Open AccessArticle

Determination of Crack Depth in Brickworks by Ultrasonic Methods: Numerical Simulation and Regression Analysis

Alexey N. Beskopylny

^1,*

Sergey A. Stel’makh

Evgenii M. Shcherban’

Vasilii Dolgov

⁴,

Irina Razveeva

Nikita Beskopylny

⁴,

Diana Elshaeva

and

Andrei Chernil’nik

Department of Transport Systems, Faculty of Roads and Transport Systems, Don State Technical University, 344003 Rostov-on-Don, Russia

Department of Unique Buildings and Constructions Engineering, Don State Technical University, 344003 Rostov-on-Don, Russia

Department of Engineering Geometry and Computer Graphics, Don State Technical University, 344003 Rostov-on-Don, Russia

⁴

Department of Hardware and Software Engineering, Faculty of IT-Systems and Technology, Don State Technical University, 344003 Rostov-on-Don, Russia

Author to whom correspondence should be addressed.

J. Compos. Sci. 2024, 8(12), 536; https://doi.org/10.3390/jcs8120536

Submission received: 28 October 2024 / Revised: 13 December 2024 / Accepted: 14 December 2024 / Published: 16 December 2024

(This article belongs to the Special Issue Theoretical and Computational Investigation on Composite Materials)

Download

Browse Figures

Figure 1
Appearance of experimental samples of bricks with cracks of different depths. "> Figure 2
The process of detecting cracks in bricks using the Pulsar-2.2 ultrasonic device. "> Figure 3
Scheme of installation of sensors for measuring crack depth. "> Figure 4
General diagram of a block with a crack: 1—point of pulse application; 2—location of the ultrasonic signal receiver. "> Figure 5
Comparison of experimental and numerical simulation results (Plexiglas material is the reference sample). "> Figure 6
Wave propagation in a plexiglass block at the moments of time (a) t = 2 µs, (b) t = 8 µs, (c) t = 16 µs, and (d) t = 30 µs. "> Figure 6 Cont.
Wave propagation in a plexiglass block at the moments of time (a) t = 2 µs, (b) t = 8 µs, (c) t = 16 µs, and (d) t = 30 µs. "> Figure 7
Successive development of von Mises stresses in a brick weakened by a crack at different points in time: (a) t = 9.5 µs, (b) t = 13.5 µs, (c) t = 17.5 µs, (d) t = 21.5 µs, (e) t = 23.5 µs, and (f) t = 47.5 µs. "> Figure 7 Cont.
Successive development of von Mises stresses in a brick weakened by a crack at different points in time: (a) t = 9.5 µs, (b) t = 13.5 µs, (c) t = 17.5 µs, (d) t = 21.5 µs, (e) t = 23.5 µs, and (f) t = 47.5 µs. "> Figure 7 Cont.
Successive development of von Mises stresses in a brick weakened by a crack at different points in time: (a) t = 9.5 µs, (b) t = 13.5 µs, (c) t = 17.5 µs, (d) t = 21.5 µs, (e) t = 23.5 µs, and (f) t = 47.5 µs. "> Figure 8
Dependence of UY displacements at the receiving point on the pulse propagation time: 1—without defect; 2—crack 20 mm deep; 3—crack 60 mm deep. "> Figure 9
Comparison of ultrasonic pulse signals for different crack depths. "> Figure 10
Characteristic parameters of the signal used to determine the crack depth. "> Figure 11
Experimental and predicted values for averaged parameters. "> Figure 12
Experimental and predicted values for averaged parameters taking into account the material properties. ">

Versions Notes

Abstract

Ultrasonic crack detection is one of the effective non-destructive methods of structural health monitoring (SHM) of buildings and structures. Despite its widespread use, crack detection in porous and heterogeneous composite building materials is an insufficiently studied issue and in practice leads to significant errors of more than 40%. The purpose of this article is to study the processes occurring in ceramic bricks weakened by cracks under ultrasonic exposure and to develop a method for determining the crack depth based on the characteristics of the obtained ultrasonic response. At the first stage, the interaction of the ultrasonic signal with the crack and the features of the pulse propagation process in ceramic bricks were considered using numerical modeling with the ANSYS environment. The FEM model allowed us to identify the characteristic aspects of wave propagation in bricks and compare the solution with the experimental one for the reference sample. Further experimental studies were carried out on ceramic bricks, as the most common elements of buildings and structures. A total of 110 bricks with different properties were selected. The cracks were natural or artificially created and were of varying depth and width. The experimental data showed that the greatest influence on the formation of the signal was exerted by the time parameters of the response: the time when the signal reaches a value of 12 units, the time of reaching the first maximum, the time of reaching the first minimum, and the properties of the material. Based on the regression analysis, a model was obtained that relates the crack depth to the signal parameters and the properties of the material. The error in the predicted values according to this model was approximately 8%, which was significantly more accurate than the existing approach.

Keywords:

composite materials; brickwork; ultrasonic; defect detection; numerical simulation; regression analysis

1. Introduction

Non-destructive testing (NDT) constitutes a critical methodology for evaluating and monitoring the integrity of materials and structures across diverse industrial sectors. NDT reveals hidden defects and assesses their criticality, which helps ensure an adequate level of safety in critical industries [1,2]. The application of nondestructive testing (NDT) methods is crucial for facilitating well-informed decisions concerning the repair or reconstruction of building structures. The primary methods of NDT of building structures and products include ultrasonic testing, vibration diagnostics, acoustic testing, and others [3,4]. Currently, most of the research on NDT is aimed at improving these methods. New models of NDT devices are being developed and upgraded [5,6,7], allowing the prediction of the load-bearing capacity of structures [8,9].

Ultrasonic diagnostics of building structures, as an effective monitoring method, can be used to assess the self-healing of the material [10]. The authors showed that an increase in the strength of the ultrasonic signal was closely related to the active healing of cracks in concrete. In this case, the ultrasonic method was used to interpret the state of the crack.

Non-destructive testing methods were used to evaluate the effectiveness of the crack repair [11]. The study not only identified the presence of the crack but also compared the signal after repair to prove the improved load-bearing capacity and structural integrity of concrete structures.

