantifying the paste-void spacing truly as 3D measures to overcome current methods.
Acknowledgments Financial support for this work was provided by grants from the Basic Science Research Program of the National Research
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Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (Nos. 2011‐0022883 and 2011‐0005593), and a grant from the New & Renewable Energy program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), funded by the Korean Government Ministry of Knowledge Economy (No. 2010T100200494).
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