Image-based analysis of the flexural behavior of reinforced concrete beams

Abstract

In this study, the crack width and deflection relationship developed for the serviceability evaluation of reinforced concrete (RC) beams is applied to the experimental results of RC beams to evaluate its applicability and limitations. In addition, digital image correlation (DIC) method and three-dimensional (3D) scanning technology are applied to the deformation measurement of RC beam experiments, and the results of each measurement were compared. This study aims to provide a basis for expanding the applicability of reliable digital image-based measurement techniques in the serviceability evaluation of RC structures. The DIC technique was used to accurately measure crack propagation and deflection in RC beams, and the results were compared with those obtained by conventional measurement methods such as linear variable differential transducer (LVDT) and crack width measurement equipment. In addition, 3D models of the specimens were created using 3D scanning and compared with the deformation data measured by DIC to verify their accuracy. The experimental results showed that the DIC and 3D scanning had high accuracy within 4.23% and 2.94%, respectively, compared to the displacement data measured by LVDT, and the proposed algorithm was able to evaluate the correlation between crack width and deflection.

Graphical abstract

Keywords

RC beam / flexural behavior / deformation / DIC / 3D scanning / experimental measurement

1 Introduction

Reinforced concrete (RC) structures, which are economical and durable, comprise the majority of modern buildings and are designed to satisfy safety and serviceability within their expected service life, although their performance can be degraded over time by various deterioration factors [1]. Such factors can include internal chemical reactions like the alkali-silica reaction, a critical issue when considering the use of alternative aggregates such as waste glass or volumetric instability from industrial byproducts like steel slag [2,3]. In other words, the desirable performance of RC structural members under service loads must be secured [4]. In particular, it is important to control the crack width and deflection of the structural members within the allowable range to ensure the serviceability of the structure [5]. Excessive cracking in concrete members is not only aesthetically unpleasant, but can also lead to structural defects such as reduced stiffness of members, leakage, spalling, and accelerated corrosion of reinforcement, ultimately reducing the durability and safety of the structure [6]. Therefore, it is essential to accurately assess the condition of RC structures using serviceability indicators such as crack width and deflection to maintain desirable structural performance and to perform maintenance activities such as timely reinforcement [7].

Traditional structural assessment methods are mainly based on visual inspection and mechanical measurement inspection, except for non-destructive test methods [8–10]. However, they cannot only be time-consuming, but they can also pose a safety risk when assessing the condition of highly damaged members and leaves room for subjective judgment by the inspectors [11–13] Therefore, there is a need to develop an efficient, easy, and unambiguous assessment method that eliminates subjective judgment [14] Recently, digital image correlation (DIC) technique has been actively studied to analyze the cracks and deformations of RC members using digital images and obtain objective data [15–18] DIC is a non-contact optical technique algorithm that can accurately measure the surface deformation of an object, and has been applied to study various aspects such as crack initiation, propagation, and deflection of RC beams [19,20]. Based on these findings, Meiramov et al. [21] developed a model to evaluate the correlation between crack propagation and deflection in RC beams. This model has the potential to improve the accuracy of serviceability assessment based on image data, but experimental cases including design conditions and loading scenarios of various structures should be conducted to further validate its reliability and applicability in daily practice. In addition, three-dimensional (3D) scanning techniques that read the space to generate a point cloud with 3D coordinates and generate a 3D model [22], can be utilized to provide the applicability of non-contact optical measurement techniques.

Therefore, the objectives of this study can be summarized as two main parts. First, a flexural test on RC beam was performed and the experimental results were compared with the model for crack width and deflection relationship [21] to evaluate the applicability and limitations of the model. Second, by comparing the accuracy of DIC and 3D scanning techniques, this study aims to provide a rationale for the use of digital image-based measurement techniques that are more accurate and reliable in evaluating the serviceability of RC beams.

