Construction and Building Materials 37 (2012) 93–101
Contents lists available at SciVerse ScienceDirect
Construction and Building Materials
journal homepage: www.elsevier.com/locate/conbuildmat
Determination of air-void parameters of hardened cement-based
materials using X-ray computed tomography
Kwang Yeom Kim a, Tae Sup Yun b,⇑, Jinhyun Choo c,1, Dong Hun Kang b, Hyu Soung Shin a
a
Korea Institute of Construction Technology, 283 Goyangdae-ro, Ilsanseo-gu, Goyang 411-712, Republic of Korea
School of Civil and Environmental Engineering, Yonsei University, Yonsei-ro 50, Seodaemun-gu, Seoul 120-749, Republic of Korea
c
Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
b
h i g h l i g h t s
" The 3D X-ray CT imaging provides efficient and reliable estimation of air-voids parameters for cement-based materials.
" The spacing factor in 3D space is applicable to the quantification of heterogeneous distribution of air-voids.
" The representativeness of parameters increases by minimizing sampling effects.
a r t i c l e
i n f o
Article history:
Received 14 June 2012
Received in revised form 29 June 2012
Accepted 13 July 2012
Keywords:
X-ray CT
Cement
Air-void parameters
Air content
Spacing factor
a b s t r a c t
This paper presents an attempt to tackle limitations in the two-dimensional (2D) stereological characterization of the air-void parameters of hardened cement-based materials by employing three-dimensional
(3D) X-ray computed tomography (CT), a technique capable of simultaneously imaging numerous sections within a specimen. Using three hardened cement paste specimens composed of different air-void
systems, we performed sensitivity analyses in terms of the number of traverse lines employed for a single
section and the number of sampling sections across the height of a specimen. Parameters for a single section converged rapidly as the number of traverse lines increased, although unacceptable variations were
in evidence across multiple sections. When the number of sampling sections exceeded about 10, a set of
representative air-void parameters was successfully obtained within a standard variation of less than 10%
of average values. The spacing factor and air content measures obtained via CT image analysis were in
good agreement with previously reported data and with the original spacing factors defined for 3D space.
Some advantages found in the use of X-ray CT imaging for determining air-void parameters are discussed.
Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction
The determination of the air-void parameters of cement-based
materials is essential in assessing the freeze–thaw durability of
those materials [1]. Quantitative air-void characterization has generally been carried out via stereological examination of twodimensional (2D) surface sections to gain an understanding of
the three-dimensional (3D) features of a material, a useful technique when there is a lack of 3D information. In practice, a set of
air-void parameters (typically the air content and the spacing factor, which in fact are 3D quantities) are determined via stereological examination of a 2D polished section using an optical
⇑ Corresponding author. Tel.: +82 221235805; fax: +82 23645300.
E-mail addresses: [email protected] (K.Y. Kim), [email protected] (T.S. Yun),
[email protected] (J. Choo), [email protected] (D.H. Kang), hyushin@
kict.re.kr (H.S. Shin).
1
Formerly at: Korea Institute of Construction Technology, 283 Goyangdae-ro,
Ilsanseo-gu, Goyang 411–712, Republic of Korea.
0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.conbuildmat.2012.07.012
microscope, by means of the linear-traverse method or the pointcount method described in ASTM C457 [2]. Even for a single section, these conventional methods demand highly time-consuming
and tedious work (approximately 3 h to obtain the parameters of a
single polished section); hence, several alternative methods have
been proposed to overcome the shortcomings of these conventional procedures, whether by employing different stereological
methods [3,4] or by using other imaging devices [5–7]. Although
these methods have enabled more efficient and objective determination of parameters, they still require a great deal of effort for
sample preparation so as to examine a number of sections. Since
the spatial distribution of air-voids is heterogeneous, however,
parameters obtained from single sections may be sensitive to the
number and location of the sections sampled.
X-ray computed tomography (CT) imaging is a nondestructive
method for obtaining a large number of consecutive sectional
images of the internal microstructure of specimens of interest. It
has been used in several studies to characterize the engineering
properties of cement-based materials in terms of such parameters
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K.Y. Kim et al. / Construction and Building Materials 37 (2012) 93–101
(a) Non-AE
(b) AE-1
(c) AE-2
Fig. 1. 3D X-ray CT images of the air-void systems of the tested specimens. Each specimen has a diameter of 10.5 mm and a height of 8.9 mm after cropping from original
reconstructed images in order to eliminate the noise and irregularity of the boundary surface.
as air-void space [8], spatial distribution of air content under axial
loading [9], and clogging [10]. In addition to these applications, it is
feasible to utilize X-ray CT 2D sectional images to determine the
air-void parameters of cement-based materials, including by
means of the linear-traverse method, as an alternative to conventional stereological methods. If this concept is viable, it offers the
possibility of using X-ray CT imaging to estimate air-void parameters and their spatial distributions while avoiding the excessive
time and costs in preparing specimens and processing data. It is
also expected that the effects of heterogeneity of air-void distributions can be reduced by increasing representativeness.