Ultrasonic methods are used to detect cracks in underwater concrete structures [12]. The authors proposed a method for detecting defects in concrete structures in underwater structures based on reflected ultrasonic echo signals using convolutional neural networks. It should be noted that methods based on reflected signals contain a significant amount of noise and require very labor-intensive processing algorithms.

The most difficult part of using ultrasonic methods is signal processing, and in most cases, this is solving the inverse problem of reconstructing the geometry of a defect using a known amplitude–time signal. In recent years, machine learning algorithms have been actively used to solve such problems [13,14,15,16]. The methodology of this approach is based on the numerical analysis of processes occurring during ultrasonic exposure to an object [17,18,19,20,21], and the subsequent construction of machine learning algorithms to solve the inverse problem of determining the location and geometry of a defect. The use of convolutional neural networks allows for a deep analysis of crack images, which solves the problem of automating the monitoring of buildings and structures.

Ultrasonic flaw detection is a fairly common NDT method and can be used to control and search for defects in welded joints, pipelines, sheet products, composite materials, and other products [22,23,24]. Ultrasonic techniques represent a highly effective means of detecting flaws and ensuring quality control within building materials, structures, and processes. This is true for various types of material—both stone and metal. Let us consider the most significant studies on ultrasonic methods in construction in recent years. The application of Gaussian process regression (GPR) to calibrate existing SonReb transform models has been studied; this approach exploits GPR’s strengths in handling nonlinearity and uncertainties. Analysis of experimental data from the literature demonstrates that the GPR calibration method is highly effective, surpassing, in most instances, the standard multiplicative and additive techniques used for SonReb model calibration [25]. This paper presents a novel methodology for assessing anchor bolt corrosion severity, leveraging multi-scale convolutional neural networks (MS-CNN). This method accounted for the multi-mode propagation and signal dispersion characteristics of ultrasonic guided waves within the context of non-destructive testing, based on an analysis of anchor bolt corrosion mechanisms [26]. The characteristics of concrete modified with green hwanto (NSH), a widely accessible Asian construction material, were examined by this investigation, in which the cement was partially substituted. Due to the inert nature of NSH, this research endeavored to establish the ideal cement replacement ratio and the quantitative strength properties of the resultant composite. The NSH concrete’s specific gravity, compressive strength, ultrasonic pulse velocity (UPV), and stress–strain coefficient (NSHC) were determined. Moreover, a predictive model was developed to determine compressive strength through regression analysis of compressive strength and UPV values [27]. Non-destructive testing data were used to develop probabilistic linear and multilinear regression models for predicting the compressive strength of concrete. Furthermore, a fully probabilistic method [28] was employed to analyze the correlation between ultrasonic testing data and achieved concrete strength, including an assessment of the associated measurement error. An internet protocol (IP) camera-based object detection system was employed to locate workers within the crane’s operational range, and ultrasonic sensors measured the distance to nearby obstacles. To prevent crane lifting collisions, both applications were designed for concurrent functionality. Promising results from field tests and evaluations of the integrated system were observed [29]. A study was conducted to evaluate the effectiveness of combined methodologies utilizing dual and triple applications of diverse non-destructive testing methods for concrete. Employing NDT measurements and compressive strength data, response surface methodology was utilized to conduct the analyses, resulting in the development of four distinct mathematical models [30]. Methods employing isocurves to establish compressive strength profiles in reinforced concrete structures, based exclusively on non-destructive evaluations, were established [31]. Findings from the SonReb method, which assessed ultrasonic pulse velocity and its correlation with dynamic and static elastic moduli, most closely approximated the benchmark compressive strength values [32]. A novel, geometrically adaptable ultrasonic tomography system (UTS) was previously engineered for the non-destructive evaluation of structural damage in historical columns. The innovative nature of this nondestructive system stemmed from its ability to transcend the common shortcomings of its predecessors. Automated inspection and the production of multiple tomographic slices along the column’s height were enabled by this method. The method was suitable for diverse column types and materials [33,34,35].

A lot of work has already been devoted to the study and detection of defects in bricks and brickwork structures, in which various methods have been used for this purpose. These include piezoresistive sensors for detecting cracks and monitoring deformations [36] and a method of breaking quartz optical fibers glued to the surface of the masonry using epoxy glue to detect and monitor the development of defects in order to determine the residual life of the building’s structural elements [37,38]. The urgent need to examine brickwork, a common construction solution, now demands our attention. Non-destructive electroacoustic techniques, specifically resonance pulse and ultrasonic pulse methods, were employed to predict the service life of unbranded fired bricks, quantified by freeze–thaw cycle resistance. The determination of four durability classes for solid bricks was achieved [39] by analyzing initial and residual mechanical properties after freeze–thaw testing. A method for assessing deterioration in brick building materials involves longitudinal monitoring of compressive strength. Nevertheless, the assessment of the bricks’ strength necessitates laboratory sample analysis, a procedure occasionally infeasible. Alternatively, ultrasonic wave velocity can be a useful non-destructive tool for indirectly assessing the strength properties of bricks [40].

However, there is a lack of work that studies the defect geometry in bricks more precisely [41,42]. For example, such a parameter of a defect as its depth is almost never mentioned [43,44,45,46,47]. Thus, the scientific novelty of the research lies in the study of the processes of propagation of ultrasonic waves in brick with surface cracks and the development and debugging of an ultrasonic method that allows for the accurate determination of the depth of surface cracks in brick with the ability to predict their further growth.

The purpose of this article was to study the processes occurring in ceramic bricks weakened by cracks under ultrasonic exposure and to develop a method for determining the crack depth based on the characteristics of the obtained ultrasonic response. In the first stage, the interaction of the ultrasonic signal with the crack and the features of the pulse propagation process in ceramic bricks were considered using numerical modeling with the ANSYS software (ver. 2023 R1). The practical significance of the study lies in the possibility of timely repairs, as well as forecasting the durability of bricks and the life cycle of structural elements of masonry made from it.

