Experimental Investigation of Concrete Crack Depth Detection Using a Novel Piezoelectric Transducer and Improved AIC Algorithm

Abstract

Ultrasonic pulse velocity (UPV) has shown effectiveness in determining the depth of surface-open cracks in concrete structures. The type of transducer and the algorithm for extracting the arrival time of the ultrasonic signal significantly impact the accuracy of crack depth detection. To reduce the energy loss in piezoceramic-based sensors, a high-performance piezoceramic-enabled smart aggregate (SA) was employed as the ultrasonic transducer. For the extraction of ultrasonic signal arrival time in concrete, a novel characteristic equation was proposed, utilizing the slope of the signal within a shifting window. This equation was subsequently applied to modify Maeda’s function, with the arrival time of ultrasonic waves defined as the moment corresponding to the minimum Akaike information criterion (AIC) value. Six plain concrete specimens with artificial cracks were prepared and one reinforced concrete beam with a load-induced crack was used for validation. The average deviation of the testing of 492 points on 12 human-made cracks was around 5%. The detection results of 11 measurement points of a crack in a reinforced concrete beam show that three measurement points have a deviation of about 17%. The experimental results demonstrated that the novel piezoelectric transducer and improved AIC algorithm exhibit high accuracy in detecting the depth of concrete cracks.

1. Introduction

Concrete is extensively utilized in the construction of key infrastructure such as buildings, bridges, and dams [1]. However, concrete structures are prone to various forms of degradation, with surface-visible cracks posing significant challenges. These cracks not only undermine the structural strength of concrete but also accelerate the corrosion of embedded reinforcement when they reach the reinforcement level [2,3,4]. As corrosion progresses, the bond between the rebar and the concrete weakens, which can eventually lead to a complete loss of adhesion and cause concrete spalling. To evaluate the structural condition of concrete components, engineers can analyze crack patterns and determine the extent of deterioration, allowing them to implement timely repairs and reinforcement measures. Such an approach is crucial for maintaining the load-bearing capacity of concrete elements throughout their designed service life [5,6,7]. Therefore, the accurate detection of concrete cracks is critical for safeguarding the structural integrity of concrete infrastructures.

Surface-open cracks in concrete are typically characterized by three primary parameters: length, width, and depth. Surface cracks are detected by visual tests, the ultrasonic method, the thermographic method, and digital image correlation (DIC) [8]. The thermographic method utilizes an initial scan of the concrete surface using an infrared camera when the maximum heat exchange between the structure and the environment occurs in direct sunlight [9]. DIC technology is designed for non-contact measurement of displacement and crack assessment of loaded planar and spatial concrete elements [10]. Advances in research have highlighted the potential of computer vision (CV) techniques in accurately detecting crack length and width by analyzing images of concrete surfaces [11,12,13]. Despite these achievements, CV-based methods face limitations in reliably capturing the spatial distribution of cracks, which can introduce substantial inaccuracies when estimating the depth of surface-open cracks [14,15]. In recent years, innovative techniques for crack detection and imaging have been developed, offering improved capabilities for crack assessment [16,17,18,19,20]. Among these, ultrasonic pulse velocity (UPV), a widely used non-destructive testing (NDT) method, has shown effectiveness in determining the depth of surface-open cracks in concrete structures [21,22,23]. Basu et al. investigated damage progression in RC structures at different levels of damage using linear and nonlinear ultrasonic techniques [24]. Kuchipudi et al. solved the problem of imaging deep internal crack planes in the concrete medium by leveraging the ultrasonic shear horizontal (SH) waves from a transducer array [25]. Kim et al. performed finite element analysis and experiments on non-cracked concrete blocks and 45 mm and 70 mm vertical cracks to estimate the crack depth in concrete using time-of-flight [26]. Dinh et al. used state-of-the-art ultrasonic shear wave devices (MIRA 3D) to collect data on concrete specimens with different built-in flaws/defects and visualized the data with a synthetic aperture focusing technique (SAFT) [27]. In the UPV test, elastic stress wave pulses are produced by a transducer on one side of the concrete and detected by a second transducer, either on the same side or the opposite side of the concrete. The velocity of the P-waves (Cp) is determined by dividing the distance (L) between the two transducers by the time (t) it takes for the waves to travel, using the formula (Cp = L/t).

