*3.2. Numerical Model*

The abovementioned slab was modeled in a commercial program LS-DYNA® [33] and is presented in Figure 2a. A three-dimensional model was built using 8 nodes hexahedron 7 mm × 7 mm constant stress solid elements of type ELFORM 1. This type of element, with a single integration point, was chosen for better computational efficiency considering the relatively simple stress-state and shape of the modeled structure. Viscous control of hourglass (type 1) was chosen as it is recommended for higher velocity waves and is computationally the cheapest. Considering the relatively low size of mesh, good results were obtained with this simple modeling method and explicit integration.

**Figure 2.** Isometric view of Finite Element Models (**a**) model of 50 cm × 50 cm × 7 cm plate for validation; (**b**) model of infinitely large slab for layout testing.

Vertical displacements were constrained in corners on the lower face of the plate. The material was modeled as perfectly elastic, with modulus of elasticity 38 GPa, density 2400 kg/m<sup>3</sup> and Poisson ratio 0.2, corresponding to C20/25 concrete [10]. The excitement was applied by force with sine function variability of 2 kN. Such variability is commonly used and its magnitude does not influence the results thanks to the elastic material model [6,9]. The excitation impulse lasted for 8.4 × <sup>10</sup>−<sup>6</sup> s, corresponding to a 2 mm ball [6]. Vertical displacement of the node in location of the transducer was registered for 2 ms, with a time step of 1.4 × <sup>10</sup>−<sup>3</sup> ms.

#### *3.3. Signal Processing*

To validate the model, two signals collected in different ways needed to be compared. During the experiment, variation of current voltage due to pressure waves acting on piezoelectric in transducer was registered, while the direct displacement of node could be obtained from the model. This is why a proper filtering is important [17].

For validation, the surface (Rayleigh) wave was removed by cutting the first 0.5 ms of signal. Then, the Butterworth filter was applied for frequencies outside <sup>1</sup> <sup>2</sup> *f–*2*f* window, where *f* is the frequency expected due to plate thickness. The filtering was needed mostly due to numerical noise and eigenvibrations present in numerical results, as well as high frequency noise due to the concrete inhomogeneity in slabs. Then, the Fast Fourier Transform (FFT) was used to present and compare the frequency spectrum.

#### *3.4. Results*

Thickness of the tested plate, and depth of possible fault, can be found on the basis of the passage time of the pressure wave through the material. Since the wave is reflected multiple times from the bottom and top surfaces, frequency of the wave passage is used. The velocity of wave can be obtained from the empirical Equation (1) [6]:

$$C\_p = \sqrt{\frac{E(1-\nu)}{\rho(1+\nu)(1-2\nu)}}\tag{1}$$

where *E* stands for Young's modulus of elasticity of concrete, *ρ* for density of concrete and *ν* is Poisson's ratio. This velocity is, however, dependent on the element's shape; thus, for plates, an apparent velocity should be used [8,9], leading to the Equation (2):

$$T = \frac{\mathbb{C}\_{pp}}{2f} \tag{2}$$

where *f* stands for frequency of signal, *T* for thickness (depth) of element and *Cpp =* 0.96*Cp* is the reduced, apparent wave velocity for the concrete plate with *υ* = 0.2 due to resonance and the creation of Lamb waves [34,35].

A good correlation between registered signals and their frequency spectra was obtained. The dominating frequency from experiment is 27.40 kHz, while from the model it is

27.19 kHz. With *Cpp* = 3830 m/s, the thickness of 70.0 mm and 70.4 mm can be calculated, respectively.

Thus, the model was validated and good agreement with the experiment was found.

#### **4. Experimental Studies on a Large Span Floor**

The bigger the spacing between impactor and transducer, the larger the distance that wave travels in the material. Because of this, the area tested at once can be increased, reducing the time needed for the whole slab or floor, and IE can be used to test a certain volume of concrete at once. This is why balance between the reliability of results and the distance between impactor and receiver needed to be found.

An experiment was prepared to investigate the maximum distance between the impact and read-out points at which results remain clear and reliable. Because the circular wave reflects not only from faces of the element but from other boundaries as well, interference may influence the results. To avoid this, the large span 40 cm thick concrete floor was chosen. The span-to-depth ratio was big enough to considered it as an element of infinite area.

Measurements were taken in the three directions (each 45◦) to avoid influence of reinforcement. The distance between points of impact and signal reception varied from 10 cm to 300 cm. A 12 mm impactor was used according to the geometry of slab and detection ability as presented by Carino [9]. Each measurement was repeated three times.

