Evaluation of Air Voids in Concrete Based on Cross-Section Images of Its Test Specimens

Abstract

Concrete is a material that is widely used in construction and other industries due to its strength and durability. Many characteristics of concrete that are important for its operation, in particular crack resistance, frost resistance, and water resistance, directly depend on the distribution structure and percentage of air voids in concrete. The problem of assessing air voids in concrete based on images of sections of their test samples is considered, the solution of which is relevant for determining the grade of concrete during non-destructive testing of building structures and critical infrastructure facilities. A three-dimensional modelling of the distribution of air voids in concrete was carried out based on a uniform distribution for different air content percentages, which made it possible to substantiate the reliability of assessing the three-dimensional distribution of air voids from two-dimensional images. A method for assessing air content based on the Otsu segmentation-method with subsequent filtering out by geometric shape has been developed. It was tested on real images of sections of test concrete samples. The presented results of experimental studies demonstrate an increase in the reliability of air voids segmentation in images of cross-sections of concrete test specimens using the proposed method, and make it possible to state that the percentage of air voids can indicate concrete strength.

1. Introduction

Concrete, as a universal and durable building material, is widely used in industry to manufacture building structures, reinforced concrete structures, and concrete products, as well as monolithic and reinforced concrete structures [1,2,3]. The main components of concrete are cement, sand, aggregate, and water, the ratio of which determines the grade of the concrete mix and its class. Stabilizers, plasticizers, water repellents, and other chemical and active mineral additives are added to their composition to obtain strong, durable concrete mixtures with the necessary performance properties [4,5]. At the same time, it should be noted that the porosity of concrete is not only a characteristic of its structure, but also one factor that determines its mechanical behaviour under load. Studies [6,7,8,9] have shown that even single voids or microcracks can significantly change the limit state of structures.

Important characteristics of concrete, such as crack resistance, frost resistance, and water resistance, directly depend on the distribution structure and percentage of air voids in concrete [10,11]. Air voids in concrete are formed naturally due to physicochemical processes during solidification or air entrapment during mixing, due to the addition of air-entraining and micro-gas-forming additives. As stress absorbers in concrete, the optimal content and uniform distribution of air voids help slow down microcrack formation at the precritical failure stage [12]. In general, recognizing the spatial architecture of structurally heterogeneous natural and artificial composite structures is an urgent problem of modern materials science. These tasks include the analysis of the porosity of rocks and bone tissue [13,14] and the study of the behaviour of materials with globular [15] and elongated [16,17] inclusions, in particular, polymer-filled concrete [18]. It is also important to determine the porosity in the near-surface regions of oxidized valve group metals from images of flat grinds [19,20,21,22], as well as to study the uneven concentration of voids and inclusions in functionally gradient materials [23,24]. No less important is the information on concrete porosity for using injection technologies to renovate building structures with macroscopic damage [25,26,27,28,29,30].

Therefore, estimating the air content in concrete is important and relevant. The research aimed to estimate the size of air voids in concrete and their size distribution. To achieve this goal, the following tasks had to be solved:

–

to perform a three-dimensional modelling of the distribution of air voids in concrete, to study the distribution of voids estimated from two-dimensional sections and thus justify the estimation of the three-dimensional distribution from two-dimensional images;

–

to develop a method for segmenting air voids in the images of sections of concrete test specimens.

It should be noted that this study does not explore how the environmental factors affect the air void formation and concentration during the curing period.

2. The Literature Review

Let us look at the primary methods of studying porosity by image analysis. Optical non-destructive testing methods, such as ultrasonic, magnetic, radiographic, etc., are widely used to determine the condition of concrete products, buildings, and structures, particularly critical infrastructure. The simplicity and accessibility of modern means of obtaining images in digital form and the development of methods for their processing stimulate their all-round application in various branches of industry, science, and technology, including construction for assessing the roughness, porosity, structural state, and homogeneity of hardened cement-based mortars.