2. Materials and Methods

2.1. Material Properties

The main material under study was ceramic brick, measuring 250 mm × 120 mm × 65 mm. The average density of the brick was from 1706 kg/m³ to 1986 kg/m³. The compressive strength of the brick under study varied from 16.9 MPa to 32.1 MPa, and the flexural strength was from 2.15 MPa to 4.03 MPa (strength grade, M150). The water absorption of the brick was 8.1%. The frost resistance grade was not less than F50 (the brick could withstand at least 50 freeze–thaw cycles). Several experimental samples of ceramic brick were artificially made to have defects in the form of cracks of varying depth. Figure 1 illustrates brick samples exhibiting cracks of varying depth.

For the experimental study, 110 ceramic bricks with cracks were selected. The cracks in the bricks had two origins. Some of the bricks had artificially made cracks (Figure 1), and some had natural cracks. The depth of the cracks and the properties of the bricks, the strength R_c, and the density ρ in the experimental samples are presented in Table 1.

2.2. Ultrasonic Crack Detection Method

The Pulsar-2.2 (NPP Interpribor, Chelyabinsk, Russia) was used as a device for ultrasonic crack detection. The main technical characteristics of the device are presented in Table 2. The appearance of the device and the process of detecting cracks in bricks are shown in Figure 2.

The operating principle of the device is based on measuring the time it takes for an ultrasonic pulse to travel from the emitter to the receiver in the product material. The depth of the cracks was measured in accordance with the diagram shown in Figure 3.

At the beginning of the measurement, the sensors were installed in the range of points I-P1, and time

t_{1}

was measured, then the sensors were installed at points I-P2, and time

t_{a}

was measured. The calculation of the crack depth (H_cr) occurred automatically according to the following formula:

H_{c r} = \frac{a}{2} \sqrt{{(\frac{t_{1}}{t_{a}})}^{2} - 1}

(1)

Here, a is the measurement based on concrete without defects (the position of sensors I-P2), with the mandatory condition a = l; l is the measurement based on concrete through a crack (the position of sensors I-P1). This approach, in accordance with the instructions for the device [48], can lead to an error of 40%. At the same time, the use of such a device is attractive for various reasons. It is inexpensive and can be purchased by any construction organization, unlike expensive tomographs. The device is lightweight and mobile and can be used in hard-to-reach places. Therefore, in this work, we took it as a basis and improved the method for processing the results.

3. Modeling Ultrasonic Pulse Action Using FEM

The use of algorithms for solving inverse problems, including machine learning, is effective when the processes occurring in the structure under pulsed ultrasonic exposure are understood. Thus, before proceeding to solving the inverse problem, that is, determining the geometry of the defect based on the known response, it is advisable to solve the direct problem, that is, determining the response with known characteristics of the defect.

3.1. Statement of the Problem

Let us consider the spatial problem of wave propagation from ultrasonic action in an elastic medium. The object (brick, brickwork, concrete beam, etc.) occupied a position in space in accordance with Figure 4. The coordinate axes were directed parallel to the edges of the parallelepiped, and the origin of coordinates was placed in the far lower corner formed by the intersection of the horizontal (longitudinal and transverse) and vertical edges (Figure 4). A crack with a depth h, an opening width δ, and a length L was located at a distance x₀ from the origin of coordinates and came out onto the surface along which an ultrasonic pulse was applied. At point 1, located at a distance of 0.06 m from the edge of the crack, an ultrasonic pulse F(t) was applied. At point 2, the ultrasonic signal receiver was located.

The equations of wave propagation in an elastic medium, assuming the absence of volume forces, have the form

(λ + G) \frac{\partial e}{\partial x} + G \nabla^{2} u - ρ \frac{\partial^{2} u}{\partial t^{2}} = 0

(2)

(λ + G) \frac{\partial e}{\partial y} + G \nabla^{2} v - ρ \frac{\partial^{2} v}{\partial t^{2}} = 0

(3)

(λ + G) \frac{\partial e}{\partial z} + G \nabla^{2} w - ρ \frac{\partial^{2} w}{\partial t^{2}} = 0

(4)

Here, e is the volume expansion;

\nabla

is the Nabla operator; u, v, and w are the displacements along the x, y, and z axes; and

λ

and G are the Lame parameters.

The deformation components are related to the displacements by dependencies

ε_{x} = \frac{\partial u}{\partial x}; ε_{y} = \frac{\partial v}{\partial y}; ε_{z} = \frac{\partial w}{\partial z}

(5)

The relationship between stress and strain is described by Hooke’s law:

σ_{x} = λ e + 2 G ε_{x}, σ_{y} = λ e + 2 G ε_{y}, σ_{z} = λ e + 2 G ε_{z}

(6)

The problem was solved using the finite element method with the help of the ANSYS software package under the following boundary and initial conditions. Let us designate the lower surface of the object as Ω. Then

{U Y (x, t)|}_{Ω} = 0, {U Z (x_{0} = 0, t)|}_{Ω} = 0, {U X (x_{0} = 250, t)|}_{Ω} = 0, U (t_{0} = 0) = 0

(7)

The points belonging to the lower surface were fixed in the Y direction, i.e., UY = 0. The points located on the lower edge and having the coordinate x = 0 were fixed in the Z direction, UZ = 0. The points located on the lower edge with the coordinate x = 250 mm were fixed in the X direction, UX = 0.

At point 1 with coordinates

x = x_{0} + 0.06; y = b / 2, z = H,

the force was applied:

F (y) = F_{0} \sin (ω t), ω = 2 π f, f = 55 kHz, F_{0} = 10 N

(8)

3.2. Verification of the Model for a Bar Without a Crack with Known Properties

To verify a numerical model, a known exact solution is usually selected, which can be compared with the results of approximate numerical modeling. At this stage, the size of the finite element grid, condensation (if necessary) in the zones of pulse application, and signal reception were worked out. The calibration device included a plexiglass block with known properties and characteristics of ultrasonic wave transmission. Therefore, we compared the numerical solution with experimental data obtained on a calibration block with known properties.

Dynamic problems of wave propagation can lead to significant errors, so a test problem of elastic pulse propagation in a homogeneous bar with reference parameters was preliminarily considered. The bar material was plexiglass, the dimensions were 140 mm × 35 mm × 35 mm, and the propagation velocity of the longitudinal wave was 2606 m/s. A grid of 630 rectangular eight-node elements of the solid type was used for modeling. The number of nodes was 924. The experimental values were measured at point 2 (Figure 4). A comparison of the experimental data and numerical modeling results is shown in Figure 5.