This paper presents an attempt to determine the air-void
parameters of cement-based materials by implementing the methods designated in ASTM C457 on a large number set of X-ray CT
sectional images. Specifically, an experimental investigation of
sensitivities to sampling conditions was conducted for three hardened cement paste specimens prepared to exhibit a range of air
content, controlled by the amount of air-entraining admixtures
(AEAs) used. Prior to conducting the linear-traverse method on
the X-ray CT images of the specimens, a series of image processing
and treatment procedures were applied to the images. Thereafter,
sensitivity analyses were undertaken for the sampling conditions
in terms of the number of traverse lines on a single section and
the number of sections taken from a single specimen. The validity
of the parameters obtained via the proposed processes was assessed by comparison with published data and with the original
spacing factors in 3D space proposed by Powers [11].
Fig. 2. 2D sliced image. Dark spots indicate air-voids and bright color denotes
cement matrix.
spatial resolution of up to 6.18 lm, and its maximum voltage and current are
225 kV and 3.0 mA, respectively, providing sufficient penetrating ability. The CT
images used in this study were obtained at 150 kV and 100 lA. A CCD camera
was used as a flat-panel detector to collect X-ray attenuation information after
the radiation had passed through the specimen. The detector measures at
409.6 409.6 mm with a pixel pitch of 200 lm and 2.5 lp/mm (line pairs per millimeter) of limiting resolution. The maximum wobbling allowance of the manipulator, which determines the scanning location of the rotating specimen, was 5 lm.
This value lies within the range of correction ability during the reconstruction process. Each image gathered in this study had a pixel size of 0.0108 0.0108 mm with
1024 1024 pixels. A total of 1024 images were taken at intervals of 0.0087 mm.
2. Experimentation
2.1. Materials and sample preparation
Three specimens were prepared by adding varying amounts of AEAs to cement
mixtures to control air-void entrainment. The mix ratio of cement, sand and water
for the three specimens was the same, at 2:5:1. The amount of AEAs (sodium lauryl
ether sulfate, SLES) was 0%, 3%, and 8% of cement weight for the Non-AE, AE-1 and
AE-2 specimens, respectively. Specimens were carefully mixed for 5 min (1 min before adding water and 4 min after adding water) to facilitate the reaction. The maximum specimen size for the X-ray CT device is limited because the required size of a
representative specimen depends on the size of the aggregate involved. Therefore,
in preparing the specimens, only fine aggregates were used [2]. Compared with the
irregular characteristics (in terms of distribution, shape, and size) of entrapped air
in the Non-AE specimen hardened without AEAs, more uniform air-void systems
were expected in the AE specimens. Each specimen was cast in a cylindrical plastic
container of 100 mm diameter and 200 mm height for 7 days following 24 h of
moist conditioning. To compare the air-void parameters obtained via the conventional and proposed methods, the linear-traverse method was conducted for the
original specimens using an optical microscope, as described in ASTM C457. Thereafter, the specimens were cut to a cylinder 12 mm in diameter and 10 mm in height
for X-ray CT imaging.
2.2. Acquisition of CT images
The CT equipment used in this study was the X-EYE CT System (SEC Corporation, Korea). The microfocus X-ray tube in this system is capable of attaining a high
2.3. Enhancement of CT images
Fig. 1 provides a 3D visualization of the qualitative differences in the air-void
systems among the specimens by stacking the raw CT images. Note that the marginal boundary volume of the specimens is cut slightly in the images so that the size
of the 3D stacked image is smaller than that of the cored cylindrical specimens. Xray CT images commonly contain certain inherent artifacts, namely cupping and
rings, that stem from beam-hardening and data inconsistencies in image reconstruction [12,13]. Therefore, prior to extracting quantitative information from the
X-ray CT images, it was necessary to apply a series of image processing and treatment techniques to the raw CT images. Differences in the absorption of X-ray energy passing through a specimen result in beam-hardening, which manifests in
‘‘cupping,’’ wherein the periphery of a specimen appears light while the center is
markedly darker. In addition, X-ray beam instability and defective detector elements (e.g., dead pixels in a CCD) often cause periodic ring-shaped artifacts emanating from the image center corresponding to the rotational axis of the CT device.