Concrete surface images of different scales are used in [31,32,33,34] to determine micro- and macro-voids. To achieve minor errors, it is essential to obtain high-quality images. Therefore, the authors of the aforementioned papers pay special attention to sample surface preparation (grinding and polishing) and apply additional image processing algorithms that increase their contrast. An important step is the selection of the binarization threshold, the main image processing parameter on which the reliability of void detection largely depends. In particular, in the paper [34], the Otsu automatic threshold binarization algorithm was used at the beginning of processing and then its value was adjusted manually. The methods for contrasting voids in images, such as painting the surface with black paint and applying fine white powder that accumulates in the voids, are also described.

The emergence of simple image registration and processing methods has significantly simplified the possibility of practical use of the stereological method [35] for establishing quantitative indicators of the volume distribution and void size in concrete. It is assumed that the voids have a convex shape [36]. The advantage of this approach is the fundamental ability to quantify both open and closed voids. An analysis of the errors that arise when applying stereological methods to estimate the equivalent void diameter in a volume from two-dimensional images is given in [37]. In general, the techniques developed in metallography are successfully used to study various characteristics of concrete, particularly the effect of the size of coarse aggregate on its frost resistance [38].

The above works do not establish a link between the number and size of voids and concrete strength. In addition, the authors focus solely on determining the quantitative indicators of spherical voids, which are typical for concrete foamed with special additives. Implementing the above approaches requires lengthy surface preparation, which is extremely difficult to provide.

The possibility of determining the strength of concrete based on the texture of images (percentage of aggregate, cement matrix, and macrovoids) was shown in [39], where images obtained with a digital camera were used, and in [40], where images obtained with an electron microscope were used. In the study [39], a relationship between the parameters obtained by digital image processing methods and the compressive strength of concrete was established based on regression analysis. Such methods make it possible to evaluate the characteristics of concrete based on empirical knowledge and preliminary data obtained in the laboratory.

A description of various image processing methods used to determine the composition of multiple components of hardened concrete can be found in [41,42]. Evaluation of the dependence of the strength of foamed concrete on the number of voids and the deviation of their size from sphericity was investigated in [43]. Optimization of technological modes of forming voids of a given size and number in foamed concrete is used in the construction of tunnels described in [44].

The results of recently published works confirm the relevance of research in obtaining information about concrete based on the analysis of its surface images. For example, in [45], voids of various sizes were detected by neural networks based on the processing of concrete surface images and the authors assessed the quality of concrete by their relative area and maximum diameter. Using image analysis methods, they studied the properties of cement stone formed in new concrete compositions with additives of natural lime materials. They found an almost linear dependence of their strength on the number of voids [46].

The presence of voids in the concrete structure is one of the critical factors affecting its strength. Even a small number of voids can significantly affect the strength of concrete. Therefore, detecting voids in concrete should be given considerable attention. Detecting them is complicated because the voids do not differ in colour characteristics from the conditional background, so their detection requires additional manipulations with concrete samples.

The 2016 version of ASTM C 457, “Standard Test Method for Microscopic Determination of Parameters of the Air-Void System in Hardened Concrete”, includes a contrast enhancement procedure [47]. This standard describes the procedure of determining the parameters of the air-void system in hardened concrete through microscopic examination. The parameters are air content, specific surface, void frequency, spacing factor, and paste-air ratio. It includes linear-traverse method, modified point-count method, and contrast enhanced method. The procedures require a skilled and experienced operator to use a microscope to fulfil the necessary measurements. Studies show that the amount of air and the size distribution of air voids are essential for the frost resistance of concrete [48]. According to a study by Mehta and Monteiro [49], a 5% increase in the presence of air voids reduces the strength of concrete by 25%.

The cross-sectional area of the concrete can be analysed by linear analysis (1D). The development of automated image analysis methods allows data from a polished concrete cross-section to be obtained in three ways: point analysis (0D), linear analysis (1D), and cross-sectional analysis (2D) [38] (see Figure 1).