2 Experimental program

2.1 Specimen detail

The key variables in the experimental program considered in the flexural tests of RC beams in this study are the number and size of tensile rebars. As shown in Fig. 1, two test specimens CB-1 and CB-2, were planned, and the tensile rebars were of different sizes to have similar tensile reinforcement ratios as shown in Table 1: three D13 rebars with a diameter of 12.7 mm and two D16 rebars with a diameter of 15.9 mm, respectively. This arrangement keeps the overall tensile reinforcement ratio nearly constant while varying only bar diameter and number, thereby allowing a direct assessment of the influence of bar size and longitudinal spacing on crack initiation, spacing and width. Concrete mix, cover, span, support conditions and the loading protocol were held identical so that observed differences in cracking behavior can be attributed primarily to the reinforcement configuration. For compressive reinforcement, two D10 rebars with a nominal diameter of 9.53 mm were placed at the top, and U-shaped D10 rebars were used for shear reinforcement at 120 mm spacing. The beam specimen was fabricated with a total length of 2100 mm, and the span between supports was set to 2000 mm. The cross-sectional dimensions of the beams were 200 mm wide and 300 mm high, and the concrete cover thickness was planned to be 40 mm. All specimens were designed in accordance with the flexural and shear provisions of ACI 318-19 to ensure flexural failure [23]. The material properties of the reinforcing bars and concrete used for the specimens are presented in Table 2. The material tests were performed on cylindrical concrete specimens of φ100 × 200 mm, which were made from the same batch as the concrete used to fabricate the beam specimens, and the compressive and splitting tensile strengths were measured to be 29.97 and 2.92 MPa, respectively, based on KS F 2405 (Method of Test for Compressive Strength of Concrete) and KS F 2423 (Method of Test for Splitting Tensile Strength of Concrete) [24,25]. According to KS D 3504 (Steel Bars for Concrete Reinforcement), the yield strengths of the rebar were 451.64, 459.95, and 443.86 MPa for D10, D13, and D16, respectively, with corresponding yield strains of 0.00225, 0.00227, and 0.00222, respectively [26].

2.2 Test setup and instrumentation

Figures 2 and 3 show the experimental setup and the locations where the linear variable differential transducers (LVDTs) and strain gauges were installed, respectively. The experiments were conducted in a four-point loading method according to the test method for the flexural performance of concrete beam members of Korea SPS-F KOCED 0011-7504 [27]. The span length was set to be 2000 mm and simply supported at 50 mm from both ends of the specimen as shown in Fig. 4. A two-point load was applied to the top of the beam using a hydraulic actuator with a 1000 kN load capacity. The distance between the load points is 650 mm, and the shear span length is 675 mm.

DIC is based on non-contact optical techniques including image registration and tracking for 2D-based image change measurements. To measure the deformation, including deflection and strain, in the DIC region shown in Fig. 4, the specimen was painted white and then black speckles with a diameter of about 5 mm were applied as shown in Fig. 2(c). The size and distribution of the speckles were manually controlled to create a random, isotropic, and high-contrast pattern. This was intended to provide sufficient unique features for the DIC algorithm to accurately track deformation fields across the surface, in accordance with established best practices for the technique. A total of nine strain gauges were attached to the longitudinal rebars and stirrups, and the LVDTs were installed to measure the vertical displacement of the specimen at mid-span and at two quarter points of the span, as shown in Fig. 3. The span from the mid-span to a support was set as the measurement area to analyze the displacement and strain in the maximum bending moment and the shear regions [28].

The loads were measured at four loading steps for each specimen: 1) first cracking; 2) 65% of the design-strength load; 3) design-strength load (nominal moment strength; no strength-reduction factor applied); and 4) yield load of the tensile reinforcement. For CB-1 the measured loads were 28.17 (first cracking), 72.90 (65% of design-strength), 111.34 (design-strength load), and 114.34 kN (yield load); the calculated nominal design strength for CB-1 was 111.90 kN. For CB-2 the measured loads at the same four steps were 31.66, 75.72, 111.56, and 122.73 kN, respectively. The calculated nominal design strength for CB-2 was 117.07 kN. The crack widths measured at each loading step were analyzed by comparing them with the crack widths analyzed using the DIC method.