Measurements show that the maximum distance between impactor and receiver giving reliable results is around 90 cm and above this distance, the wave reaching transducer was too weak (Figure 3). It has to be stressed that energy produced by the smaller ball is lower, and thus, this distance would decrease. This result can be influenced by the type of the concrete used and serves merely as estimation of possibility of change Impact-Echo from punctual into volumetric method. Taking into account the expected range of thicknesses of slabs to be tested with the device under design, as well as convenience of its use, a square 60 cm × 60 cm was assumed as a maximal testing area. Furthermore, it was concluded that an automated impact procedure should be implemented to make uniform the subsequent readouts. The exact results and discussion can be found in [31].

**Figure 3.** Frequency spectra of measurements taken at a large span floor in distance of 10 cm, 60 cm and 90 cm from impactor; frequency due to thickness marked with dashed line.

#### **5. Finite Element Model of Plate with Voids**

Knowing the maximum dimensions of the IE module that could be incorporated into the automated scanner combining different NDT techniques [5], the best layout was pursued. The IE module should allow for testing in an automated way the biggest possible area at once. At this stage, the presence or lack of fault or void should be determined. The depth and exact location within the tested area can be found using more precise testing later. In this way, the large area of slab can be scanned in a quicker manner, showing the points of possible further interest.

#### *5.1. Numerical Model Modification*

It was decided to model the plate for further investigation as an infinitely large slab. The purpose of this was to avoid possible reflections from the boundaries of the element. To do this, a square plate 90 cm × 90 cm × 20 cm was modeled with further extension to obtain a circular external surface (Figure 2b). To this side surface, nonreflective boundary conditions were assigned. The vertical supports were assigned at the mid-span on the whole perimeter.

The void was modeled by removal of elements in the box 20 cm × 20 cm × 2 cm at mid-depth (Figure 4). The expected peaks, calculated with formula (2), are presented in Table 1, respectively, for the top and bottom of the void, and for the thickness of whole element. Since the element's size, material properties and finite elements type remained the same as in validated model, no additional verification or validation was needed.

**Figure 4.** The plate with void: (**a**) view and (**b**) section.



#### *5.2. Possible Linear Layouts*

The standard IE layout consist of one impactor and one receiver. If the void or fault is below one of them or between them, it can be detected.

The first considered layout was one receiver and one impactor spaced by 40 cm, moving along the line perpendicular to them. This way, subsequent cross-sections of slab can be examined. However, to obtain the necessary resolution, many measurements were needed (e.g., every 10 cm), leading to a time-consuming procedure.

To cover a bigger area at once, a set of four impactor–receiver pairs each spaced at 10 cm, covering an area of 30 cm by 40 cm, can be used. All the impactors would be released at same time. However, due to wave interference, the readouts were difficult to analyze, and this approach was given up. Furthermore, the release of impactors at exactly the same time could be problematic.

The third layout would be a modification of the above. Instead of using four impactors, only one could be used. However, the distance between the impactor and each of the receivers would not be equal and analysis of such a signal would be difficult.

On the basis of the numerical models of the three abovementioned arrangements, it was decided that for the proper layout, the distance between each of receivers and impactor should be equal. Furthermore, to avoid interference of waves, only one impactor should be used for the IE module.

#### *5.3. Square Layout*

As mentioned above, it was decided that the distance between impactor and all transducers should be equal for sake of simplicity of comparison. Although the maximum distance between points of impact and read-out was found to be 90 cm, the IE module should fit within the UIR integrated scanner. Therefore, the distances were reduced. The transducer layout should allow diagnostics of the largest possible area at once. This is why the square scheme was investigated with piezoelectric receivers in points 1 to 4 (Figure 5). Then, the applicability of this layout with different positioning of void was modeled.

**Figure 5.** Square measurement system layout: (**a**) isometric and (**b**) top views.

#### *5.4. Signal Processing*

The signal was processed in similar way as in the experimental validation (see Section 3.3). Filtering out the frequencies outside of <sup>1</sup> <sup>2</sup> *f* –4 *f* was performed to exclude the eigenvibrations of plate and numerical noise, but to keep the high-frequency waves due to reflections from the void. The Raleigh wave was removed by cutting out first 0.5 ms of signal.

#### **6. Results of Simulations**

The results are compared in both qualitative and quantitative ways. The qualitative way is by comparison of frequency spectra and peaks that they reveal. This process can be automatized in the scanner. The quantitative ways used in this paper are: (I) integration of the frequency spectra, and (II) calculation of the root mean square (RMS) of the frequency spectra. The outcome of the comparison should be whether some anomaly in the measurement results can be spotted, and thus, if the void can be detected and indicate that there exists a need for further testing of the area.

#### *6.1. Solid Plate (No Void) vs. Plate with Void*

First, the comparison between solid plate and plate with void below the impactor and transducer was done.