Wolter et al. [50] used close-range photogrammetry to automate the analysis of air voids in hardened concrete without contrast enhancement. First, polished flat concrete sections with different air contents (void numbers) were analysed using photogrammetry. Then, classical and contrast enhancement techniques were applied to the same flat sections. The method based on photogrammetry showed some potential, but the smallest air voids could not be detected during the research. This requires a higher camera resolution and/or noise reduction techniques.

Warren [51] used turpentine and fluorescent dye No. 5GA (Magnaflux Corporation) to fill the voids of the concrete. The surface was photographed under ultraviolet light and the void sizes were manually determined.

The authors of [38] used a fluorescent powder to fill air voids for better contrast and to facilitate the separation of voids from the background. Then, using ultraviolet light to highlight the air voids and conventional light to detect the aggregate particles, six images of 30 × 80 mm in size with a resolution of 3.4 μm/pixel were taken for each concrete section. The paper presents a comparative analysis of the air void structure parameters obtained from actual concrete samples, including the aggregate-air-paste system. These characteristics were obtained in three ways:

(1)

Based on significant simplifications adopted in the Powers model and the linear analysis method.

(2)

By the Philleo method [52]. The method proposed by Philleo requires only knowledge of the total air volume in the paste and the number of voids per unit volume of the paste.

(3)

Using a method that takes into account, in addition to the actual structure of air voids and aggregate grains, surface measurements.

The differences in the results for the three methods analysed indicate that the approach based on the influence of aggregate and air voids on the structure is more accurate than the other approaches. The authors believe that a better description of the void structure parameters will allow them to be more accurately related to the freeze-thaw resistance of concrete.

Schouenborg et al. [53] analysed the basic methods for estimating air content:

• The line-traverse method records the number and lengths of chords longer than 0.008 mm of air voids along a set of test lines (traverses). The ratio of the total length of the chords to the length of the test lines determines the air content in the test sample.
• The modified method of counting points calculates the number of void fragments that cross the traverse lines and the frequency with which equidistant points (index points) fall on the voids. This method does not provide a distribution of voids by size.

The basic formula for calculating air void content is as follows:

$$V_l={\displaystyle \frac{l_l}{l_{tot}}}·100\%,$$

(1)

where $l_l$ is the length of the chords in the air voids and $l_{tot}$ is the total length of the test lines.

The distribution of air voids by size is calculated as follows:

$$n_{d,j}={\displaystyle \frac{2}{\pi }}·\left({\displaystyle \frac{n_{a,j}}{{∆}_j{a}_j}}-{\displaystyle \frac{n_{a,j+1}}{{∆}_{j+1}{a}_{j+1}}}\right),$$

(2)

where $n_{d,j}$ is the number of air voids per volume with class size $d_j, d_{j+1}$; $n_{a,j}$ is the number of chords in the voids per unit length with class size $d_j, d_{j+1}$; ${∆}_j=d_{j+1}-d_j, a_j=\left(d_{j+1}+d_j\right)/2.$

The air content with a class diameter $d_j, d_{j+1}$ is calculated by the formula

$$V_{l,j}={\displaystyle \frac{\pi }{6}}·n_{d,j}{a}_j^3.$$

(3)

3.

Contrast enhancement techniques—image processing methods that increase images’ local or global contrast.

Molendowska [54] studied the effect of image quality on the results of determining the parameters of air voids in concrete. The focus was on technical aspects of preparing a scanned image of a concrete surface, which was then subjected to two-dimensional surface analysis. Image processing aimed to separate connected voids and eliminate various aggregate and cement mortar defects. The specific void surface area was determined using the equivalent diameter or perimeter of the air void as the basis of the calculation. The three-dimensional distribution of air voids was reconstructed using the Schwarz–Saltikov method based on 2D measurements. The results of the 2D method were compared with the results of the linear displacement method (1D) by EN 480-11 (“Additives to concrete, mortar and liquid cement mortar. Test methods.”). The tests confirm the need for image correction before measurement. Comparative tests showed a good correspondence between the parameters of the air void system determined by 2D analysis and the chord length method according to EN 480-11. The NIS-Elements program was used to analyse the input image. Lines were drawn along the image and the chord lengths were measured manually using the NIS-Elements tool. NIS-Elements records the chord lengths and allows you to export the recorded data to a spreadsheet. When input data such as paste volume and total line length are added, the calculations are completed according to EN 480-11. The NIS-Elements program separates the voids in the clusters automatically or manually using image editing tools. During the analysis, three options for separating air voids were adopted: no separation, automatic separation, and manual separation.