Arrival time-picking algorithms can be categorized into three types: frequency domain analysis methods [28], time domain analysis methods [29], and time–frequency analysis methods [30]. However, research on automatic picking algorithms for ultrasonic wave arrival times in concrete is rarely reported. The Short/Long Time Average ratio (STA/LTA) [31] and Akaike information criterion (AIC) [32] methods have proven effective for the automatic detection of signal arrival times and are commonly applied in the automatic picking of arrival times for microseismic events. Vanderkulk et al. [33] used the absolute value of signal amplitudes as the characteristic function and employed the STA/LTA picker to detect the arrival times of seismic P-waves. Allen [34] proposed a frequency-sensitive eigenfunction that incorporates the square of the first-order difference of the signals in addition to the squared characteristic function, thereby capturing changes in signal frequency through the squared first-order difference. Baer and Kradolfer [35] modified the amplitude and frequency weights in Allen’s characteristic equation. Cheng et al. [36] proposed an adaptive characteristic equation, building upon Allen’s equation, to accommodate signals with varying signal-to-noise ratios. They demonstrated the feasibility of this equation for detecting the arrival time of P-waves. However, the use of AlC for arrival time picking in ultrasonic signal processing for concrete structures requires further improvement.

The experimental system for detecting concrete crack depth using the UPV method primarily consists of the following components: a function generator, a signal amplifier, an oscilloscope, ultrasonic sensors, and a computer for signal processing [37,38,39]. Among these, the type of sensors used and the algorithm for extracting the arrival time of the ultrasonic signal significantly impact the accuracy of crack depth detection. Piezoceramic-based ultrasonic transducers have proven to be both feasible and effective in laboratory tests, where they have been used as smart aggregates (SAs) for detecting damage in concrete structural elements [40,41,42,43]. Song et al. creatively proposed piezoelectric smart aggregates and applied them to damage monitoring and detection of concrete structures [44]. Conventional piezoelectric ultrasonic sensors face significant challenges in detecting concrete cracks due to substantial energy loss during ultrasonic wave transmission, which can lead to considerable errors in determining the arrival time of the ultrasonic signal [45,46,47,48,49]. To reduce the energy loss in piezoceramic-based sensors, we employed a high-performance piezoceramic-enabled SA as an ultrasonic sensor, which is based on the acoustic impedance matching principle recently proposed by Li et al. [50]. In addition, for the extraction of ultrasonic signal arrival time in concrete, a novel characteristic equation was proposed, utilizing the slope of the signal within a shifting window. This equation was subsequently applied to modify Maeda’s function, with the arrival time of ultrasonic waves defined as the moment corresponding to the minimum Akaike information criterion (AIC) value, further enhancing the accuracy of ultrasonic signal detection.

The primary objective of this study is to demonstrate the feasibility of using the high-performance piezoelectric ceramic SA and the proposed arrival time extraction algorithm for detecting crack depth in concrete. Six plain concrete specimens with artificial cracks were prepared in the laboratory [51,52]. To further validate the effectiveness of the system, a reinforced concrete beam with a crack induced by loading was tested with the proposed method. The artificial cracks were delicately examined at 41 measuring points, and the load-induced cracks were examined at 11 measuring points. The experimental results demonstrated that the proposed detection method using a novel piezoelectric transducer and the improved AIC algorithm exhibits high accuracy in detecting the depth of concrete cracks.

2. The Principle of Crack Depth Detection

The principle of ultrasonic detection of vertical concrete cracks. The transducers were configured using a one-sided flat measurement method, which involves two scenarios: non-crack and crack-spanning acoustic time measurements. In this setup, the transducers referred to as the actuator and the sensor were positioned on the same side of the crack. Acoustic travel times ($t_1,t_2,t_3,\dots t_i$) were recorded based on the separation distance (${\mathrm{S}}_1{=50\mathrm{mm},\mathrm{S}}_2{=100\mathrm{mm},\mathrm{S}}_3=150\mathrm{mm},\dots {,\mathrm{S}}_{\mathrm{i}}$) between the actuator and sensor. The relationship between travel time and distance was established using a regression curve, expressed as follows:

(1)$S_i=a+b{t}_i$

where b represents the slope, corresponding to the ultrasonic wave velocity; a is the intercept. During the experiment, the actual ultrasonic propagation path length $s_i$ can be expressed as follows:

(2)$s_i=\left|a\right|+S_i$

The speed of the ultrasonic wave v without crossing the crack can be expressed as follows:

(3)$v=b$

The formula for the crack depth h can be expressed as follows:

(4)$h={\displaystyle \frac{s_i}{2}}\sqrt{{({\displaystyle \frac{t_{i}v}{s_i}})}^2-1}$

The principle of ultrasonic detection of vertical cracks is shown in Figure 1.