While careful hardware calibration (e.g. geometric calibration and beam-shaping
filtering) can improve noise homogeneity in the projection image and in turn reduce beam-hardening, the radially spaced ring artifacts persist in the raw images.
These ring artifacts can be satisfactorily removed via a series of image processing techniques. As shown in Fig. 2, the CT image can be expressed as P(x,y) in the
Cartesian coordinate system, where dark spots in the image indicate air-voids
and bright regions denote the cement matrix. To reduce ring artifacts, a coordinate
transformation and Fourier transformation were conducted as shown in Fig. 3a:
P(x,y) was transformed to polar coordinate P(r,h) where the horizontal strips exist
mainly at low values of r, originating from ring artifacts in a Cartesian space. The
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K.Y. Kim et al. / Construction and Building Materials 37 (2012) 93–101
(a)
θ
r
(b)
(c)
Fig. 3. Image processing procedure: (a) CT image transformed to the polar coordinate plotted in Cartesian space; (b) CT image after removal of horizontal stripes; (c) CT image
after noise reduction in Cartesian coordinate. Arrows and circle denote the same indicative air-voids in both polar and Cartesian space.
Fourier transformation placed these stripes on the high-frequency end of the spectrum, allowing them to be removed via low-pass filtering [14]. A low-pass notch filter was applied to bypass all frequencies except those in the designated frequency
band. The sharp-edged off–on–off notch filter generally magnifies discontinuity;
thus, a Gaussian filter was applied to the filter to smooth the edge. The results of
the inverse Fourier transformation, by which the unfavorable horizontal strips were
effectively removed without destroying the original air-voids, are presented in
Fig. 3b. The images were finally transformed to Cartesian space (Fig. 3c). The same
indicative air-voids in both Cartesian and polar space are denoted by arrows and a
circle in Fig. 3b and c. Note that after noise reduction the image size was
9.47 mm 9.47 mm (877 877 pixels).
Segmentation of the air-voids and cement-matrix in the CT images was conducted via thresholding (e.g., a binary conversion of the images with respect to a
threshold value). The distribution of the pixel values is plotted in Fig. 4a, where
two unique pixel groups exist, based on the higher pixel values of the cement matrix as compared to the air-voids. Once the threshold value T is determined, pixel
values greater than T assume a zero value, while those smaller than T become unity
(e.g., 1). Thus, the selection of the threshold value T critically affects the quantification of the air-voids and corresponding air-void parameters [15]. The most common
and readily applicable method is to minimize intra-class variance via Otsu’s method
[16], as employed in a vast number of image processing studies. This method iteratively computes the class probability of two arbitrarily divided classes via a
threshold value, and determines T when intra-class variance is minimized. This process is iteratively applied to the entirety of the 2D images to extract air-voids. The
binary image finally obtained is shown in Fig. 4b.
3. Determination of air-void parameters from CT images
The determination of air-void parameters from X-ray CT images
is executed via a series of procedures. First, the region of interest
(ROI) is defined by cropping the circular binary image (Fig. 4b) into
a square image of pixel size B B (491 491 pixels is equivalent
to 5.3 mm 5.3 mm). Then, the linear-traverse method designated
in ASTM C457 [2] is undertaken to estimate the air-void parameters via the following steps (see the schematic illustrated in Fig. 5):
Step 1: Select the number of traverse lines (i) equivalently
spaced on each section image of size B B.
Step 2: Select the number of section images (j) among the total
number of square section images available (K).
Step 3: Calculate the total number of air-voids (N) intersecting
all the selected traverse lines of a specimen and the total number of air-void pixels (S) for each line.
Then, the total traversed length (Tt) for each section image becomes B i dx where dx is the pixel size, which varies depending
on the imaging conditions of the CT device. The length traversed
through the air-voids (Ta) on a selected section image is equal to
S dx. The air content, void frequency, specific surface, and spacing
factor are then calculated via the equations summarized in Table 1.