Ojala et al. [37] investigated the estimation of air voids in concrete by digital image analysis combined with the Schwarz–Saltikov transform. The results show that their combination estimates the air content with greater accuracy than without the Schwarz–Saltikov transform; the correlation between the air content obtained by the digital image analysis method and the thin section method is as good as the correlation between the pressure saturation method and the thin section method. The voids on the surfaces were filled with epoxy paste with blue pigment. Excess epoxy was removed by sanding with 60, 120, 200, and 400 grit abrasive papers. The maximum sanding height was limited to 0.2 mm. All the voids thus appeared perfectly blue, while the rest of the area remained unchanged (i.e., the cement stone and aggregate were visible). The surface roughness is significant, as any surface defect can be mistaken for an air void and thus cause a significant error. An Epson Perfection V370 Photo flatbed scanner (Shinjuku, Tokyo, Japan) digitized the surfaces. A 70 × 70 mm square scanning area was chosen to cover the samples’ circular cross-sections. It turned out that 1200 dots per inch (DPI) provided the optimal spatial resolution and speed during the scanning process, corresponding to 0.021 mm/pixel.

Digital image processing, in particular the method of multiclass level-grid segmentation, provides effective detection of defects in complex textures [55]. In [56], such approaches were used to identify dimples in fractographic images, and in [57], to determine damage zones in a non-metallic brake pad material, similar to the problem of detecting voids in concrete.

Threshold segmentation methods based on the Otsu method are widely used in investigations of porosity. Rezaei et al. recognized the single-threshold and two-threshold Otsu algorithms as the best among global threshold methods when studied the effectiveness of different thresholding techniques in segmenting micro CT images of porous carbonates to estimate porosity [58]. Many modifications of the Otsu method take into account the features of the segmentation problem being solved. For example, the authors introduce three weighting factors (the fitting curve slope of the mineral content, Otsu threshold, and the approximate percentage of the region of interest in the image) to obtain an improved MP-Otsu [59]. Further 3D fracture model of the coal is reconstructed from the CT image via the developed MP-Otsu and then the permeability is calculated [60]. Otsu segmentation can be applied not only to grayscale images or RGB colour model images, Chengzhen et al. for example developed a multi-stage adaptive Otsu thresholding algorithm working with the HSV colour model and combining segmentation using adaptive thresholds in the Hue (H) channel, complemented by Otsu thresholding in the Saturation (S) and Value (V) channels for void segmentation in rock thin-section images [61].

In general, the literature review shows the relevance of studying the composition and properties of cement mixtures. It substantiates the feasibility of studying air voids in concrete using digital images of the surfaces of sections of concrete test specimens. The problem of correlation between the percentage of voids by area in two-dimensional images of cross-sections and the volume air content in a three-dimensional sample remains open. The novelty of this study is the modelling of a concrete cube with different percentages of air content and the analysis of its cross-sectional images to validate the estimation of the volume air content from two-dimensional cross-sectional images.

3. Materials and Methods

3.1. Materials and Equipment Used in the Experiment

The concrete test specimens were made by Sika-Ukraine LLC (Kyiv, Ukraine) in a cubic shape measuring 10 × 10 × 10 cm using standard technology by simply mixing the components. The concrete solution was poured into steel molds and vibro-compacted. The concrete had hardened for 1 month at room temperature of approximately 22 °C and 80% humidity; afterwards, it was tested. The quantitative composition of the concrete test samples is given in

Table 1. Concrete compositions per m³.