In general, Figure 5 shows that in the initial phase of the signal response, there was good agreement between the experimental and numerical analysis results. Further discrepancies in the data were due to the reflection of waves from the walls of the bar.

Also, modeling the propagation of a pulse in a medium without defects allowed us to better understand the mechanics of the transmission of disturbances and oscillations. Figure 6 shows the sequential propagation of disturbances along the X axis.

From the presented fragments, it was evident that the disturbance propagated uniformly from the point of pulse application in all directions. The longitudinal wave, running along the surface along the X axis and having the highest speed, transmitted the disturbance further to the receiver. The points on the surface moved along a trajectory close to an ellipse due to the Poisson effect. Next came the transverse wave, more energetic, and then the vertical displacements of the surface points became several times higher than those with a longitudinal wave. In Figure 6b–d it is evident that the disturbance also propagated radially and covered the areas of the rear wall and side walls. The wave reflected from these surfaces also contributed to the overall response, which was recorded at point 2 by the receiver.

4. Results of Direct Calculation of Ultrasonic Pulse Propagation Through a Brick Weakened by a Crack

Direct calculation of ultrasonic pulse propagation for bodies weakened by cracks in accordance with Figure 4 was carried out numerically using the ANSIS software package. Figure 7 shows the von Mises stress fields when an ultrasonic pulse propagates through a body weakened by a crack.

Figure 7 demonstrates the successive development of von Mises stresses in a brick with a crack 60 mm deep and 2 mm thick. The brick was cut across its entire width. It can be seen that at the initial stage (Figure 7a,b), the disturbance field was spherical. Successively expanding, the field propagated to the crack (Figure 7c), and at this point the crack broke the wave front.

Figure 7d,e show that the wave front bent around the crack from below, maintaining its spherical nature and involving neighboring points of the medium in the oscillation process. The further wave propagation pattern was associated with reflection from the brick walls, which created a flow of reflected waves and created an error in the analysis of the received signal.

Figure 7 also shows that the longitudinal wave front moved ahead (shown in soft blue in the figures). Following at a certain distance was the transverse wave front (shown in green or red spots in the figures). This was a more energetic and powerful wave, lagging in phase behind the longitudinal one.

Figure 7f shows that at the moment when the pulse reached the surface in the receiver zone, the transverse wave was reflected from the back wall (shown in red) and the bottom and followed the longitudinal wave, bending around the crack. This is clearly visible on the graph due to the sharp increase in the oscillation amplitude.

Figure 8 demonstrates the dependence of the UY displacements at the receiving point on the pulse propagation time.

Figure 8 shows the oscillations of the receiving point along the Uy axis at different moments in time for a brick without a crack (1), with a crack 20 mm deep (2), and with a crack 60 mm deep (3). It was evident that the time during which the pulse reached the receiving point was different and was determined by the same material properties and crack depth. This can be an effective parameter for constructing an algorithm for calculating the crack depth to solve the inverse problem of restoring the crack characteristic with known values of the input data.

5. Results of Experimental Measurements and Discussion

5.1. Analysis of Characteristic Signal Parameters

The results of the experimental measurement of ultrasonic pulse signals for different crack depths are shown in Figure 9.

Figure 9 illustrates the signal features when an ultrasonic pulse passed through bricks with different cracks. These features clearly demonstrated a signal shift along the time axis, and the deeper the crack, the more time it took for the pulse to reach the receiving point. The characteristic points here were the moments of time and the amplitude values of the signal.

Thus, at the initial stage of the analysis, the following characteristic parameters were adopted that characterized the relationship of the signal with the crack geometry (Figure 10):

T_{0}

, the time (μs) when the signal reaches a value of 12 units;

T_{1}

and

X_{1 m a x}

, the time (μs) to reach the first maximum and the level of the first maximum; and

T_{2}

and

X_{1 m i n}

, the time (μs) to reach the first minimum and the level of the first minimum.

5.2. Correlation and Regression Analysis of Time and Amplitude Parameters of the Signal

Analysis of the full data array showed that with a single measurement of the parameters, the dispersion of the predicted results was significant (Table 3).

Table 3 shows that the crack depth correlated with the time parameters, but there was no correlation with the amplitude parameters.

To reduce data dispersion, it was decided to average the results for objects with the same properties. In practice, this meant that the device must make five measurements and select the average value for a more accurate prediction. Weakly correlated amplitude parameters were also excluded, and quadratic time terms were added to account for possible nonlinearity.

Table 4 shows that the correlation of the crack depth with the time parameters of the signal increased significantly:

r_{T 0} = 0.89900

r_{T_{0}^{2}} = 0.90157

r_{T 1} = 0.89097

r_{T_{1}^{2}} = 0.89390

r_{T 2} = 0.89221

, and

r_{T_{2}^{2}} = 0.89579

. It was also clear that the quadratic terms contributed to the increase in the tightness of the relationship. The regression curve from the time parameters had the form

H_{c r} = 127.0 - 7.949 T_{0} + 0.0798 T_{0}^{2} + 21.29 T_{1} - 0.158 T_{1}^{2} - 16.87 T_{2} + 0.111 T_{2}^{2}

(9)

A comparison of experimental and predicted values is illustrated in Figure 11.

The regression equation presented in Figure 11 shows several important aspects. First, the regression line went from 0 at an angle of 45°. This meant that the predicted values, on average, corresponded well to the experimentally measured ones when the averaging sample was increased. Second, the confidence limits were symmetrically located and showed an error of about 14% at the top of the interval, which was significantly less than the existing 40%. This allowed us to take the next step in improving the crack depth prediction algorithm.

5.3. Correlation and Regression Analysis of Signal Time Parameters Taking into Account Material Properties

To further reduce data dispersion, it was decided to include material properties such as strength and density in the regression model. Indeed, the time it took for a pulse to travel a certain distance depended not only on the crack geometry but also on the speed of the ultrasonic wave, which was determined by the material density and elastic modulus. Determining the elastic modulus of bricks was difficult, and determining the density was associated with simple measurements.