For the detection of inclined cracks, it is not only necessary to measure their depth, but also their direction. The principle of ultrasonic detection of inclined cracks is shown in Figure 2. After measuring the ultrasonic velocity in the concrete, the two transducers are placed at positions $A_1,B_1$ and $A_2,B_2$, respectively, taking $A_1{B}_1=A_2{B}_2=2K$. Measure the travel time $t_1$ when the ultrasonic wave propagates through $A_{1}C+C{B}_1$ and $t_2$ when it propagates through $A_{2}C+C{B}_2$. The resulting equations are as follows:

(5)$A_{1}C+C{B}_1=v{t}_1=2a_1$

(6)$A_{2}C+C{B}_2=v{t}_2=2a_2$

(7)$b_1^2=a_1^2-K^2, b_2^2=a_2^2-K^2$

Therefore, the two elliptic equations are obtained by taking $A_1,B_1$ and $A_2,B_2$ as the foci and $a_1,b_1$ and $a_2,b_2$ as the long and short axes, respectively:

(8)${\displaystyle \frac{x_1^2}{a_1^2}}+{\displaystyle \frac{y_1^2}{b_1^2}}=1, {\displaystyle \frac{x_2^2}{a_2^2}}+{\displaystyle \frac{y_2^2}{b_2^2}}=1$

Taking the same coordinate system, the following can be obtained:

(9)${\displaystyle \frac{x_1^2}{a_1^2}}+{\displaystyle \frac{y_1^2}{b_1^2}}=1$

(10)${\displaystyle \frac{{(x_1+m)}^2}{a_2^2}}+{\displaystyle \frac{y_2^2}{b_2^2}}=1$

Obviously, the end of the crack must be at the intersection of the two ellipses. Therefore, solving Equations (9) and (10) can locate the coordinates of the end of the crack.

The arrival time of the ultrasonic wave can be determined by analyzing changes in the amplitude and frequency of the signal received by the sensor. To enhance the detection sensitivity, a characteristic equation was utilized to amplify these changes. However, to minimize deviations and improve accuracy, traditional characteristic equations based on signal amplitude or its difference were discarded. Instead, a characteristic equation employing the slope of the signal within a shifting window was adopted. Figure 3 provides a visual representation of the AIC picker applied to the ultrasonic signal recorded in a concrete component, demonstrating the effectiveness of the proposed characteristic function. This function can be written as follows:

(11)$CF(i)=\left|{\displaystyle \frac{n{{\displaystyle \sum }}_{j=0}^{n}j·t(i+j)-\left({{\displaystyle \sum }}_{j=0}^{n}j\right)\left({{\displaystyle \sum }}_{j=0}^{n}t(i+j)\right)}{n{{\displaystyle \sum }}_{j=0}^n{j}^2-{\left({{\displaystyle \sum }}_{j=0}^{n}j\right)}^2}}\right|$

where $t(i)$ is the time series and $n$ is the length of the shifting window. The characteristic function (CF) was subsequently utilized to refine the AIC function, enhancing its precision in detecting arrival times. The modified AIC function incorporating CF can be expressed as follows:

(12)$\mathrm{AIC}(i)=i·\log \left(\mathrm{var}\left(CF[1,i]\right)\right)+(L-i)\log \left(\mathrm{var}\left(CF[i+1,L]\right)\right)$

where L is the length of the AIC window, $\mathrm{var}(CF[1,i])$ is the variance of CF from 1 to i, and i ranges from 1 to L. The arrival time of ultrasonic waves is determined as the point corresponding to the minimum value of the modified AIC function. Through a process of trial and error, a shifting window of 2 µs was selected for fitting the signal data, while a 200 µs window was utilized for calculating the AIC values.

3. Experimental Investigation

Six plain concrete specimens with artificial cracks were prepared in the laboratory, as shown in Figure 4. Concrete elements were designed for a compressive strength of 30 MPa. The water–cement ratio was 57%. The details of the mix proportions of concrete specimens are shown in Table 1. The dimensions of these specimens are all 500 mm × 500 mm × 200 mm. The artificial cracks with a designed depth range from 40 mm to 110 mm were created by inserting a greased plastic plate of 3 mm thickness in the mold before concrete pouring and vibrating operations. The detailed design of concrete cracks is shown in Figure 5. The concrete specimens and crack information are shown in Table 2. Specimens SP1-SP4 have cracks of constant depth. Specifically, cracks in SP3 and SP4 have an inclined angle of 30°. Specimens SP5 and SP6 have cracks with changing depth to further test the performance of the proposed crack depth detection method. The length of each crack was 500 mm. Each crack had 41 sets of measurement points spaced 10 mm apart sequentially along the length of the crack. During the test, the transducers were attached to the surface of the concrete member using the grease as a coupling agent.