Concrete Grade	Mobility Class	Cement CEM II/A-LL 42.5, PC “Ivano-Frankivskcement”, Ivano-Frankivsk, Ukraine, kg	Sand * (Kovalska, Rozvadiv, Lviv region, Ukraine), kg	Crushed Stone Fraction (15–20 mm), kg	Water, kg
C10	S4	230	740	1170	200
C15		280	700	1160	200
C20		310	690	1150	200
C25		350	670	1140	205
C30		390	645	1140	210

* Sand moisture content 3.5%.

.

Test sections from cubic samples of 10 × 10 × 10 cm were obtained by cutting on a grinding machine equipped with a diamond wheel. The quality of surface treatment is very important because any surface defect can be mistaken for an air void and thus causes a significant error. So, to achieve a flat surface, each sample was carefully polished on Struers LaboPol-5 grinding machine (Struers ApS, Ballerup, Denmark) using successively finer silicon carbide grinding paper 320 grit (40.5 mkm), then 400 grit (25.8 mkm), and finally 600 grit (15.3 mkm). Compressed air was used to remove dust from the specimen between each polishing stage. The polishing time on each step was between 5 and 10 min. The grinding pressure was increased from 30 N to 100 N in 10 N step. As mentioned, the polishing procedure in this study was stopped at grit 600 because the surfaces at the end of this step had a good quality. Sections of a concrete test sample are demonstrated in Figure 2.

The distribution of voids in concrete was evaluated on sections of cubic test specimens of 10 × 10 × 10 cm made of concrete of different grades (C10, C15, C20, C25, and C30).

Images of the concrete specimen cross-sections surfaces were recorded with a digital camera NIKON D-7000 (Nikon Corporation, Tokyo, Japan) with a Nikon NIKKOR Z 50 mm f/1.8 lens (Nikon Corporation, Tokyo, Japan) mounted on the developed laboratory setup with the ability to change its height from the specimen surface. Illumination was provided by four identical LED light sources placed on each side of the sample at a low height, which makes it possible to use their combinations to obtain images of sections of concrete test specimens at different angles of light incidence. The scale of the images was 30 μm/pixel, which allowed to obtain clear images on which voids with a size of 90 μm and more can be detected. The images acquisition was carried out in an optical laboratory, which excluded any influence of uncontrolled natural light. The resulting images are suitable for several methods for detecting voids in concrete. A photo of the laboratory setup is shown in Figure 3.

During the research, one part of the concrete samples of each brand was tested for compression to obtain the actual value of concrete strength [62] and the other part was cut and photographed to determine the quantitative void size. The cube samples were tested, stored in a positive temperature dry room, and manufactured more than 4 months before the experiment. A total of six specimens of each composition were tested. Three control samples of each concrete grade were tested by the standard method of pressing by ASTM International, C39/C39M: “Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens” [63]. The residual strength of concrete was determined, taking into account a correction factor based on the geometric dimensions of the cube:

$$R=0.95F/S\left(\mathrm{M}\mathrm{P}\mathrm{a}\right),$$

(4)

where F is the crushing force (N) and S is the cube face area (mm²). The remaining cubes of different compositions were cut into three parts, thus obtaining four cut surfaces per sample and photographed after polishing.

3.2. Methods of Modelling Air Voids in Concrete

The volumetric concentration of air voids is an informative feature that correlates with the concrete grade. To estimate the volumetric concentration of voids by sections, 3D modelling of voids was performed. We modelled a cube of size 512 × 512 × 512 pixels with spheres of different diameters to simulate voids. In Figure 4, the modelled voids of two different sizes are demonstrated.