2.3 Measurements of digital image correlation and three-dimensional scanning

The accuracy of strain measurement by the DIC method depends on many factors, including the DIC computer algorithm, lighting conditions, camera lens quality, out-of-plane motion in the image, and uneven surfaces. To minimize errors and discrepancies from experimental values, digital images of the specimen were taken by a high-resolution camera in the proper lighting condition. The camera was positioned perpendicular to the surface of the specimen at a fixed distance. During the loading phases, conducted at a displacement rate of 2 mm/min, images were captured continuously every 30 s, corresponding to one image per 1 mm of vertical displacement to record the full deformation history. To improve the data accuracy at the predefined serviceability stages, the loading was also paused at each step. The quantitative DIC analysis for these specific stages was then performed by correlating the stable image captured during the pause with the image taken from the interval immediately prior to it, providing a highly reliable data set.

The open source program Ncorr, based on MATLAB code, was utilized to derive the displacement and strains from the measured images [29]. Ncorr is a 2D DIC algorithm that combines additional improvements to the DIC algorithm. In addition, the Ncorr-post MATLAB program was used to post-process the Ncorr results and obtain strain data along the beam length at the crack opening location [30]. This program served as a post-processing extension to process, visualize, and export the data provided by Ncorr [29].

The 3D scanning technique uses a light detection and ranging sensor to generate a point cloud containing the 3D coordinates of an object, which is post-processed to create a 3D model for visual analysis of structural deformation. By analyzing the coordinates of the point cloud measured at each loading step, the distance between the points was evaluated as the deformation, and the relative vertical deformation from the reference point could be defined as deflection. The experiment was paused at each loading step and the measurements obtained through 3D scanning were compared with the measurement results from DIC analysis and LVDT to verify the reliability of the data obtained with the 3D scanning technique.

3 Application of the crack width-deflection model

The DIC analysis data obtained from the experiments in this study allows the correlation of crack width and deflection in RC beams to be analyzed, which was evaluated by the crack width-deflection correlation model proposed by Meiramov et al. [21]. In the model, the curvature distribution of RC beams under bending moment is idealized, and the correlation between the crack width and deflection is theoretically derived based on the relationship between reinforcement and concrete strains in which the crack width data derived by analyzing DIC is set as an input variable to calculate corresponding deflection of RC beams. Before a crack occurs, all sections of the concrete contribute to the flexural stiffness, which allows to assume the same curvature distribution along the axis of the member as the bending moment distribution. However, after cracking in the maximum moment zone, as the load increases, the curvature distribution tends to increase locally with cracking concentrated in the maximum moment zone [31–33].

This means that the distribution of curvature within the shear span, rather than in the maximum moment zone, is relatively small, and most of the deformation due to bending moments is concentrated in the maximum moment zone. Therefore, the curvature distribution along the span is simplified to an idealized rectangular shape in which the magnitudes of curvature and width are defined as the maximum curvature and length of the maximum moment zone, respectively [34]. Based on the rectangular shape idealized curvature distribution within the maximum moment zone, the flexural behavior and deflection of the beam can be simply evaluated.

On the other hand, as shown in Fig. 5, after a flexural crack occurs in a RC beam, the concrete at the crack surface can no longer resist the tensile force, and the tensile stress generated by the additional load is resisted entirely by the reinforcement, which increases the stress of the reinforcement [35]. Therefore, the strain of the reinforcement increases at the crack surface and a part of the applied stress is resisted by concrete between the cracks. The average crack width (w_{\text{ave}}) in RC is a function of the average crack spacing (l_{\mathrm{s}}), the average strain of the reinforcement ({\epsilon }_{\mathrm{s}\mathrm{\_}\text{ave}}), and the average strain of concrete ({\epsilon }_{\mathrm{c}\mathrm{\_}\text{ave}}) within the crack spacing, as follows:

(1)w_{\text{ave}}=l_{\mathrm{s}}({\epsilon }_{\mathrm{s}\mathrm{\_}\text{ave}}-{\epsilon }_{\mathrm{c}\mathrm{\_}\text{ave}}).