The minimum lengths of the accumulated traverse lines for the linear-traverse method given in ASTM C457 are specified with respect
to the aggregate sizes of target materials (e.g. 1397 mm for a specimen with 4.75 mm aggregates). Therefore, at least 264 lines
(1400 mm) should be selected and examined to satisfy this
requirement in the case of a 4.75 mm aggregate. It is obvious that
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K.Y. Kim et al. / Construction and Building Materials 37 (2012) 93–101
(a)
(b)
Threshold value T
Air-voids
Solid
Fig. 4. (a) Histogram of pixel values. (b) Binary image (white color denotes the identified voids).
the set of air-void parameters should be determined at numbers i
and j, where these are large enough for the standard deviation of
the parameters to fall within an acceptable tolerance (e.g. 10%
of the average values of the parameters used in this study).
4. Results and discussion
The air-void parameters obtained via the proposed CT-based
method were validated via two steps. First, based on the sensitivity
analyses in terms of the numbers of traverse lines and sectional
images from a given specimen, representative values of the air content and spacing factors were determined. Thereafter, the values
obtained were compared with previously reported data and with
the original spacing factor in 3D space proposed by Powers [11].
4.1. Number of traverse lines per sectional image
The sensitivity of parameters to the number of traverse lines
was first examined by computing the air content and spacing factors based on 5 and 491 (maximum) traverse lines being drawn for
each image. The distributions of both parameters obtained from
1024 images are plotted in Fig. 6. It is clearly shown that the formation of entrained-air via AEAs resulted in higher air content
and a lower spacing factor with smaller standard deviations. The
higher variation in the parameters when using five traverse lines
suggests the necessity of employing a sufficient number of traverse
lines for analysis. To determine how many lines are sufficient for a
single sectional image, the variations were calculated in the means
and standard deviations of the parameters as the number of traverse lines i increased from 5 to 491, as shown in Fig. 7. In other
words, statistical values represented by histograms, as shown in
Fig. 6, for a given number of traverse lines were computed from
1024 images for varying numbers of traverse lines i. The means
and standard deviations, as shown in Fig. 7, exhibit a converging
trend even before i reaches the minimum requirement for traversed length (264 lines) given by ASTM C457 [2]. The deviation
of parameters in the AE-2 specimen was smaller than those of
other specimens, owing to the more uniform air-void distributions
achieved by air-entrainment.
4.2. Number of sectional images per specimen
As demonstrated above, the air-void parameters determined
from a single sectional image do not appear to exhibit representativeness. Thus, it was investigated whether, when using a sufficient
Select i lines from
each square image
whose size is B×B
Select j images among K images
Fig. 5. Schematic diagram for selection of traverse lines and sectional images from
a 3D CT image.
number of traverse lines i (= 491), evolutions of parameters could
be established by increasing the selected number of section images
j. From the 1024 sectional images available for each specimen, j
images were randomly selected separately, and then the averages
of the parameters from the selected j images were calculated. This
process was performed 1024 times for each random selection case.
All cases of the selection of j images were considered, whereupon
the number of average air-void parameters corresponded to
C(1024,j) where C denotes the combination.
The evolutions of mean, maximum, and minimum of the averaged parameters of j images are shown in Fig. 8 as j increases from
1 to 1024. The range of the parameters fluctuates when j is low, but
the range becomes noticeably smaller as j increases. More importantly, the mean of the parameters (solid symbol) remains quasiconstant when j becomes larger than 10, and virtually converges
to the values averaged from all 1024 sections, thus corresponding
to the entire 2D image set. This convergence indicates that the
parameters obtained by averaging the values of the 1024 sections
may be representative for a given specimen.
Subsequently, the air-void parameters averaged from a complete set of CT images (i.e. 1024 sectional images) were compared
to those obtained from a single instance of 2D sectional data. Table 2 summarizes two sets of air-void parameters from the same
specimen, one estimated via X-ray CT imagery and another (values
in parenthesis) estimated via a polished section viewed through an
optical microscope. It was observed that the parameters obtained
from a single polished section differed somewhat from the averaged values derived from the CT image analysis. However, it is
notable that the values obtained from the single section lie within
the range of possible variations of the parameters shown in Fig. 8.
This observation implies that the discrepancy in values may be
K.Y. Kim et al. / Construction and Building Materials 37 (2012) 93–101
97
Table 1
Summary of air-void parameter equations from ASTM C457.