Next, we modelled the voids in a concrete cube based on a uniform distribution for different volume concentrations. This is a limitation, as voids can form clusters or chains. Modelling such void co-location may be the subject of further research. The modelled distribution with different sizes of air voids in concrete cube and air content of 0.25% (a), 0.5% (b), and 5% (c) is demonstrated in Figure 5. By analysing the images of the slices of the modelled cube, it is possible to calculate the air content by cross-sectional area. Ten images of slices of modelled cubes were analysed in this experiment. Cross-sections of a fragment of modelled cube with air content of 0.25% (a), 0.5% (b), and 5% (c) are demonstrated in Figure 6. Results of modelling air voids in concrete are discussed in Section 3.1.

3.3. Method for Segmentation of Concrete Voids on Digital Images of Test Specimen Sections

The concrete samples were pretreated with several reagents to increase the contrast of various concrete components. The 1% solution of phenolphthalein C₂₀H₁₄O₄ of reagent grade purity (Sphera Sim, Lviv, Ukraine) and the 5% solution of sodium hydroxide NaOH (Sphera Sim, Lviv, Ukraine) were used. Contrasting calcium carbonate (orange chalk) was used to fill the air voids. Next, the filler (chalk) was removed from the smooth surface of the concrete section. Thus, the contrasting filler remained only in the air voids and areas around the aggregates. This allowed for the enhancement of the visibility of air voids in the images maximizing the distinction between filled voids and background and prevent intensity overlaps between voids and aggregates and further application of an image segmentation technique. When processing an image of a surface of a concrete test specimen, the RGB image model was used. This model allows us to process the image’s red, green, and blue channels separately. The R image component of the RGB colour model was the most relevant for detecting voids, so it was used for further processing. In Figure 7, the initial image of the surface of a 10 × 10 cm concrete test specimen of C30 grade (a), as well as its red R (b), green G (c), and blue B (d) components of the RGB colour model are shown. If necessary, before applying the segmentation stage directly, in some instances it is advisable to perform pre-processing of the image to increase its contrast, improve its quality [64], restore colours [65], and highlight contours [66].

We used the statistical method of segmentation by Otsu [67] in the R component. The Otsu method was chosen because it shows good results if the histogram has a bimodal distribution, i.e., it has two distinct peaks, indicating the existence of two classes of values in the data. The method is based on the within class variance minimization. It can be used when the object area is smaller in comparison with the background region. The threshold level T* is calculated by maximizing the variance between classes:

$$T^{*}=\arg max\left\{{\sigma }_b^2\left(T\right)\right\},$$

(5)

where

$${\sigma }_b^2\left(T\right)=P_0\left(T\right){({\mu }_0\left(T\right)-\mu )}^2+P_1\left(T\right){({\mu }_1\left(T\right)-\mu )}^2,$$

(6)

$P_0\left(T\right),P_1\left(T\right)$ are cumulative probabilities, ${\mu }_0\left(T\right),{\mu }_1\left(T\right)$ are mean values, and ${\sigma }_0^2\left(T\right),{\sigma }_1^2\left(T\right)$ are variances of the two classes. Next, we use an ellipse approximation of each object to reject elongated shapes. Note that the cumulative probabilities in Formula (5) can be interpreted in the general case as functions described in [68,69,70,71].

The advantage of the proposed method is its simplicity of use for processing images of concrete cross-sections. Increasing the contrast between the background and air voids by surface treatment and using the R component as the most relevant part of the image allows us to apply a segmentation method that does not require additional parameters or training.

4. Results and Discussion

Diagnosing concrete based on the analysis of its structure is essential for assessing the condition of an existing structure and for the initial selection of concrete composition. Samples can be cut out of the concrete structure or made in the laboratory as test specimens. In both cases, preparation for testing is essential when examining samples. Grinding should be performed similarly for all specimens using the same auxiliary materials. The phenolphthalein solution and chalk should also be applied in the same way. This will ensure reliable results of computer image analysis. The qualitative results obtained as segmented voids on the images and the quantitative results in size, distribution, and other indicators are essential for concrete quality diagnostics.

4.1. Results of Modelling Air Voids in Concrete

Modelling air voids in concrete was performed according to the method described in Section 3.2.