Assuming that the strain distribution in the maximum moment zone where cracks are concentrated is constant under service load, the sum of the total crack widths in that region ({\displaystyle \sum w_{\text{cr}}}) can be expressed with the span length where the cracks are concentrated (l_{\text{crp}}) instead of the average crack spacing (l_{\mathrm{s}}), as follows:

(2)\sum w_{\text{cr}}=l_{\text{crp}}({\epsilon }_{\mathrm{s}\mathrm{\_}\text{ave}}-{\epsilon }_{\mathrm{c}\mathrm{\_}\text{ave}}).

The crack concentration length (l_{\text{crp}}) can be either the maximum moment region or the distance between two loading points, 650 mm is used for the specimens in this study. Rearranging Eq. (2) gives the average rebar strain ({\epsilon }_{\mathrm{s}\mathrm{\_}\text{ave}}) as

(3){\epsilon }_{\mathrm{s}\mathrm{\_}\text{ave}}=\frac{{\displaystyle \sum w_{\text{cr}}}}{l_{\text{crp}}}+{\epsilon }_{\mathrm{c}\mathrm{\_}\text{ave}},

where the average concrete strain ({\epsilon }_{\mathrm{c}\mathrm{\_}\text{ave}}) is assumed to be 2/3 of the cracking strain ({\epsilon }_{\text{cr}}) assuming a parabolic tensile strain distribution of concrete as shown in Fig. 5. In addition, based on the linear strain distribution as shown in Fig. 6, the curvature (ϕ) is defined as follows:

(4)\varphi =\frac{{\epsilon }_{\mathrm{s}\mathrm{\_}\text{ave}}}{(h-kd)},

where k is the lever arm coefficient, h is the overall height of the beam, and d is the effective depth. The lever arm coefficient (k) is defined by the theory of elasticity [36] and is derived by considering the ratio of the elastic modulus of the concrete to the reinforcement and the tensile reinforcement ratio as follows:

(5)k=-n\rho \pm \sqrt{{\rho n}^2+2\rho n},

where ρ is the reinforcement ratio and n is the elastic modulus ratio of steel to concrete (E_s/E_c), with E_s and E_c being the elastic moduli of steel and concrete, respectively. The curvature of Eq. (4) is used as the maximum value of the assumed curvature distribution ({\varphi }_{max}), and the deflection (δ) of the mid-span due to the bending moment is calculated by considering the idealized curvature distribution in the maximum moment zone, as follows:

(6)\delta =\left(\frac{l}{2}-\frac{l_{\text{crp}}}{4}\right){\varphi }_{max}\frac{l_{\text{crp}}}{2}.

Thus, by substituting the average rebar strain from Eq. (3) and the curvature from Eq. (4) into Eq. (6), the deflection (\delta) can be expressed, as follows:

(7)\delta =\left(\frac{l}{2}-\frac{l_{\text{crp}}}{4}\right)\frac{{\displaystyle \sum w_{\text{cr}}+{\epsilon }_{\mathrm{c}\mathrm{\_}\text{ave}}{l}_{\text{crp}}}}{2\left(h-kd\right)}.

In addition, replacing the average strain in concrete by {\displaystyle \frac{2{\epsilon }_{\text{cr}}}{3}} then the relationship between the deflection (\delta) and the sum of the total crack widths ({\displaystyle \sum w_{\text{cr}}}) can be obtained as follows:

(8)\delta =\left(\frac{l}{2}-\frac{l_{\text{crp}}}{4}\right)\frac{{\displaystyle \sum w_{\text{cr}}+{\displaystyle \frac{2{\epsilon }_{\text{cr}}}{3}}{l}_{\text{crp}}}}{2\left(h-kd\right)}.

This equation can be used to calculate the deflection (\delta) using the total crack width ({\displaystyle \sum w_{\text{cr}}}) as an input variable, and the sum of the total crack width ({\displaystyle \sum w_{\text{cr}}}) can also be calculated using deflection (\delta) as an input variable. However, only the deflection due to bending moment is considered in Eq. (8), but not the deflection due to shear.