Thus, an analysis of the correlation coefficients of the already obtained parameters and the parameters characterizing the properties of the material was carried out. The data are given in Table 5.

Table 5 shows that the density of the material made a significant contribution to the correlation. On this basis, a new regression equation was obtained:

H_{c r} = - 378.4 - 32.89 T_{0} + 0.299 T_{0}^{2} + 36.29 T_{1} - 0.308 T_{1}^{2} - 2.265 T_{2} + 0.026 T_{2}^{2} - 1.58 R_{c} + 0.157 ρ

(10)

A comparison of the experimental and predicted values according to model (10) is illustrated in Figure 12.

It was evident that the inclusion of material properties in the model (10) significantly increased the accuracy of the predicted crack depth values. As can be seen from the graph, the error was less than 8%.

5.4. Limitations of the Proposed Method and Directions for Future Research

The following can be specified as limitations of the application of this method. Heterogeneity of the material within one brick can lead to an increase in error. At the current stage of research, we proceeded from the fact that within one brick, its properties were homogeneous and isotropic. That is, heterogeneity occurred between different bricks and was taken into account in the regression equation by the density parameter.

The model was also sensitive if the crack penetrated several bricks connected with cement mortar at once. In this case, the heterogeneity of the material increased, and the error also increased.

As further research, the authors plan to apply machine learning methods to analyze the ultrasonic signal. It seems appropriate to apply different machine learning methods and compare their effectiveness. Next, the authors plan to study the problem of detecting and determining the geometric characteristics of hidden defects.

6. Conclusions

The conducted research allowed us to draw the following conclusions.

A numerical analysis of the propagation of an ultrasonic pulse in ceramic bricks weakened by a defect in the form of a crack was conducted. The analysis showed that the crack broke the wave front and made it travel a longer distance to the signal reception point.
Experimental measurements on bricks with cracks also showed that the pulse curves had characteristic time shifts, which could be effectively used to predict the crack depth.
Characteristic parameters characterizing the signal were identified. Such parameters included time characteristics and material properties. The conducted correlation and regression analyses made it possible to obtain a model for determining cracks using the ultrasonic method. It was shown that the error of such a model was 8%, which was significantly lower than the device’s passport data of 40%.

Author Contributions

Conceptualization, I.R., S.A.S., E.M.S., N.B., A.C. and D.E.; methodology, A.N.B., N.B. and I.R.; software, V.D., N.B., I.R. and A.C.; validation, S.A.S., E.M.S., N.B. and A.N.B.; formal analysis, I.R. and A.C.; investigation, I.R., S.A.S., E.M.S., A.N.B., V.D., N.B., A.C. and D.E.; resources, S.A.S. and E.M.S.; data curation, I.R.; writing—original draft preparation, S.A.S., E.M.S., N.B. and A.N.B.; writing—review and editing, S.A.S., E.M.S. and A.N.B.; visualization, S.A.S., E.M.S., A.N.B. and N.B.; supervision, A.N.B.; project administration, A.N.B.; funding acquisition, E.M.S. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

Data is contained within the article.

Acknowledgments

The authors would like to acknowledge the administration of Don State Technical University for their resources.

Conflicts of Interest

The authors declare no conflicts of interest.