Table 2. Estimating of air content by area for 10 cross-sectional images of a modelled concrete cube with a proportion of air voids of 0.25% of the volume.

Section Number	1	2	3	4	5	6	7	8	9	10	Averaged
Number of void pixels	488	822	709	307	1210	601	907	634	434	567	668
Air content, %	0.19	0.31	0.27	0.12	0.46	0.23	0.35	0.24	0.17	0.22	0.29

estimates the void concentration by cross-sectional area of the modelled concrete cube with air content of 0.25%. The estimated particle concentration by area ranges from 0.17% to 0.46%. The average concentration by area is equal to 0.29.

Table 3. Estimating of air content by area for 10 cross-sectional images of a modelled concrete cube with a proportion of air voids of 0.5% volume.

Section Number	1	2	3	4	5	6	7	8	9	10	Averaged
Number of void pixels	964	1688	1337	1367	1889	1530	1377	1377	1190	1325	1404
Air content, %	0.37	0.64	0.51	0.52	0.72	0.58	0.53	0.53	0.45	0.51	0.54

estimates the void concentration by cross-sectional area of the modelled concrete cube with air content of 0.5%. The estimated particle concentration by area ranges from 0.37% to 0.72%. The average concentration by area is equal to 0.54.

Table 4. Estimating of air content by area for 10 cross-sectional images of a modelled concrete cube with a proportion of air voids of 5% volume.

Section Number	1	2	3	4	5	6	7	8	9	10	Averaged
Number of void pixels	12,801	11,545	13,107	13,343	13,076	12,433	12,099	13,608	13,123	12,189	12,801
Air content, %	4.88	4.4	5	5.09	4.99	4.74	4.62	5.19	5.01	4.65	4.88

estimates the void concentration by cross-sectional area of the modelled concrete cube with air content of 5%. The estimated particle concentration by area ranges from 4.4% to 5.19%. The average concentration by area is equal to 4.88.

Thus, the above results of modelling voids in a cube of concrete based on a uniform distribution for different volumetric concentrations make it possible to justify estimating the volumetric distribution of air voids from two-dimensional images of the surfaces of concrete sections.

4.2. Results of Concrete Void Segmentation from Digital Images of Test Specimen Sections

The results of the experiments are shown in Figure 8 and Figure 9. In particular, Figure 8 shows the input images (a), (d), and (g) of C10, C15, and C25 grades, respectively, and the results of segmentation of cement stone (background) and voids (object) by known adaptive thresholding method [72]—(b), (e), (h) and by our method proposed in Section 3.3—(c), (f), (i). Figure 8 shows graphs of the void size distribution for test samples of concrete of different grades—C10, C15, and C25. The average percentage of voids by cross-section of test concrete cube, the average rate of aggregate, and the average compressive strength of concrete according to experiments are shown in

Table 5. Evaluation of concrete components by analysing the surface of its sections and determining the compressive strength of concrete.

Concrete Grade	Average Air Content for the Sample, %	Average Percentage of Aggregate for the Samples, %	The Average Compressive Strength of Concrete According to Experiments, MPa	Concrete Specific Density, kg/m3
C10	4.28	42.50	13.30	2275
C15	1.22	47.00	21.70	2300
C25	0.65	44.50	36.10	2370

.

Results of the experiment for a number of samples were compared to ground truth data of an expert in the non-destructive testing. Figure 10 presents the example of the comparison of segmentation obtained by the proposed method and air void detection provided by an expert for image fragment with air void cluster of the test sample C25 (Figure 8g).

It should be noted that when an air void’s edge was crumbled or irregular, an expert extrapolated the round contour of the air void. The criterion for the validity of void segmentation is an error in air content assessment. We can conclude that the performance of the proposed method closely resembles the results from an expert by comparing the segmentation results. The error of the proposed method is 0.11%, according to quantitative analysis. This assessment of the accuracy validates the effectiveness of the proposed method of concrete void segmentation from digital images of test specimen sections.