A function/arbitrary waveform generator (Uni-Trend Technology, Dongguan, China) was employed to produce pulse signals, while a digital oscilloscope (Uni-Trend Technology, Dongguan, China) was utilized to capture and store the received signals. The digital oscilloscope operates at a sampling rate of 50 MHz. A high-voltage pre-amplifier (Yunhao Technology Co., Shanghai, China) was utilized to enhance the amplitude of the pulse signal. Ultrasonic signals were excited and received using a pair of high-performance piezoceramic-based transducers designed on the principle of acoustic impedance matching, as developed by Li et al [50]. Figure 6 depicts the structural composition of the transducer. To ensure stable signal transmission and minimize interference, all experimental instruments were interconnected using cables equipped with bayonet nut connectors (BNCs). These BNC cables were selected for their ability to reduce signal interference effectively. Figure 7 presents a schematic diagram of the ultrasonic pulse-echo experimental setup. The ultrasonic pulse, generated by the waveform generator, was amplified by the amplifier before being delivered to the actuator. The ultrasonic pulse generated by the generator was amplified by the amplifier and arrived at the actuator. A five-cycle sine wave served as the excitation signal for the actuator, with a center frequency of 50 kHz and an initial amplitude of 2 V. After amplification by the high-voltage pre-amplifier, the output amplitude increased to 500 V. The amplified ultrasonic pulse propagated through the concrete, reached the sensor, and was subsequently recorded by the digital oscilloscope.

4. Results and Discussion

The design depth and detection depth of different cracks are shown in Figure 8. All the results of the crack depth calculation are listed in Appendix A. The experimental results show that for the four vertical cracks with fixed depths in specimens SP1-SP2, the average errors of depth detection were 3%, 3%, 4%, and 5%, and the maximum errors were 5%, 6%, 8%, and 10%, respectively. For the four cracks with an inclination angle of 30° in specimens SP3-SP4, the average errors of detection were 4%, 5%, 5%, and 6%, and the maximum errors were 7%, 8%, 10%, and 11%, respectively. For the four vertical cracks with varying depths in specimens SP5-SP6, the average errors of detection were 4%, 6%, 5%, and 6%, and the maximum errors were 10%, 10%, 11%, and 12%, respectively.

The detection errors for different cracks are shown in Figure 9. As the crack depth increases, the error of detection has a tendency to become larger, and this tendency is clearly reflected in the maximum detection error of each crack. Due to the increase in crack depth, the ultrasonic wave propagation distance in the concrete increased, and more sound waves were absorbed and refracted by the concrete, which led to a larger error in picking up the arrival time of ultrasonic waves and adversely affected the results of the calculation of crack depth. For cracks of the same depth, the detection error for inclined cracks is larger than that for vertical cracks. This is because when using the double ellipse method, the same measurement point needs to carry out two groups of detection, both groups of detection error, thus generating a larger error than the vertical cracks with only one group of detection for each measurement point. The detection error also increases when the crack depth varies along its length. When the crack depth varies, the diffraction point of the ultrasonic waves at the bottom of the crack is not necessarily directly below the transducer, which also introduces a greater error in the detection process.

There are other factors that can affect the accuracy of the detection, such as the coupling agent between the sensor and the concrete, the ultrasonic wave velocity measurement error, and external environmental noise. The coupling agent used in this experiment is butter, but there are other scholars who use Vaseline as the coupling agent for surface-adhesive sensors. Compared with petroleum jelly, butter has better compactness and adhesion, which can transmit ultrasonic waves well and stick the transducers tightly to the concrete surface. For the ultrasonic wave velocity measurement, we measured the propagation time at 50 mm, 100 mm, and 150 mm transducer intervals, and then the slope of the linear fit between the distance and time was used as the ultrasonic wave velocity. This improves the accuracy of wave velocity detection, and if the concrete member is long enough, increasing the number of different transducer spacings should result in a more accurate calculation of wave velocity. It is better to conduct the experiment in the time period when the external noise is low. We repeated the measurements three times for each pair of measurement points to minimize the error caused by external noise to reduce the noise interference.