References

Silva, M.I.; Malitckii, E.; Santos, T.G.; Vilaça, P. Review of Conventional and Advanced Non-destructive Testing Techniques for Detection and Characterization of Small-scale Defects. Prog. Mater. Sci. 2023, 138, 101155. [Google Scholar] [CrossRef]
Torbali, M.E.; Zolotas, A.; Avdelidis, N.P.; Alhammad, M.; Ibarra-Castanedo, C.; Maldague, X.P. A Complementary Fusion-Based Multimodal Non-Destructive Testing and Evaluation Using Phased-Array Ultrasonic and Pulsed Thermography on a Composite Structure. Materials 2024, 17, 3435. [Google Scholar] [CrossRef] [PubMed]
Mailyan, L.R.; Stel’makh, S.A.; Shcherban’, E.M.; Khalyushev, A.K.; Smolyanichenko, A.S.; Sysoev, A.K.; Parinov, I.A.; Cherpakov, A.V. Investigation of Integral and Differential Characteristics of Variatropic Structure Heavy Concretes by Ultrasonic Methods. Appl. Sci. 2021, 11, 3591. [Google Scholar] [CrossRef]
Lyapin, A.; Beskopylny, A.; Meskhi, B. Structural Monitoring of Underground Structures in Multi-Layer Media by Dynamic Methods. Sensors 2020, 20, 5241. [Google Scholar] [CrossRef]
Han, G.; Lv, S.; Tao, Z.; Sun, X.; Du, B. Evaluation of Bolt Corrosion Degree Based on Non-Destructive Testing and Neural Network. Appl. Sci. 2024, 14, 5069. [Google Scholar] [CrossRef]
Adams, M.; Huijer, A.; Kassapoglou, C.; Vaders, J.A.A.; Pahlavan, L. In Situ Non-Destructive Stiffness Assessment of Fiber Reinforced Composite Plates Using Ultrasonic Guided Waves. Sensors 2024, 24, 2747. [Google Scholar] [CrossRef]
Kim, J.-W.; Choi, H.-W.; Kim, S.-K.; Na, W.S. Review of Image-Processing-Based Technology for Structural Health Monitoring of Civil Infrastructures. J. Imaging 2024, 10, 93. [Google Scholar] [CrossRef]
Shah Mansouri, T.; Lubarsky, G.; Finlay, D.; McLaughlin, J. Machine Learning-Based Structural Health Monitoring Technique for Crack Detection and Localisation Using Bluetooth Strain Gauge Sensor Network. J. Sens. Actuator Netw. 2024, 13, 79. [Google Scholar] [CrossRef]
Liu, Z.; Xu, W.; Xu, Q.; Shi, M.; Luo, Y. Load Testing and Analysis of a Large Span Through Simply-Supported Steel Box Arch Bridge. Appl. Sci. 2024, 14, 11418. [Google Scholar] [CrossRef]
Singla, R.; Sharma, S.; Siddique, R. Nondestructive Evaluation of Autonomic Crack Healing in Concrete Using Ultrasonic Wave Propagation. J. Mater. Civ. Eng. 2024, 36, 04024328. [Google Scholar] [CrossRef]
Asvitha, V.S.; Kumar, R.M.S. Effectiveness of Xanthan Gum-based composite in repairing cracks in reinforced concrete structures. Mater. Res. Express 2024, 11, 095701. [Google Scholar] [CrossRef]
Wang, W.; Li, Y.; Li, Y. A method for detecting defects in reinforced concrete structures of underwater tunnels based on ultrasonic echo signal and CNN. AIP Adv. 2024, 14, 115213. [Google Scholar] [CrossRef]
Krolik, A.; Drelich, R.; Pakuła, M.; Mikołajewski, D.; Rojek, I. Detection of Defects in Polyethylene and Polyamide Flat Panels Using Airborne Ultrasound-Traditional and Machine Learning Approach. Appl. Sci. 2024, 14, 10638. [Google Scholar] [CrossRef]
Beskopylny, A.N.; Shcherban’, E.M.; Stel’makh, S.A.; Mailyan, L.R.; Meskhi, B.; Razveeva, I.; Kozhakin, A.; El’shaeva, D.; Beskopylny, N.; Onore, G. Detecting Cracks in Aerated Concrete Samples Using a Convolutional Neural Network. Appl. Sci. 2023, 13, 1904. [Google Scholar] [CrossRef]
Siracusano, G.; Garescì, F.; Finocchio, G.; Tomasello, R.; Lamonaca, F.; Scuro, C.; Carpentieri, M.; Chiappini, M.; La Corte, A. Automatic Crack Classification by Exploiting Statistical Event Descriptors for Deep Learning. Appl. Sci. 2021, 11, 12059. [Google Scholar] [CrossRef]
Tanveer, M.; Elahi, M.U.; Jung, J.; Azad, M.M.; Khalid, S.; Kim, H.S. Recent Advancements in Guided Ultrasonic Waves for Structural Health Monitoring of Composite Structures. Appl. Sci. 2024, 14, 11091. [Google Scholar] [CrossRef]
Liang, H.; Zhang, J.; Yang, S. Location Detection and Numerical Simulation of Guided Wave Defects in Steel Pipes. Appl. Sci. 2024, 14, 10403. [Google Scholar] [CrossRef]
Palma-Ramírez, D.; Ross-Veitía, B.D.; Font-Ariosa, P.; Espinel-Hernández, A.; Sanchez-Roca, A.; Carvajal-Fals, H.; Nuñez-Alvarez, J.R.; Hernández-Herrera, H. Deep convolutional neural network for weld defect classification in radiographic images. Heliyon 2024, 10, e30590. [Google Scholar] [CrossRef]
Zhang, H.; Ning, X.; Pu, H.; Ji, S. A novel approach for the non-destructive detection of shriveling degrees in walnuts using improved YOLOv5n based on X-ray images. Postharvest Biol. Technol. 2024, 214, 113007. [Google Scholar] [CrossRef]
Beskopylny, A.N.; Stel’makh, S.A.; Shcherban’, E.M.; Razveeva, I.; Kozhakin, A.; Meskhi, B.; Chernil’nik, A.; Elshaeva, D.; Ananova, O.; Girya, M.; et al. Computer Vision Method for Automatic Detection of Microstructure Defects of Concrete. Sensors 2024, 24, 4373. [Google Scholar] [CrossRef]
Razveeva, I.; Kozhakin, A.; Beskopylny, A.N.; Stel’makh, S.A.; Shcherban’, E.M.; Artamonov, S.; Pembek, A.; Dingrodiya, H. Analysis of Geometric Characteristics of Cracks and Delamination in Aerated Concrete Products Using Convolutional Neural Networks. Buildings 2023, 13, 3014. [Google Scholar] [CrossRef]
Shen, X.; Lu, X.; Guo, J.; Liu, Y.; Qi, J.; Lv, Z. Nondestructive Testing of Metal Cracks: Contemporary Methods and Emerging Challenges. Crystals 2024, 14, 54. [Google Scholar] [CrossRef]
Ottosen, L.M.; Kunther, W.; Ingeman-Nielsen, T.; Karatosun, S. Non-Destructive Testing for Documenting Properties of Structural Concrete for Reuse in New Buildings: A Review. Materials 2024, 17, 3814. [Google Scholar] [CrossRef] [PubMed]