In the case of the solid plate, the peak due to thickness (9.95 kHz) was clearly visible for all sensors (Figure 6). The second highest peak (18.0 kHz) lied the around half-depth (10.4 cm) and might be the result of wave interference. The integral and RMS values (Table 2) were slightly different, possibly due to numerical noise. However, the obtained variation remained below 3%. Thus, if the absolute value of variation (Δ) of both integral and RMS is outside of 10% interval of the Reference Value (RV), the fault is detected. If only one value is outside of the interval, it indicates warning. The RV was taken as the mean value of integrals and RMS from a solid plate.

**Figure 6.** Frequency spectra, solid plate; expected frequency marked with dashed line.


**Table 2.** Integral and RMS of frequency spectrum, solid plate.

<sup>1</sup> Reference Value (RV); Detected Y—Yes, N—No, W—Warning.

When the void was located below impact point (Figure 7, Table 3), a big difference could be noticed from the previous case in the value of the integral and RMS. The values were smaller as the energy was largely dumped by discontinuity. Additional peaks for frequencies about 22.4 kHz were visible in the frequency spectrum, which allowed for detection of the void in the investigated area (Figure 8).

If the void was located only under one transducer (Figure 9), it was highly affected by dumping, as visible in Table 4. However, the sensor No.3 was surprisingly slightly dumped as well, possibly by interference with wave reflected from edge of the fault. In frequency spectra (Figure 10) for test point 1, the decrease in magnitude of peak due to plate thickness (9.95 kHz) was clear, as well as the additional peak due to the void (22 kHz).

**Figure 7.** Scheme of void and IE device layout.

**Table 3.** Integral and RMS of frequency spectrum, void below impactor.


Detected Y—Yes, N—No, W—Warning.

**Figure 8.** Frequency spectra, void below impactor; expected frequency marked with dashed line.

**Figure 9.** Scheme of void and IE device layout, void below sensor 1.

**Table 4.** Integral and RMS of frequency spectrum, void below sensor 1.


Detected Y—Yes, N—No, W—Warning.

**Figure 10.** Frequency spectra, void below sensor 1; expected frequency marked with dashed line.

#### *6.2. Edge of Void below Impactor*

Another interesting case is the location of edge of the void directly below the impact point (Figure 11). While comparing the integrals and RMS values (Table 5) or frequency spectra obtained here and for the solid plate, a reduction of energy delivered to transducers was visible. It is most evident for sensors close to the void (i.e., 1 and 4, Figure 12). Thus, the void can be detected and its approximated location can be given, but not the depth.

**Figure 11.** Scheme of void and IE device layout, edge below impactor.

**Table 5.** Integral and RMS of frequency spectrum, edge below impactor.


Detected Y—Yes, N—No, W—Warning.

#### *6.3. Void Moving Away from Impactor*

One more situation is the void moving away from the impact point (or, rather, when the scanner is moving away from the void, (Figures 13 and 14). Although the frequency spectra (Figures 15 and 16) did not precisely reveal the depth of the void, its location could be determined. Not only did the transducer closest to the fault reveal the biggest dumping of energy (Tables 6 and 7) as described previously, but also a linear relation between received energy and void position could be found. In the Figure 17, the variation

of RMS values with respect to reference value of solid slab are presented for three cases, as well as the linear fit quality.

**Figure 13.** Scheme of void and IE device layout, edge 5 cm from impactor.

**Figure 14.** Frequency spectra, edge 5 cm from impactor; expected frequency marked with dashed line.

**Figure 15.** Scheme of void and IE device layout, edge 15 cm from impactor.

**Figure 16.** Frequency spectra, edge 15 cm from impactor; expected frequency marked with dashed line.


**Table 6.** Integral and RMS of frequency spectrum, edge below impactor.

Detected Y—Yes, N—No, W—Warning.



Detected Y—Yes, N—No, W—Warning.

#### *6.4. Summary*

Simulations presented above clearly show that with a square set of 4 transducers and 1 impact point, the impact-echo method turns into volumetric, and a void can be detected if it lays within the area covered by the device. Its approximated position can be given in any case. However, the depth can be found only if it lays below the impact point or under one of the sensors. However, this precision is sufficient and thus, the proposed scheme can be adopted in UIR-Scanner.

The sensitivity of setup regarding minimum detectable fault was not analyzed. It can be expected that ability of detection is restricted by limits of impact-echo method [21], e.g., ratio of minimal lateral dimension of void to stress wavelength (impactor size) and element's depth. Furthermore, the numerical model presents an idealized medium, which is not the case in real application. Therefore, during the implementation of proposed layout into UIR-Scanner, the limitations and problems that are inherent in the chosen NDT method need to be borne in mind [36], i.e., (1) reflection coefficient R between fault and medium

needs to be large enough; (2) possible multiple reflections, e.g., due to reinforcement, can impair obtained results; (3) source of external vibrations and difference in vibration modes between types of plates can influence results.