Parameters
Equations
Air content (%)
A = (Ta/Tt) 100
Void frequency (mm
n = N/Tt
1
)
Specific surface (mm–1)
Spacing factor (mm)
a = 4N/Ta
L = 3/a[1.4(l + Tp/Ta)1/3–1] when P/A > 4.342
L = Tp/4N when P/A < 4.342
(a) Non-AE
(b) AE-1
(c) AE-2
Fig. 6. Distributions of air content and spacing factor of three specimens.
attributed to the heterogeneity of the air-void distribution in the
specimens, thus substantiating our postulation that the parameters
determined from a single section may be sensitive to the number
of specimens and the location of specimens within the section. In
addition, as shown in Table 2, the determination of air content
from the single polished section failed to capture the higher airvoids entrained in the AE-2 specimens, presumably due to the heterogeneous distribution of air-voids.
4.3. Validation of the parameters
This section evaluates the validity of the air-void parameters
obtained through X-ray CT imaging. The air content and the spac-
ing factors have an inversely proportional relationship with each
other [6]. Although the relationship is not strongly correlated, it
can serve as a useful guide for validating the values of the parameters obtained in this study. The relationship between air content
and spacing factors derived from this study (solid symbols) was
superimposed on the data from the literature (open symbols)
[6,17,18], and, as is clearly shown in Fig. 9, the obtained values exhibit good quantitative agreement with previously reported data.
The characterization of 3D air-void configuration by reconstructing sliced images allows for deriving the spacing factor in
3D space as originally suggested by Powers [11]. Indeed, the
equations suggested in ASTM C457 (Table 1) were devised based
on the principle of stereology that aims for the estimation of 3D
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K.Y. Kim et al. / Construction and Building Materials 37 (2012) 93–101
(a) Non-AE
(b) AE-1
(c) AE-2
Fig. 7. Variations in the mean and one standard deviation of air content and spacing factor according to the number of traverse lines i, for the three specimens.
characteristics based on a 2D examination when 3D information is
not available. However, when 3D information is available, it is better to calculate the air-void parameters rather than estimate them
via any hypothesis or employing any principles. The spacing factor
was originally suggested as half the distance between two diagonally adjacent voids in a cubic assembly, assuming that all voids
are mono-sized spheres equally spaced throughout the entire volume [11]. Obviously, this distance cannot be measured by conventional optical methods; hence the stereology-based linear-traverse
method or modified count methods have been widely used to estimate the spacing factor. Unlike optical devices, however, X-ray CT
enables air-voids to be characterized and then the spacing factor to
be derived directly in 3D space.
To calculate the spacing factor in 3D, the spatial configuration of
the air-voids was quantified by stacking the binary air-void images,
as shown in Fig. 10. It may be seen that the air-voids are randomly
distributed without spatial bias, and that the number of air-voids
increases markedly by air entrainment. The air-void objects, each
of which was composed by combining the interconnected air-void
voxels, were quantitatively defined and the number of voxels for
each air-void object was obtained. The total number of air-voids,
mean volume, and equivalent diameter of the air-voids for
each specimen are shown in Fig. 10. The distribution curves
of the equivalent diameters of air-voids were well-fitted to the
log-normal distribution. As expected, the total number of air-voids
increased with the amount of AEAs.
The 3D configuration of air-voids can be idealized by conceptualizing them as mono-dispersed spheres whose number and total
volume are equivalent to the original air-voids randomly distributed in the specimens. To determine the spacing factor in 3D,
spheres were equally spaced in a cubic volume, as illustrated in
Fig. 11. The spacing factor can then be determined based on ideally
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K.Y. Kim et al. / Construction and Building Materials 37 (2012) 93–101
(a) Non-AE
(b) AE-1
(c) AE-2
Fig. 8. Evolution of average air content and spacing factor with an increasing number of selected images j. The error bar denotes one standard deviation.
Table 2
Estimated air-void parameters.
Specimen
Non-AE
AE-1
AE-2
VOI size (mm3)
Air content (%)
Void frequency (mm
255.353
3.780 (6.3)
6.902 (6.8)
8.271 (6.7)
0.128 (0.156)
0.326 (0.223)
0.508 (0.270)
1
)
Spacing factor (mm)
Specific surface (mm
0.535 (0.403)
0.263 (0.291)
0.190 (0.240)
16.367 (9.8)
21.152 (13.1)
25.113 (16.1)
1
)
Note: Values in parentheses are those estimated from optical-microscopic examination of a polished section.
re-distributed spheres by considering the definition of the spacing
factor. Therefore, results for the spacing factors from the original
definition derived from the 2D stereological method using a sufficient number of 2D section images were compared with the values
from the direct 3D method described herein. It can be postulated
that the conventional 2D stereological method is acceptable for
estimating representative spacing factors, provided that a sufficient number of traverse lines and 2D sampling sections are used.