5. Further Validation

To further validate the effectiveness of the proposed method, one reinforced concrete beam (120 mm × 200 mm × 1500 mm) with a crack was prepared. To detect the depth of this crack, 11 measurement points spaced 10 mm apart along the length of the crack were selected. In order to determine the depth of the crack directly after the ultrasonic detection, the crack was stained in red ink and was then subjected to three-point bending in a bending testing machine to completely disconnect the beam along the existing crack, as shown in Figure 10. The cracks on the side of the beam were sealed using adhesive clay, and red ink was used to fill the concrete crack from above, ensuring a full supply of ink during the dyeing process. A rubber mallet was used to gently tap the beam and then the beam was left for a period of time to ensure that the cracks were adequately dyed.

The detection results and direct measurement results are shown in Table 3. Among the 11 points of this measurement, the errors of point 3 and point 9 reached 25.7 mm and 26.81 mm, respectively, and the detection results were larger than the actual measurement depth. The results of the analysis may be due to the ultrasonic wave propagation in the rebar below these two points, resulting in a reduction in the energy transmitted to the sensor. The ultrasonic wave arrival time extracted by the application algorithm is delayed, which results in larger values in the calculation results. The measurement error of point 10 reaches −26.94 mm, and the detection result is smaller than the actual measurement depth. The results of the analysis may be due to the fact that there is partial contact in the area above the bottom of the crack at this point, which causes the ultrasonic signal to be transmitted to the sensor earlier. Overall, the detection errors of the remaining eight points are all less than 10%, and the detection errors of five of them are less than 5%. The experimental results demonstrate the feasibility of the proposed method in detecting surface cracks in reinforced concrete specimens and also provide a potential guideline for identifying the location of reinforcement bars in concrete cracks.

The reliability of the aforementioned detection method was thoroughly validated in the laboratory. However, in practical applications, the forms of cracks are complex and diverse. For instance, the presence of reinforcing steel in concrete can affect the propagation paths of ultrasonic waves, leading to significant detection errors. Moreover, damage in concrete often results in multiple intersecting cracks rather than a single crack, posing substantial challenges to the detection of crack depth. Our objective is to achieve imaging of internal cracks in concrete. In future work, we plan to apply Bayesian probability theory to crack depth detection and explore additional transducer array configurations.

6. Conclusions

In this paper, the experimental investigation of concrete crack depth detection using a new method based on a novel piezoelectric transducer and the improved AIC algorithm was conducted. A high-performance piezoceramic-enabled SA was employed as the ultrasonic transducer. For the extraction of ultrasonic signal arrival time in concrete, a novel characteristic equation was proposed, utilizing the slope of the signal within a shifting window. Six plain concrete specimens with artificial cracks were prepared and one reinforced concrete beam with a load-induced crack was used for validation. The conclusions are as follows:

• The artificial crack detection experimental results show that for the four vertical cracks with fixed depths in specimens SP1-SP2, the average errors of depth detection were 3%, 3%, 4%, and 5%, and the maximum errors were 5%, 6%, 8%, and 10%, respectively. For the four cracks with an inclination angle of 30° in specimens SP3–SP4, the average errors of detection were 4%, 5%, 5%, and 6%, and the maximum errors were 7%, 8%, 10%, and 11%, respectively. For the four vertical cracks with varying depths in specimens SP5-SP6, the average errors of detection were 4%, 6%, 5%, and 6%, and the maximum errors were 10%, 10%, 11%, and 12%, respectively. The results show that the average deviation of the testing of 492 points on 12 human-made cracks was around 5%. This shows that the high-performance SA and ultrasonic time-of-arrival extraction algorithms we used are highly accurate and feasible for detecting the depth of concrete cracks by the UPV method.

• The detection results of 11 measurement points of a crack in a reinforced concrete beam show that the three measurement points with the presence of reinforcing bars underneath have a deviation of about 17%. The detection errors of the remaining eight points are all less than 10%, and the detection errors of five of them are less than 5%. The presence of reinforcing steel in concrete can introduce a significant error in crack depth detection results. The presence of rebar below the measurement point is a significant increase in the error. However, it is possible to use the sudden change in the crack depth detection value to determine the location of the rebar in the crack.

• The experimental results demonstrated that the novel piezoelectric transducer and improved AIC algorithm exhibit high accuracy in detecting the depth of concrete cracks. The present work paves the way for accurate concrete internal crack imaging and thus precise concrete damage evaluation.

