# Concrete Delamination Depth Estimation Using a Noncontact MEMS Ultrasonic Sensor Array and an Optimization Approach

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background on Rayleigh and Lamb Waves

## 3. Materials and Methods

#### 3.1. Numerical Simulations

#### 3.2. Experimental Setup and Procedures

#### 3.2.1. Concrete Specimen

_{3}(length × width × thickness) was produced. Table 2 summarizes the mixture design proportions used to produce the concrete specimen. An acrylic panel (400 × 400 × 2 mm

_{3}) was inserted at a depth of 60 mm on the top of the rebar when the specimen was cast, to simulate a delamination defect. The cross-sectional dimensions of the concrete specimen are illustrated in Figure 3. The concrete specimen was cured for 28 days, and the measured 28-day compressive strength was 31.8 MPa.

#### 3.2.2. Ultrasonic Scanning Data Collection

#### 3.3. Ultrasonic Data Processing Approach to Estimate Delamination Depth

## 4. Results

#### 4.1. Ultrasonic Scanning Data for Pristine and Delamination Cases

#### 4.2. Delamination Depth Estimation Results

## 5. Discussion

## 6. Conclusions

- (1)
- Within an appropriate frequency region, Rayleigh waves are generated in a full-depth concrete region, whereas Lamb waves are generated above a delamination (shallow-depth) region.
- (2)
- The proposed ultrasonic data processing approach updates the P- and S-wave velocities of the tested concrete element using the measured Rayleigh wave velocity.
- (3)
- The proposed data processing approach estimates the thickness of shallow delamination in concrete with an acceptable accuracy.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Example dispersion curves for Lamb waves in a linear, isotropic plate. The assumed ${c}_{P}$, ${c}_{S}$, and d values are 3730 m/s, 2280 m/s, and 0.06 m, respectively.

**Figure 2.**(

**a**) Overall structure of the numerical simulation model and (

**b**) the excitation signal. The pristine and delaminated concrete cases were modeled as concrete with thicknesses of 250 mm and 60 mm, respectively. In both cases, a concrete and two air layers are surrounded by perfectly matched layers (PMLs) to eliminate boundary reflections.

**Figure 4.**Illustration of the contactless ultrasonic sensor array system to collect scanning data from concrete samples. CN board is a connector board that makes the connection between the output ends of the amplification board and the digital oscilloscope.

**Figure 5.**Overview of the proposed ultrasonic data processing approach to estimate the delamination depth of concrete.

**Figure 6.**Ultrasonic scanning data: (

**a**) pristine concrete case (numerical simulation), (

**b**) delamination case (numerical simulation), (

**c**) pristine concrete case (experiments), and (

**d**) delamination case (experiments).

**Figure 7.**Frequency–wavenumber domain magnitude spectra: (

**a**) pristine concrete case (numerical simulation), (

**b**) delamination case (numerical simulation), (

**c**) pristine concrete case (experiments), and (

**d**) delamination case (experiments). Lamb wave dispersion curves are overlaid on the magnitude spectra, where the red and blue lines indicate symmetric and anti-symmetric Lamb wave modes, respectively.

**Figure 8.**Objective history for numerical simulation results: (

**a**) objective history for Step 1 in the data processing approach and (

**b**) objective function for Step 2 over the search space. The actual delamination depth is 0.06 m.

**Figure 9.**Comparison between dispersion curves extracted from the numerical simulation data (Figure 7b) and those theoretically computed with the estimated delamination depth.

**Figure 10.**Objective history for experimental results: (

**a**) objective history for Step 1 in the data processing approach and (

**b**) objective function for Step 2 over the search space. The actual delamination depth is 0.06 m.

**Table 1.**Summary of the numerical simulation parameters for the pristine and delaminated concrete models. An increased mass density was used for the air layer to improve the simulation stability.

Material Properties | |||
---|---|---|---|

P-wave speed (m/s) | S-wave speed (m/s) | Mass density (kg/m^{3}) | |

Concrete | 3727 | 2282 | 2400 |

Air | 343 | 240 | |

Simulation Parameters | |||

Grid spacing (dx and dy) | 1 mm | ||

Time step (dt) | 0.0268 μs | ||

Time duration (T) | 1 ms | ||

Number of sensing points | 900 | ||

Sensor spacing | 1 mm |

Designed Compressive Strength (MPa) | Maximum Aggregate Size (mm) | Water-to-Cement Ratio | Unit Weight (kg/m^{3}) | ||||
---|---|---|---|---|---|---|---|

Water | Cement | Fine Aggregate | Coarse Aggregate | Super-Plasticizer | |||

30 | 15 | 0.43 | 169 | 392 | 825 | 952 | 3.528 |

**Table 3.**Summary of results for the update of bulk wave velocities (${c}_{P}$ and ${c}_{S}$ ) and estimation of the depth of concrete delamination.

Numerical Simulations | Experiments | |||
---|---|---|---|---|

Update of the P- and S-wave velocities | ||||

${c}_{P}$ | ${c}_{S}$ | ${c}_{P}$ | ${c}_{S}$ | |

Initial guess (m/s) | 4000 | 2000 | 4000 | 2000 |

Updated velocity (m/s) | 3739.2 | 2270.9 | 3580.6 | 2157.1 |

Actual velocity (m/s) | 3727 | 2282 | ||

Delamination depth estimation | ||||

Estimated depth (m) | 0.06 | 0.0506 | ||

Actual depth (m) | 0.06 | 0.06 |

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**MDPI and ACS Style**

Song, H.; Hong, J.; Choi, H.; Min, J.
Concrete Delamination Depth Estimation Using a Noncontact MEMS Ultrasonic Sensor Array and an Optimization Approach. *Appl. Sci.* **2021**, *11*, 592.
https://doi.org/10.3390/app11020592

**AMA Style**

Song H, Hong J, Choi H, Min J.
Concrete Delamination Depth Estimation Using a Noncontact MEMS Ultrasonic Sensor Array and an Optimization Approach. *Applied Sciences*. 2021; 11(2):592.
https://doi.org/10.3390/app11020592

**Chicago/Turabian Style**

Song, Homin, Jinyoung Hong, Hajin Choi, and Jiyoung Min.
2021. "Concrete Delamination Depth Estimation Using a Noncontact MEMS Ultrasonic Sensor Array and an Optimization Approach" *Applied Sciences* 11, no. 2: 592.
https://doi.org/10.3390/app11020592