4 Test results and discussion

4.1 Strain gauge measurements

Figure 7 plots the strains in the reinforcing bars measured from the strain gauges versus the load, and the locations of the strain gauges installed on the reinforcing bars can be found in Fig. 3. To facilitate interpretation, the gauges were labeled to identify their precise locations. The prefixes denote the type and general location of the reinforcement: ‘LR’ for ‘Loading Reinforcement’ (on longitudinal reinforcement under the loading points), ‘R’ for reinforcement at the mid-span, and ‘SR’ for ‘Shear Reinforcement’. The number following the prefix specifies the position of a specific bar of reinforcement within the cross-section. Specifically, the numbering begins from the bottom row and proceeds upwards, and from left to right within each row. For instance, in a section with two rows and two columns of longitudinal reinforcement, the bottom-left bar of reinforcement is designated as 1, the top-left bar as 2, the bottom-right bar as 3, and the top-right bar as 4. As shown in Fig. 7 (a), in specimen CB-1, the strains of LR1 and LR3 attached to the tension rebars in the tension section and R1 and R2 strain gauges attached to the tension rebars and compression rebars in the mid-span, respectively, were above the yield value. On the other hand, the strains of LR2 and LR4 attached to the compression reinforcement in the tension section and SR1, SR2, and S1 strain gauges attached to the shear stirrups were below the yield value. As shown in Fig. 7 (b), only the LR1 and LR3 strain gauges attached to the tensile reinforcement in the loading sections of the CB-2 specimen were above the yield value. Strain data for the R1 strain gauge attached to the tension bar in the mid-span was not available due to damage to the gauge. Furthermore, the strain gauges R2 and LR2 on the compression reinforcement exhibited an anomalous sign change from compression to tension at higher load levels. This is attributed to the buckling of the compression reinforcement, which led to erroneous readings from the gauges. Since the tensile rebars yielded in the maximum moment sections, the loading points and mid-span sections, and the stirrups in the shear span did not yield, it can be concluded that all of the specimens failed in bending rather than shear. Figure 7 shows the strain gauge readings with some local drops in load. These drops are attributed to localized events such as micro-cracking and subsequent stress redistribution.

4.2 Load–displacement measurements

Figure 8 shows the deflection distribution of the specimen along the span measured using three LVDTs installed at the bottom of the specimen. The deflection distribution is plotted for each loading step, and the deflection is concentrated in the mid-span as the load increases. It is noted that at the initial cracking stage (Step 1), the deflection measured by the central LVDT may appear locally smaller due to the non-uniform nature of initial crack formation; however, a consistent trend is observed as the load increases. Figure 9 shows the load–displacement relationship analyzed using LVDT and DIC method at the mid-span along with the vertical displacement field image at failure. These overall behaviors are obtained by averaging of the collected data points to effectively filter out the localized fluctuations of loads. The displacement field image in Fig. 9 illustrates the final failure state of the specimen. The large displacement observed here, approximately 80 mm for CB-1, should be distinguished from the deflections analyzed at the serviceability stages (Steps 1–4) shown in Fig. 8. In the displacement field images, high intensity of deformation is indicated as red color, while colors closer to dark blue mean low intensity of deformation. Specimens CB-1 and CB-2 have almost similar reinforcement ratios, with 3-D13 and 2-D16 rebars, respectively. The results show that CB-2, which has a slightly larger reinforcement ratio, has a higher yield strength and yield load, but is not significantly different from CB-1. The load-deflection curve using the DIC measurement data was very similar to the load–deflection curve using the displacement data from the LVDT. Figure 10 shows the failure of the specimens in the four-point loading test. Both specimens failed by concrete crushing in the compression zone within the two loading points, with most of the crack propagation concentrated in the maximum moment zone.

Table 3 compares the deflection measurement results at design strength loads obtained using LVDT, DIC, and 3D scanning for each specimen. Similar design strength loads were obtained for specimens CB-1 and CB-2 based on nominal moment strength because they have similar reinforcement ratios and concrete cover thickness. The LVDT-measured deflections at the design strength for both specimens were similar at 6.8 and 7.1 mm, respectively. The deflections from the DIC data showed an error of 4.12% and 4.23% compared to the LVDT measured deflections, respectively, while the deflections from the 3D scanning showed an error of 2.94% and 1.41% for each specimen.