Author Contributions

Conceptualization, W.L., J.Z. and W.Y.; methodology, W.L. and J.Z.; validation, W.L., J.Z. and K.M.; formal analysis, W.L., J.Z. and W.Y.; investigation, W.L., J.Z. and K.M.; resources, W.L. and X.Z. (Xuefeng Zhao); data curation, W.L. and J.Z.; writing—original draft preparation, J.Z.; writing—review and editing, W.L.; visualization, J.Z.; supervision, W.L., X.Z. (Xue Zhang) and X.Z. (Xuefeng Zhao); project administration, W.L., X.Z. (Xue Zhang) and X.Z. (Xuefeng Zhao); funding acquisition, W.L. and X.Z. (Xuefeng Zhao). All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data will be made available by the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

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Figures and Tables

Figure 1. The principle of ultrasonic crack depth detection of vertical cracks.

Figure 2. The principle of ultrasonic crack depth detection of inclined cracks.

Figure 3. A graphical representation of the AIC picker applied to ultrasonic signals received in concrete elements.

Figure 4. Six plain concrete specimens with artificial cracks.

Figure 5. The details of the concrete cracks.

Figure 6. The structural composition of the piezoceramic-based ultrasonic transducer.

Figure 7. Schematic layout of the experimental setup.

Figure 8. The design depth and detection depth of different cracks.

Figure 8. The design depth and detection depth of different cracks.

Figure 9. The detection errors for different cracks.

Figure 10. Direct measurement of crack depth.

Table 1

The details of the mixed proportions of concrete specimens.

Design Compressive Strength (MPa)	Test Compressive Strength (MPa)	W/C (%)	Unit Quantity (kg/m3)
			Sand	Gravel	Water	Cement
30	32.58	57	720	1200	172	300

Table 2

Overview of concrete specimens and cracks.

Specimen	Crack	Depth/mm	Inclined Angle
SP1	1	40	0
	2	60	0
SP2	1	80	0
	2	100	0
SP3	1	40	30°
	2	60	30°
SP4	1	80	30°
	2	100	30°
SP5	1	40~50	0
	2	60~70	0
SP6	1	80~90	0
	2	100~110	0

Table 3

The results of crack depth detection and direct measurement (unit: mm).

Points	Detection	Measurement	Deviations	Percent
1	147.88	143	4.88	3.41%
2	154.00	151	3.00	1.99%
3	179.70	154	25.70	16.69%
4	138.06	151	−12.94	−8.57%
5	175.46	161	14.46	8.98%
6	185.18	169	16.18	9.58%
7	159.97	168	−8.03	−4.78%
8	166.39	162	4.39	2.71%
9	184.81	158	26.81	16.97%
10	124.06	151	−26.94	−17.84%
11	140.71	139	1.71	1.23%