Several works are investigating the usefulness of image analysis for characterizing air-void systems in concrete [73,74,75,76,77]. Modelling of air voids in concrete cube made it possible to compare the experimental and modelled surface layers and further predict the properties of such concrete. Analysis of modelled layers emphasized the necessity of averaging the estimated air content on larger concrete surfaces. It also showed a minor estimation error for the model with a higher air content. Estimating the rate of voids and analysing the surface of concrete samples can determine the features that correlate with the concrete grade.

Analysing the results of air void concentration, one can see a decrease in the average air void concentration in the sections of stronger concrete grades.

The procedure for determination of parameters of the air-void system in hardened concrete described in ASTM C457 [47] is a tedious and time-consuming process. The differences in methods, equipment, and concrete cube preparation quality are the factors that contribute to variation in air void measurements, in addition to operator skills and training. The proposed method analyses the entire surface of the concrete section (2D), as opposed to the linear-traverse method (1D) [47]. It can also be used in fields without the traversing devices described in this standard.

According to the general concepts of stress concentration in solids, it is important to note that the strength characteristics of a porous body are influenced not only by the size of the voids, but also by the relative position of the voids (the closer the worse), i.e., the percentage of voids inversely correlates with the strength of concrete, which has been empirically confirmed. The shape of the defects is also of great importance: globular defects are acceptable, flattened crack-like defects are unacceptable.

The results of studies [78] indicate that with an increase in the content of GO graphene oxide reinforcing agent, the amount of PVP dispersant increases simultaneously, which leads to the formation of too much gas during the dispersion process, and, accordingly, to the formation of too many voids, which reduces the flexural strength of concrete. In addition, randomly distributed voids and water have a significant impact on the strength of reinforced concrete specimens. It was found that at temperatures below 600 °C, water evaporates and new voids are formed, which also causes significant fluctuations in compressive strength.

In general, applying image processing methods to concrete surface images to determine their characteristics, particularly strength, is a promising area of research. The advantage of the proposed method is that due to the surface treatment of the concrete sample and the use of the R component of the image, the Otsu method can be used, which has no additional parameters. The results obtained in this work can be used to develop a methodology for assessing the strength of concrete in operating structures based on images of its surface. To do this, it will be necessary to accumulate a larger dataset of photos of the concrete surface of real operating structures. In further research, we plan to analyse the difference in air void content in test samples of concrete of different grades with concrete of the corresponding grades after operation and to analyse the component composition of concrete.

5. Conclusions

Modern approaches to the image-based assessment of air voids on concrete surfaces are analysed. It is shown that the problem of segmentation of the air voids and determining their percentage in concrete is relevant and essential for assessing the characteristics of concrete. The voids in a concrete cube were modelled based on a uniform distribution for different volume air content. They showed an increase in the accuracy of estimation for a higher percentage of air content with the same number of slices. This made it possible to compare experimental and modelled surface layers and further predict the properties of such concrete.

A method of image processing of concrete test cube sections for void segmentation was developed based on the Otsu method, with subsequent analysis and segregation by geometric shape. The results of experimental studies of the proposed method on authentic images of sections of test concrete samples of different grades are presented. We obtained the air content percentages for concrete grades C10, C15, and C25 equal to 4.28%, 1.22%, and 0.65%, respectively. The results make it possible to assert that the air content correlates with the concrete strength.

The proposed methodology after accumulating a sufficient amount of experimental data can be used along with other non-destructive methods to determine the strength of concrete in products and structures.

A certain limitation of the proposed method is the assumption of a uniform distribution of air voids, as voids can form clusters or chains. Modelling such void co-location may be the subject of further research. Also, the limitation is the need to analyse more sections for the samples with air content of less than 0.5%.

In the future, we plan to test the proposed technique on existing reinforced concrete structures to predict concrete strength. Extending the method to other types of concrete requires additional research. We also plan to assess void frequency, spacing factor, void chains, and clusters.