If excessive deflection of the specimen occurs due to the application of loads above the yield of the tensile reinforcement, the measurement error of the LVDT may increase the error with the displacement analyzed by DIC and 3D scanning techniques. In addition, the errors could depend on the computer algorithms and lighting conditions used, out-of-plane behavior, uneven surface texture, etc. However, even with these factors, the maximum error in deflection displacement was 4.23%, indicating that DIC and 3D scanning techniques are valid for assessing deflection in RC beams.

4.3 Crack width–deflection relationship

Figure 11 shows the strain distributions along the span length of the specimens obtained by the DIC method under the design strength load. The strain is concentrated in the cracked section where the tensile stress generated due to the bending moment exceeds the tensile strength of the concrete, and the DIC analysis shows that the relatively large strain is colored in red. This can be identified as the cracked section, and the larger the crack width, the larger the width of the corresponding area. Given the magnitude and distribution of the corresponding strains, the local crack width can be calculated, and the sum of the total crack widths across the span (\sum w_{\text{cr}}) is also determined by integrating the strains in the maximum moment zone over the span length and subtracting the elastic deformation of the concrete. The relationship between crack width and deflection determined from the experimental data and DIC analysis was evaluated with the crack width-deflection correlation model. However, in order to accurately evaluate the deflection at the mid-span of RC beams, it is necessary to add the contribution of the deflection due to shear as well as the bending moment [15,21,37]. Therefore, the crack width-deflection correlation was modified by adding the deflection due to the shear deformation occurring in the shear span ({\delta }_{\mathrm{s}}) to the deflection due to the bending moment ({\delta }_{\mathrm{f}}) at the maximum moment section expressed in Eq. (8). In other words, the deflection at the mid-span ({\delta }_{\mathrm{m}}) is represented as follows:

(9){\delta }_{\mathrm{m}}={\delta }_{\mathrm{f}}+{\delta }_{\mathrm{s}}.

The deflection due to shear ({\delta }_{\mathrm{s}}) can be obtained as follows:

(10){\delta }_{\mathrm{s}}={\gamma }_{xy}\times a,

where a is the length of the shear span, and {\gamma }_{xy} is the shear strain which can be calculated from the DIC data as follows [20]

(11){\gamma }_{xy}=\frac{1}{2}\left(\frac{\mathrm{d}u}{\mathrm{d}y}+\frac{\mathrm{d}\nu }{\mathrm{d}x}+\frac{\mathrm{d}u}{\mathrm{d}x}\frac{\mathrm{d}u}{\mathrm{d}y}+\frac{\mathrm{d}\nu }{\mathrm{d}x}\frac{\mathrm{d}\nu }{\mathrm{d}y}\right),

where u and \nu are the horizontal and vertical displacements, respectively.

Figure 12 compares the experimental relationship between crack width and deflection with the one predicted by the model in Eq. (9). To generate the comparison curves, a set of experimental total crack widths measured at predefined load stages was used as a common input. The value of the total crack width at each stage was determined by combining two sources: DIC data was used for the bending region, while a digital crack width detector was used for the shear span. Since the DIC observation area covered only a half-section of the bending region, the sum of the crack widths measured in this area was doubled to represent the entire zone. The experimental curve (‘DIC_Exp’) plots these total crack widths against the corresponding deflections measured by the LVDT. The model curve (‘Estimated’) plots the same crack widths against the deflections calculated using the proposed model.