Appendix A. The Results of the Crack Depth Calculations

	SP1-Crack1		SP1-Crack2		SP2-Crack1		SP2-Crack2		SP3-Crack1		SP3-Crack2
	Design (mm)	Detect (mm)	Design (mm)	Detect (mm)	Design (mm)	Detect (mm)	Design (mm)	Detect (mm)	Design (mm)	Detect (mm)	Design (mm)	Detect (mm)
0	40	-	60	-	80	-	100	-	40	-	60	-
1	40	-	60	-	80	-	100	-	40	-	60	-
2	40	-	60	-	80	-	100	-	40	-	60	-
3	40	-	60	-	80	-	100	-	40	-	60	-
4	40	-	60	-	80	-	100	-	40	-	60	-
5	40	40.34	60	62.31	80	74.51	100	108.78	40	37.80	60	57.71
6	40	40.20	60	62.67	80	74.99	100	107.52	40	38.28	60	62.08
7	40	41.67	60	63.10	80	86.01	100	101.00	40	42.37	60	60.61
8	40	39.14	60	56.51	80	86.20	100	102.45	40	37.43	60	58.88
9	40	41.03	60	59.16	80	81.02	100	101.74	40	38.45	60	55.27
10	40	41.01	60	57.98	80	74.01	100	94.15	40	37.32	60	63.03
11	40	39.52	60	62.52	80	76.39	100	96.02	40	39.65	60	58.25
12	40	40.27	60	59.42	80	78.00	100	99.42	40	37.08	60	61.16
13	40	38.30	60	63.45	80	84.37	100	94.61	40	42.38	60	62.61
14	40	38.22	60	57.33	80	73.41	100	106.89	40	38.18	60	55.73
15	40	40.12	60	58.02	80	73.79	100	93.90	40	37.56	60	55.98
16	40	41.12	60	57.02	80	75.50	100	94.52	40	38.84	60	60.54
17	40	41.74	60	56.94	80	82.03	100	93.41	40	39.74	60	59.84
18	40	38.52	60	63.10	80	83.15	100	94.55	40	37.61	60	64.22
19	40	40.28	60	60.67	80	82.01	100	98.71	40	42.97	60	63.23
20	40	39.88	60	60.42	80	79.33	100	96.22	40	38.99	60	62.53
21	40	38.05	60	57.02	80	80.64	100	108.47	40	38.78	60	55.15
22	40	39.35	60	62.97	80	77.23	100	98.60	40	37.37	60	55.39
23	40	38.65	60	61.03	80	83.33	100	93.70	40	38.79	60	55.56
24	40	41.18	60	58.75	80	75.77	100	108.10	40	37.28	60	63.22
25	40	39.24	60	60.11	80	82.54	100	109.59	40	40.03	60	64.78
26	40	40.11	60	59.18	80	75.70	100	98.78	40	41.57	60	61.98
27	40	38.66	60	56.44	80	78.21	100	92.22	40	40.79	60	56.03
28	40	40.41	60	57.82	80	81.71	100	95.16	40	37.54	60	62.41
29	40	39.05	60	56.84	80	83.81	100	98.17	40	37.49	60	55.79
30	40	40.62	60	57.34	80	74.30	100	101.90	40	41.66	60	55.87
31	40	40.76	60	57.82	80	85.84	100	95.24	40	42.43	60	61.52
32	40	40.99	60	59.31	80	83.75	100	102.06	40	40.20	60	58.15
33	40	39.80	60	56.22	80	79.82	100	104.22	40	37.65	60	61.66
34	40	38.34	60	63.38	80	79.13	100	94.43	40	41.95	60	62.69
35	40	38.92	60	63.74	80	79.28	100	92.35	40	39.03	60	60.90
36	40	41.65	60	59.92	80	77.37	100	95.93	40	38.76	60	62.59
37	40	38.61	60	59.91	80	80.12	100	96.38	40	41.48	60	57.14
38	40	41.30	60	58.64	80	80.15	100	98.48	40	37.06	60	62.54
39	40	40.15	60	63.36	80	84.32	100	100.16	40	37.29	60	65.08
40	40	41.98	60	58.90	80	84.01	100	91.71	40	41.01	60	63.96
41	40	38.31	60	56.73	80	81.96	100	95.25	40	40.62	60	55.53
42	40	39.77	60	62.35	80	78.35	100	106.02	40	40.16	60	58.56
43	40	38.43	60	59.07	80	84.24	100	90.58	40	41.38	60	58.59
44	40	41.85	60	57.83	80	80.45	100	108.58	40	41.24	60	62.00
45	40	38.02	60	59.19	80	77.97	100	104.61	40	41.69	60	61.06
46	40	-	60	-	80	-	100	-	40	-	60	-
47	40	-	60	-	80	-	100	-	40	-	60	-
48	40	-	60	-	80	-	100	-	40	-	60	-
49	40	-	60	-	80	-	100	-	40	-	60	-
50	40	-	60	-	80	-	100	-	40	-	60	-