Vasiliev, P.V.; Senichev, A.V.; Giorgio, I. Visualization of internal defects using a deep generative neural network model and ultrasonic nondestructive testing. Adv. Eng. Res. 2021, 21, 143–153. [Google Scholar] [CrossRef]
Angiulli, G.; Calcagno, S.; La Foresta, F.; Versaci, M. Concrete Compressive Strength Prediction Using Combined Non-Destructive Methods: A Calibration Procedure Using Preexisting Conversion Models Based on Gaussian Process Regression. J. Compos. Sci. 2024, 8, 300. [Google Scholar] [CrossRef]
Lopez-Miguel, A.; Cabello-Mendez, J.A.; Moreno-Valdes, A.; Perez-Quiroz, J.T.; Machorro-Lopez, J.M. Non-Destructive Testing of Concrete Materials from Piers: Evaluating Durability Through a Case Study. NDT 2024, 2, 532–548. [Google Scholar] [CrossRef]
Im, H.; Kim, W.; Choi, H.; Lee, T. Strength Prediction of Non-Sintered Hwangto-Substituted Concrete Using the Ultrasonic Velocity Method. Materials 2024, 17, 174. [Google Scholar] [CrossRef]
Miano, A.; Ebrahimian, H.; Jalayer, F.; Prota, A. Reliability Estimation of the Compressive Concrete Strength Based on Non-Destructive Tests. Sustainability 2023, 15, 14644. [Google Scholar] [CrossRef]
Yong, Y.P.; Lee, S.J.; Chang, Y.H.; Lee, K.H.; Kwon, S.W.; Cho, C.S.; Chung, S.W. Object Detection and Distance Measurement Algorithm for Collision Avoidance of Precast Concrete Installation during Crane Lifting Process. Buildings 2023, 13, 2551. [Google Scholar] [CrossRef]
Demir, T.; Ulucan, M.; Alyamaç, K.E. Development of Combined Methods Using Non-Destructive Test Methods to Determine the In-Place Strength of High-Strength Concretes. Processes 2023, 11, 673. [Google Scholar] [CrossRef]
Shcherban’, E.M.; Beskopylny, A.N.; Stel’makh, S.A.; Mailyan, L.R.; Shilov, A.A.; Hiep, N.Q.; Song, Y.; Chernil’nik, A.A.; Elshaeva, D.M. Study of thermophysical characteristics of variatropic concretes. Constr. Mater. Prod. 2024, 7, 2. [Google Scholar] [CrossRef]
Ivanchev, I. Investigation with Non-Destructive and Destructive Methods for Assessment of Concrete Compressive Strength. Appl. Sci. 2022, 12, 12172. [Google Scholar] [CrossRef]
Aparicio Secanellas, S.; Liébana Gallego, J.C.; Anaya Catalán, G.; Martín Navarro, R.; Ortega Heras, J.; García Izquierdo, M.Á.; González Hernández, M.; Anaya Velayos, J.J. An Ultrasonic Tomography System for the Inspection of Columns in Architectural Heritage. Sensors 2022, 22, 6646. [Google Scholar] [CrossRef] [PubMed]
Lou, C.; Tinsley, L.; Duarte Martinez, F.; Gray, S.; Honarvar Shakibaei Asli, B. Optimized AI Methods for Rapid Crack Detection in Microscopy Images. Electronics 2024, 13, 4824. [Google Scholar] [CrossRef]
Zhang, L.; Li, X.; Hao, S.; Yan, Q.; Wang, J.; Wang, M. A Study on the Identification of Cracks in Mine Subsidence Based on YOLOv8n Improvement. Processes 2024, 12, 2716. [Google Scholar] [CrossRef]
Meoni, A.; D’Alessandro, A.; Saviano, F.; Lignola, G.P.; Parisi, F.; Ubertini, F. Strain Monitoring and Crack Detection in Masonry Walls under In-Plane Shear Loading Using Smart Bricks: First Results from Experimental Tests and Numerical Simulations. Sensors 2023, 23, 2211. [Google Scholar] [CrossRef]
Khotiaintsev, S.; Timofeyev, V. Assessment of Cracking in Masonry Structures Based on the Breakage of Ordinary Silica-Core Silica-Clad Optical Fibers. Appl. Sci. 2022, 12, 6885. [Google Scholar] [CrossRef]
Naumov, A.A.; Dymchenko, M.E. Ceramic Bricks of Increased Frost Resistance of Kushchevsky Deposit Clay Raw Material as the Building Material within Architectural Shaping Dynamics. Mod. Trends Constr. Urban Territ. Plan. 2023, 2, 62–71. [Google Scholar] [CrossRef]
Bartoň, V.; Dvořák, R.; Cikrle, P.; Šnédar, J. Predicting the Durability of Solid Fired Bricks Using NDT Electroacoustic Methods. Materials 2022, 15, 5882. [Google Scholar] [CrossRef]
Jamshidi, A.; Sousa, L. Strength Characteristics, Ultrasonic Wave Velocity, and the Correlation between Them in Clay Bricks under Dry and Saturated Conditions. Materials 2024, 17, 1353. [Google Scholar] [CrossRef]
Chen, B.; Qiu, F.; Xia, L.; Xu, L.; Jin, J.; Gou, G. In Situ Ultrasonic Characterization of Hydrogen Damage Evolution in X80 Pipeline Steel. Materials 2024, 17, 5891. [Google Scholar] [CrossRef]
Beskopylny, A.N.; Shcherban’, E.M.; Stel’makh, S.A.; Mailyan, L.R.; Meskhi, B.; Razveeva, I.; Kozhakin, A.; El’shaeva, D.; Beskopylny, N.; Onore, G. Discovery and Classification of Defects on Facing Brick Specimens Using a Convolutional Neural Network. Appl. Sci. 2023, 13, 5413. [Google Scholar] [CrossRef]
Li, W.; Zhu, J.; Mu, K.; Yang, W.; Zhang, X.; Zhao, X. Experimental Investigation of Concrete Crack Depth Detection Using a Novel Piezoelectric Transducer and Improved AIC Algorithm. Buildings 2024, 14, 3939. [Google Scholar] [CrossRef]
Rijal, M.; Amoateng-Mensah, D.; Sundaresan, M.J. Finite Element Simulation of Acoustic Emissions from Different Failure Mechanisms in Composite Materials. Materials 2024, 17, 6085. [Google Scholar] [CrossRef]
Gaidzhurov, P.P.; Volodin, V.A. Strength Calculation of the Coupling of the Floor Slab and the Monolithic Reinforced Concrete Frame Column by the Finite Element Method. Adv. Eng. Res. 2022, 22, 306–314. [Google Scholar] [CrossRef]
Falkowicz, K. Stability and Failure of Thin-Walled Composite Plate Elements with Asymmetric Configurations. Materials 2024, 17, 1943. [Google Scholar] [CrossRef]
Nguyen, C.L.; Nguyen, A.; Brown, J.; Byrne, T.; Ngo, B.T.; Luong, C.X. Optimising Concrete Crack Detection: A Study of Transfer Learning with Application on Nvidia Jetson Nano. Sensors 2024, 24, 7818. [Google Scholar] [CrossRef]
Operating Manual for the Ultrasonic Complex PULSAR-2.2. Available online: https://www.interpribor.ru/assets/userfiles/9/91/Pulsar_22_TFT.pdf?ysclid=m4d5y0f474986336855 (accessed on 6 December 2024).