4.4. Discussion
The capability of X-ray CT to quantify the distributions of airvoid parameters has a few important implications. First, it is
important that X-ray CT can successfully capture the inherent heterogeneity of the air-void distribution with no further effort. Furthermore, variations in the parameters can be an effective means
of verifying the consistency of the parameters. As a criterion for
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K.Y. Kim et al. / Construction and Building Materials 37 (2012) 93–101
Fig. 9. Estimated air-void parameters in this study superimposed on previously
reported data.
Fig. 11. Comparison between spacing factors estimated by averaging the values
from 2D cross-sections following ASTM C457 and obtained by calculating the
distances between equivalent spherical voids rearranged in 3D space as suggested
by Powers (1954).
(a) Non-AE
(a) AE-1
(b) AE-2
Fig. 10. 3D configuration of air-voids and the distribution of equivalent air-void diameters (5.3 mm 5.3 mm 8.9 mm).
K.Y. Kim et al. / Construction and Building Materials 37 (2012) 93–101
freeze–thaw durability, air content is often used instead of the
spacing factor for the sake of convenience. Revisiting Fig. 8, one
may observe a higher variation in air content than in the spacing
factor estimated from the 2D sectional images. This observation
indicates that the determination of air content from a few crosssectional images can be misleading. This finding agrees well with
the experience of experts that many concrete specimens exhibit
desirable air content even when their spacing factors exceed specified limits [6]. This study substantiates the argument that the
spacing factor is a more reliable measure for evaluating the quality
of the dissemination of air-voids in cement-based materials. In this
regard, the quantification of air-void parameters using X-ray CT
imaging is a promising option for improving the current system
of air-void assessment.
5. Conclusions
X-ray CT is an efficient tool in the nondestructive high-resolution characterization of the microstructural configuration of materials. This paper has described the application of X-ray CT imaging
in determining the air-void parameters of cement-based materials.
As opposed to the conventional method of viewing a 2D section
through an optical microscope, the standardized stereological
method (the linear-traverse method) was conducted on a large
number set of CT images of three cement paste specimens prepared with different air-void content as generated by air entrainment. Then, the linear-traverse method was implemented for
sets of sectional CT images of the prepared specimens. The results
indicate that due to the inherent heterogeneity of air-void distribution, the parameters estimated are significantly affected by the
number of traverse lines selected for a single section and the number of sectional images selected across the volume of specimens.
However, it is also shown that using a sufficient number of traverse
lines and sectional images allows the derivation of values that can
be regarded as representative and reliable, based on comparisons
with published data and with a spacing factor calculated based
on the original definition of the spacing factor in 3D space. The
analysis of sets of X-ray CT images was also able to capture quantitative variations in the air-void parameters as controlled by air
entrainment.
The advantages offered by the X-ray CT imaging method can be
summarized as follows. First, the method requires no preliminary
physical treatment of specimens, such as cutting and polishing.
Second, the method can increase the representativeness of the
parameters by minimizing sampling effects. Finally, the method
enables quantification of the heterogeneity of air-void distribution.
In consideration of the limitations of the CT device available for
this study, the specimen sizes (and thus the applicable aggregates)
for X-ray CT imaging were intentionally restricted to obtain high
resolution imaging of air-void distribution. However, since the size
requirements for representative specimens are dependent on the
size of the aggregate involved, it should be noted that it is necessary to prepare the size of specimens in consideration of the size
of the aggregates used. With this provision taken as uncontroversial, we believe the proposed X-ray CT based method to be valid.
Admittedly, the practical size of a cored specimen (>10 cm) for a
101
gravel aggregate needs to be taken into consideration in making
the proposed method practically available, a matter which will
be investigated and reported shortly. Further, it is anticipated that
improvements in the resolution capabilities of X-ray CT images
will provide additional intriguing possibilities for the enhancement
of conventional methods of determining the air-void parameters of
cement-based materials.
Acknowledgements
This work was supported by the New & Renewable Energy program of the Korea Institute of Energy Technology Evaluation and
Planning (KETEP) grant funded by the Korean Ministry of Knowledge Economy (No. 2010T100200494) and the Basic Science Research Program of the National Research Foundation of Korea
(NRF) funded by the Ministry of Education, Science and Technology
(Nos. 2011-0022883, 2011-0005593).
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