**Figure 17.** RMS of signal received by each transducer with change of void edge distance from impact point.

#### **7. Experimental Validation of Adopted Layout**

Before implementation of an IE module in the UIR-Scanner, the layout was experimentally validated on a concrete slab using DOCter Mark IV transducers. The 50 cm thick slab of C30/37 concrete was used. At a depth of around 5 cm, a void was modeled by foamed polystyrene plate, 5 cm × 5 cm × 2 cm.

Measurements were executed with one transducer and one 2 mm impactor. The transducer was subsequently moved between positions 1 and 4, and the impact was applied in the center of setup (Figure 5). Two cases were considered—with no void, and with void below the impact point. The measurement was repeated 7 times at each measurement location (measurement A to G).

For obtained frequency spectra, Integral and RMS were calculated in range 0 Hz–70 Hz, where 70 Hz corresponds to twice the frequency due to the mid-depth of the void according to formula (2). The results for each measurement are presented in Tables 8–11.


**Table 8.** Integral of frequency spectrum (10<sup>−</sup>1), slab with no void.

**Table 9.** RMS of frequency spectrum (10<sup>−</sup>3), slab with no void.



**Table 10.** Integral of frequency spectrum (10<sup>−</sup>1), slab with void below impactor.

**Table 11.** RMS of frequency spectrum (10<sup>−</sup>3), slab with void below impactor.


For each measurement, the elastic wave was induced by separate impact and transducer was lifted and pressed again every time. Therefore, the measurements are uncorrelated. To analyze the results, and eliminate isolated events of different impact energy or imperfect contact of transducer with surface, average values from seven measurements (A to G) were calculated and presented in Tables 12 and 13 for slab without and with the void, respectively. The same criteria of detection as for numerical model were used; therefore, Δ above 10% for one of indicators (Integral of RMS) results in warning and for both indicators results in detection.

**Table 12.** Integral and RMS of frequency spectrum, solid slab.


<sup>1</sup> Reference Value (RV); Detected Y—Yes, N—No, W—Warning.

**Table 13.** Integral and RMS of frequency spectrum, slab with void below impactor.


Detected Y—Yes, N—No, W—Warning.

Despite relatively large discrepancies between individual measurements due to manual excitation of elastic stress-wave, average values clearly indicate presence of the void. The results confirm the need for automated excitation and simultaneous measurement with all four transducers. This experiment confirmed applicability of IE as a volumetric method. Therefore, the numerical modeling results were validated, and the IE module was implemented into the UIR-scanner (Figures 18 and 19) and issued for further sensitivity studies.

**Figure 18.** UIR-Scanner (a prototype) for nondestructive testing using complementary NDT methods: GPR (Ground Penetrating Radar), IE (Impact-Echo) and UPV (Ultrasonic Pulse Velocity) equipped with computer systems for signal analysis.

**Figure 19.** Impact-Echo module integrated into scanner.

### **8. Conclusions**

The aim of research presented in this paper was to find the optimal design of an Impact-Echo module for automated detection of horizontal faults in concrete slabs. The IE module was to be incorporated into integrated UIR-Scanner combining three nondestructive methods. The IE module should determine possible locations of faults in the slab in the rapid, volumetric manner. Then, in indicated locations, further tests can be conducted to confirm the outcome.

The following recommendations were issued: (1) the impact should be automated to allow comparison of magnitude of frequency spectra between the measurements; (2) layout with four transducers at corners of square 60 cm by 60 cm and one impact point in the middle should be adopted as it allows the most efficient testing; (3) clear rules for signal analysis and interpretation, with use of frequency spectra's integral and RMS, are established. They can be further introduced in the software of the scanner to automatize the procedure of detection. This layout was adopted into the UIR-Scanner, validated and issued for further experimental testing.

The current research has clearly presented that relatively simple Impact-Echo method, usually used for punctual measurement of element's thickness or detection of faults, can be modified into volumetric method by use of multiple transducers. Despite loss of precision and ability to localize the fault, this approach allows for much faster scanning of structures and opens new possibilities of application of the IE method for nondestructive testing of concrete.

**Author Contributions:** Conceptualization, B.S., T.P. and A.G.; methodology, T.P.; software, B.S.; validation, T.P. and B.S.; formal analysis, B.S.; investigation, B.S.; resources, T.P. and A.G.; data

curation, B.S. and T.P.; writing—original draft preparation, B.S.; writing—review and editing, T.P. and A.G.; visualization, B.S. and T.P.; supervision, A.G.; project administration, T.P.; funding acquisition, A.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Centre for Research and Development of Poland, grant number N R04 0024 10.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available in [31] (numerical modeling and validation of models) or is available on request from the corresponding author (validation of layout).

**Acknowledgments:** Authors are grateful to Marcin Balcerzak for fruitful discussions and help with numerical modeling.

**Conflicts of Interest:** The authors declare no conflict of interest.