SP4-Crack1		SP4-Crack2		SP5-Crack1		SP5-Crack2		SP6-Crack1		SP6-Crack2
Design (mm)	Detect (mm)	Design (mm)	Detect (mm)	Design (mm)	Detect (mm)	Design (mm)	Detect (mm)	Design (mm)	Detect (mm)	Design (mm)	Detect (mm)
80	-	100	-	40.00	-	60.00	-	80.00	-	100.00	-
80	-	100	-	40.78	-	60.78	-	80.78	-	100.78	-
80	-	100	-	41.54	-	61.54	-	81.54	-	101.54	-
80	-	100	-	42.26	-	62.26	-	82.26	-	102.26	-
80	-	100	-	42.94	-	62.94	-	82.94	-	102.94	-
80	84.86	100	98.38	43.60	41.49	63.60	59.98	83.60	77.27	103.60	95.55
80	77.78	100	98.89	44.22	43.31	64.22	68.73	84.22	92.72	104.22	94.91
80	75.06	100	102.53	44.82	41.00	64.82	58.22	84.82	86.58	104.82	98.74
80	73.06	100	89.87	45.38	47.05	65.38	70.37	85.38	84.21	105.38	96.81
80	84.57	100	95.76	45.90	45.01	65.90	60.06	85.90	94.64	105.90	96.34
80	75.06	100	106.27	46.40	50.88	66.40	68.76	86.40	89.50	106.40	109.03
80	78.12	100	104.52	46.86	45.95	66.86	66.87	86.86	85.90	106.86	117.58
80	80.87	100	91.38	47.30	48.44	67.30	63.31	87.30	94.12	107.30	119.08
80	75.45	100	91.49	47.70	44.40	67.70	68.71	87.70	88.35	107.70	100.19
80	82.38	100	90.62	48.06	46.92	68.06	62.66	88.06	89.16	108.06	107.60
80	79.74	100	88.68	48.40	45.12	68.40	70.86	88.40	92.06	108.40	105.04
80	74.15	100	98.23	48.70	51.22	68.70	70.14	88.70	85.99	108.70	109.35
80	84.74	100	103.58	48.98	52.61	68.98	62.54	88.98	83.64	108.98	102.57
80	73.29	100	105.13	49.22	47.75	69.22	62.77	89.22	90.84	109.22	97.43
80	76.54	100	100.72	49.42	51.26	69.42	64.36	89.42	96.97	109.42	107.68
80	75.59	100	91.00	49.60	47.56	69.60	62.58	89.60	87.68	109.60	100.66
80	80.52	100	103.03	49.74	50.05	69.74	68.79	89.74	81.75	109.74	96.74
80	73.14	100	91.41	49.86	53.17	69.86	74.73	89.86	88.70	109.86	122.34
80	78.41	100	91.59	49.94	50.91	69.94	71.66	89.94	85.80	109.94	108.03
80	73.36	100	90.77	49.98	48.34	69.98	70.28	89.98	87.94	109.98	122.68
80	73.49	100	91.77	50.00	47.99	70.00	75.35	90.00	96.90	110.00	117.22
80	84.78	100	92.37	49.98	49.51	69.98	64.07	89.98	87.99	109.98	96.44
80	76.50	100	93.01	49.94	49.16	69.94	75.93	89.94	87.66	109.94	114.88
80	81.74	100	95.80	49.86	48.46	69.86	64.11	89.86	86.97	109.86	115.51
80	87.80	100	95.78	49.74	50.32	69.74	69.99	89.74	82.32	109.74	113.73
80	78.87	100	93.50	49.60	52.01	69.60	64.38	89.60	84.66	109.60	111.03
80	83.27	100	94.27	49.42	48.68	69.42	70.29	89.42	80.93	109.42	101.71
80	84.34	100	109.04	49.22	48.52	69.22	62.01	89.22	87.77	109.22	116.65
80	78.87	100	104.67	48.98	45.30	68.98	72.84	88.98	84.01	108.98	101.57
80	82.61	100	101.28	48.70	44.07	68.70	73.74	88.70	84.57	108.70	105.19
80	73.44	100	92.74	48.40	46.37	68.40	74.39	88.40	86.87	108.40	118.99
80	87.29	100	93.38	48.06	46.31	68.06	75.02	88.06	80.35	108.06	117.69
80	74.75	100	90.28	47.70	49.16	67.70	67.77	87.70	87.60	107.70	105.07
80	76.07	100	109.52	47.30	51.62	67.30	64.07	87.30	91.44	107.30	102.41
80	85.00	100	104.75	46.86	50.95	66.86	61.26	86.86	81.74	106.86	109.77
80	79.79	100	101.33	46.40	46.01	66.40	66.51	86.40	92.06	106.40	117.31
80	84.52	100	95.71	45.90	43.52	65.90	67.09	85.90	77.49	105.90	116.74
80	78.25	100	92.32	45.38	47.77	65.38	68.99	85.38	83.29	105.38	107.79
80	76.19	100	102.82	44.82	47.14	64.82	59.14	84.82	75.13	104.82	100.43
80	72.23	100	111.22	44.22	46.35	64.22	66.40	84.22	78.81	104.22	113.42
80	82.91	100	92.42	43.60	45.72	63.60	63.83	83.60	74.01	103.60	102.11
80	-	100	-	42.94	-	62.94	-	82.94	-	102.94	-
80	-	100	-	42.26	-	62.26	-	82.26	-	102.26	-
80	-	100	-	41.54	-	61.54	-	81.54	-	101.54	-
80	-	100	-	40.78	-	60.78	-	80.78	-	100.78	-
80	-	100	-	40.00	-	60.00	-	80.00	-	100.00	-

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