For specimen CB-1, the deflection was somewhat underestimated by the evaluation model, but the model calculation was able to evaluate the tendency of the crack width according to the deflection quite accurately, while for specimen CB-2, the crack width-deflection relationship showed a high degree of agreement. Because both specimens were reinforced with similar reinforcement ratios, the evaluation model provided almost identical crack width-deflection relationships for the specimens, but the measured data from the experiments yielded quantitatively different results for the two specimens. However, the trend of the crack width-deflection relationship is very similar to each other, and the results of the evaluation model, as shown in Fig. 12 (c), are located between the crack width-deflection curves from the measured data. Thus, it is concluded that the evaluation model is relatively accurate in estimating the relationship between crack width and deflection of RC beams within the experimental error range. A quantitative comparison based on the deflection values showed that the proposed model predicted the experimental results with an average error of approximately 26.7% for specimen CB-1 and 7.6% for specimen CB-2.

4.4 Three-dimensional scanning and visualization

The experiment was stopped at each loading step and 3D scanning data was collected. The results of analyzing the 3D scanning results are shown in Fig. 13. The 3D model was realized from the point cloud generated on the surface of the specimen. In Fig. 14, the vertical deflection of the specimen CB-1 is analyzed for load Steps 2 and 3. The displacements are modeled at a realistic scale, so the deformation is not very visible, but the legend indicates that the deflection is present. The detailed deflection measurements from 3D scanning are summarized in Table 4, which also presents the deflection data for each load step obtained using LVDT and DIC method. The 3D scanning data was not measured after the design strength load was reached.

Figure 15 provides a visual comparison of the deflection results from LVDT and 3D scanning for the first three predefined loading steps. The data points cluster closely to the red diagonal line, which represents perfect agreement, indicating a high level of consistency between the two methods. While the overall consistency is high, it is noted that the percentage differences between the measurement methods, as numerically detailed in Table 4, are most pronounced at the initial loading stage and decrease substantially as the load increases. The large percentage errors at the first loading step, such as the 233.3% difference for the 3D Scan of CB-1, do not indicate poor measurement accuracy. Rather, they are a mathematical artifact of calculating a relative error with a very small reference value. In this instance, a small absolute difference of 1.4 mm (2.0−0.6 mm) results in a large percentage when divided by the initial LVDT deflection of only 0.6 mm. As deflection becomes more significant in subsequent stages, the percentage differences decrease to as low as 0.59%, indicating a high degree of agreement between the measurement methods under service and yield loads. Therefore, the accuracy and reliability of the DIC and 3D scanning techniques are considered valid for practical applications, especially in the load ranges critical for serviceability assessment.

5 Conclusions

The serviceability of RC beams is closely related to concrete cracking and deflection, and this study conducted an experimental study to secure the accuracy and reliability of image data-based measurement methods such as DIC and 3D scanning that can be applied for serviceability evaluation. In addition, the serviceability evaluation model of RC beams based on the relationship between crack propagation and deflection proposed in previous study was applied to the experimental results to confirm its validity. The conclusions drawn from this study are summarized, as follows.

1) DIC and 3D scanning techniques are effective methods to capture the displacement of RC beams, and the maximum error in deflection is found to be 4.23% and 2.94%, respectively.

2) There was a difference in the quantity between the calculation results of the crack width-deflection evaluation model and the experimental results, which is attributed to the experimental error, and the trend of the crack width-deflection relationship could be evaluated accurately. Therefore, when crack width or deflection measurement data are obtained, the evaluation model can be used for the serviceability evaluation of RC beams.

3) Unlike the DIC technique that requires a controlled environment such as a laboratory, it is expected to be possible to obtain deflection data at the actual structure inspection site through the 3D scanning technique that can be applied in the field and perform serviceability evaluation using the crack width-deflection evaluation model.

4) Since this study was conducted in an environment where external environmental changes such as temperature and humidity were controlled for the experiment, it is necessary to verify the reliability of the measurement in a real environment, and it is expected that the accuracy and reliability can be further secured by improving the DIC algorithm and the accuracy of the 3D scanner.

5) The results from this study can serve as a basis for further research on beam types other than simple support beams, based on an understanding of the different deflection mechanisms, including the contribution of shear to deflection. Furthermore, tests to examine the field applicability of the 3D scanning technique need to be conducted to provide a methodology for reliable data collection in real-world environments and to establish a protocol for practical application in the field by incorporating image-based measurement techniques.

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