Figure 1. Appearance of experimental samples of bricks with cracks of different depths.

Figure 2. The process of detecting cracks in bricks using the Pulsar-2.2 ultrasonic device.

Figure 3. Scheme of installation of sensors for measuring crack depth.

Figure 4. General diagram of a block with a crack: 1—point of pulse application; 2—location of the ultrasonic signal receiver.

Figure 5. Comparison of experimental and numerical simulation results (Plexiglas material is the reference sample).

Figure 6. Wave propagation in a plexiglass block at the moments of time (a) t = 2 µs, (b) t = 8 µs, (c) t = 16 µs, and (d) t = 30 µs.

Figure 7. Successive development of von Mises stresses in a brick weakened by a crack at different points in time: (a) t = 9.5 µs, (b) t = 13.5 µs, (c) t = 17.5 µs, (d) t = 21.5 µs, (e) t = 23.5 µs, and (f) t = 47.5 µs.

Figure 8. Dependence of UY displacements at the receiving point on the pulse propagation time: 1—without defect; 2—crack 20 mm deep; 3—crack 60 mm deep.

Figure 9. Comparison of ultrasonic pulse signals for different crack depths.

Figure 10. Characteristic parameters of the signal used to determine the crack depth.

Figure 11. Experimental and predicted values for averaged parameters.

Figure 12. Experimental and predicted values for averaged parameters taking into account the material properties.

Table 1. Depth of cracks and properties of bricks in the experimental samples.

Number	Crack Depth H_cr, mm	R_c, MPa	ρ, kg/m³
1	2	17.5	1706
2	2	28	1882
3	3	17.5	1706
4	5	28	1882
5	8	16.9	1745
6	9	32.1	1939
7	11	16.9	1745
8	12	32.1	1939
9	15	26.9	1946
10	18	26.9	1946
11	20	19.5	1898
12	23	19.5	1898
13	27	31	1986
14	30	31	1986
15	36	29.1	1978
16	37	29.1	1978
17	40	29.7	1988
18	44	29.7	1988
19	45	20.2	1968
20	51	30.5	1970
21	54	20.2	1968
22	54	30.5	1970

Table 2. Technical characteristics of the Pulsar-2.2 device.

Parameter Name	Value
Ultrasonic pulse propagation velocity measurement range, m/s	1000–10,000
Ultrasonic pulse propagation time measurement range, μs	10–100
Ultrasonic pulse propagation time indication range, μs	10–20,000
Pulse probing period setting limits, s	0.2–1
Ultrasonic oscillation operating frequency, kHz	60 ± 10
Power consumption, W, no more than	8.0
Device weight in full configuration, kg, no more than	2.5
Overall dimensions (length × width × height), mm, no more than:
Electronic unit	220 × 100 × 35
Surface sounding sensor	300 × 130 × 40
Through sounding sensor	52 × 50

Table 3. Correlation matrix of signal parameters for the entire data array.

	$T_{0}$	$T_{1}$	$X_{1 m a x}$	$T_{2}$	$X_{1 m i n}$	$H_{c r}$
$T_{0}$	1
$T_{1}$	0.99082554	1
$X_{1 m a x}$	0.027127349	0.061513335	1
$T_{2}$	0.970266815	0.982728065	0.025900262	1
$X_{1 m i n}$	0.147409132	0.090953549	−0.659919634	0.070534599	1
$H_{c r}$	0.597773293	0.59006444	−0.080032567	0.611358476	0.12579949	1

Table 4. Correlation matrix of averaged signal parameters.

	$T_{0}$	$T_{0}^{2}$	$T_{1}$	$T_{1}^{2}$	$T_{2}$	$T_{2}^{2}$	$H_{c r}$
$T_{0}$	1
$T_{0}^{2}$	0.99913	1
$T_{1}$	0.99447	0.99295	1
$T_{1}^{2}$	0.99469	0.99474	0.99924	1
$T_{2}$	0.98760	0.98581	0.98838	0.98767	1
$T_{2}^{2}$	0.98780	0.98740	0.98798	0.98856	0.99938	1
$H_{c r}$	0.89900	0.90157	0.89097	0.89390	0.89221	0.89579	1

Table 5. Correlation matrix of averaged signal parameters and material properties.

	$T_{0}$	$T_{0}^{2}$	$T_{1}$	$T_{1}^{2}$	$T_{2}$	$T_{2}^{2}$	$R_{c}$	$ρ$	$H_{c r}$
$T_{0}$	1
$T_{0}^{2}$	0.999	1
$T_{1}$	0.994	0.992	1
$T_{1}^{2}$	0.994	0.994	0.999	1
$T_{2}$	0.987	0.985	0.988	0.987	1
$T_{2}^{2}$	0.987	0.987	0.987	0.988	0.999	1
$R_{c}$	0.185	0.195	0.167	0.176	0.168	0.179	1
$ρ$	0.498	0.504	0.512	0.518	0.489	0.497	0.751	1
$H_{c r}$	0.899	0.901	0.890	0.893	0.892	0.895	0.293	0.701	1

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Share and Cite

MDPI and ACS Style

Beskopylny, A.N.; Stel’makh, S.A.; Shcherban’, E.M.; Dolgov, V.; Razveeva, I.; Beskopylny, N.; Elshaeva, D.; Chernil’nik, A. Determination of Crack Depth in Brickworks by Ultrasonic Methods: Numerical Simulation and Regression Analysis. J. Compos. Sci. 2024, 8, 536. https://doi.org/10.3390/jcs8120536

AMA Style

Beskopylny AN, Stel’makh SA, Shcherban’ EM, Dolgov V, Razveeva I, Beskopylny N, Elshaeva D, Chernil’nik A. Determination of Crack Depth in Brickworks by Ultrasonic Methods: Numerical Simulation and Regression Analysis. Journal of Composites Science. 2024; 8(12):536. https://doi.org/10.3390/jcs8120536

Chicago/Turabian Style

Beskopylny, Alexey N., Sergey A. Stel’makh, Evgenii M. Shcherban’, Vasilii Dolgov, Irina Razveeva, Nikita Beskopylny, Diana Elshaeva, and Andrei Chernil’nik. 2024. "Determination of Crack Depth in Brickworks by Ultrasonic Methods: Numerical Simulation and Regression Analysis" Journal of Composites Science 8, no. 12: 536. https://doi.org/10.3390/jcs8120536

APA Style

Beskopylny, A. N., Stel’makh, S. A., Shcherban’, E. M., Dolgov, V., Razveeva, I., Beskopylny, N., Elshaeva, D., & Chernil’nik, A. (2024). Determination of Crack Depth in Brickworks by Ultrasonic Methods: Numerical Simulation and Regression Analysis. Journal of Composites Science, 8(12), 536. https://doi.org/10.3390/jcs8120536

Article Menu