# Defect Detection and Characterization in Concrete Based on FEM and Ultrasonic Techniques

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

_{S}is the pulse velocity in sound concrete, V

_{C}is the pulse velocity in defect concrete, and D is the distance at which the change of slope occurs. Although this method can detect the presence of cracks, the accuracy of the measured depth is poor.

_{C}) of the ultrasonic wave is given by the following equation:

_{S}of the ultrasonic wave in the area where cracks do not exist is given by Equation (5) below. The depth of crack (H) can be obtained with Equation (6). This method of evaluating the depth of cracks is known as the T

_{C}-T

_{S}method [19].

_{C}-T

_{S}method is not accurate [20]. Since it is obtained from simple geometric calculations, the ultrasonic delay inside the transducer is not considered. In particular, when the delay time inside the transducer is long, the depth of the crack determined by Equation (6) shows a large difference from the actual value.

## 3. Concrete Crack Modeling and Simulation

## 4. Experiment with Concrete Specimen and Results

#### 4.1. Experiment Setup

#### 4.2. Experiment Setup

#### 4.3. Comparison of Sutan and Meganathan’s Equations with Simulation Results

#### 4.4. Comparison of Leslie and Cheesman’s Equations with Simulation Results

#### 4.5. An Example of Field Measurement

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Crack perpendicular to the surface and arrangement of the transducers (T

_{C}-T

_{S}method).

**Figure 7.**TOF according to the separation distance between the transmitter and the crack of (

**a**) 70 mm (

**b**) 45 mm.

**Figure 11.**Comparison of TOF with 45 mm crack, 70 mm crack, and no-crack conditions in concrete specimen.

**Figure 12.**Comparison of crack evaluation results (Sutan and Meganathan’s equations, experiment No. 1) (

**a**) 70 mm crack at 270 mm point (

**b**) 70 mm crack at 150 mm point.

**Figure 13.**Comparison of crack evaluation results (Leslie and Cheesman’s equations, experiment No. 1) (

**a**) 70 mm crack at 270 mm point (

**b**) 70 mm crack at 150 mm point.

Density | Velocity | |
---|---|---|

Longitudinal | Shear | |

2369 kg/m^{3} | 4320 m/s | 2450 m/s |

No. | Frequency | Depth of Crack | Distance between Transducers | No. of Measurement Time |
---|---|---|---|---|

1 | 65 kHz | 70 mm | 270 mm | 9 |

2 | 150 mm | 7 | ||

3 | 45 mm | 270 mm | 9 | |

4 | 150 mm | 7 | ||

5 | No crack | - | 9 |

Measurement Section (mm) | 0→540 | 60→480 | 120→420 | 180→360 | 240→300 |
---|---|---|---|---|---|

Transducer spacing (D, mm) | 540 | 420 | 300 | 180 | 60 |

Uncracked part TOF (${\mathrm{T}}_{\mathrm{S}}$, mm) | 123.8 | 97.5 | 70.1 | 41.8 | 13.8 |

Cracks TOF (${\mathrm{T}}_{\mathrm{C}}$, mm) | 133.3 | 103.0 | 75.7 | 48.9 | 22.6 |

Crack-depth evaluation result (t, mm) | 107.7 | 71.4 | 61.6 | 54.9 | 38.9 |

Accuracy (%) | 153.9% | 102.1% | 87.9% | 78.4% | 55.6% |

**Table 4.**Crack-depth evaluation result with case No. 2 (70 mm crack at 150 mm point) simulation TOF.

Measurement Section (mm) | 0→300 | 60→240 | 120→180 |
---|---|---|---|

Transducer spacing (D, mm) | 300 | 180 | 60 |

Uncracked part TOF (${\mathrm{T}}_{\mathrm{S}}$, mm) | 67.9 | 41.9 | 13.8 |

Cracks TOF (${\mathrm{T}}_{\mathrm{C}}$, mm) | 80.4 | 51.5 | 24.1 |

Crack-depth evaluation result (t, mm) | 95.0 | 62.6 | 41.5 |

Accuracy (%) | 135.7% | 89.5% | 59.3% |

Measurement Section (mm) | 0→540 | 60→480 | 120→420 | 180→360 | 240→300 |
---|---|---|---|---|---|

Transducer spacing (D, mm) | 540 | 420 | 300 | 180 | 60 |

Uncracked part TOF (${\mathrm{T}}_{\mathrm{S}}$, mm) | 123.8 | 97.5 | 70.1 | 41.8 | 13.8 |

Cracks TOF (${\mathrm{T}}_{\mathrm{C}}$, mm) | 130.8 | 100.4 | 72.6 | 45.1 | 16.8 |

Crack-depth evaluation result (t, mm) | 92.0 | 51.0 | 40.4 | 36.6 | 20.8 |

Accuracy (%) | 131.4% | 72.8% | 57.7% | 52.3% | 29.7% |

Measurement Section (mm) | 0→300 | 60→240 | 120→180 |
---|---|---|---|

Transducer spacing (D, mm) | 300 | 180 | 60 |

Uncracked part TOF (${\mathrm{T}}_{\mathrm{S}}$, mm) | 67.9 | 41.9 | 14.1 |

Cracks TOF (${\mathrm{T}}_{\mathrm{C}}$, mm) | 76.4 | 46.4 | 17.5 |

Crack-depth evaluation result (t, mm) | 77.3 | 42.8 | 21.8 |

Accuracy (%) | 110.4% | 61.1% | 31.1% |

Water | Cement | Aggregate | Total | ||
---|---|---|---|---|---|

Fine (Sand) | Coarse (3/4 Inch) | Coarse (1–1/2 Inch) | |||

6.66% | 13.55% | 29.11% | 25.34% | 25.34% | 100% |

Distance of Transducers (mm) | 60 | 120 | 180 | 240 | 300 | 360 | 420 | 480 | 540 |
---|---|---|---|---|---|---|---|---|---|

No. 1 (70 mm crack) | 49.0 | 77.4 | 99.7 | 128.1 | 179.3 | 182.5 | 194.2 | 206.4 | 219.3 |

No. 3 (45 mm crack) | 53.7 | 79.7 | 103.6 | 130.7 | 157.6 | 165.6 | 176.7 | 189.6 | 201.6 |

No. 5 (uncracked) | 48.5 | 78.4 | 104.6 | 131.0 | 156.3 | 167.6 | 179.7 | 191.5 | 202.8 |

Measurement Distnace (mm) | 60→240 | 120→180 |
---|---|---|

Distance of transducers (${\mathrm{X}}_{0}$, mm) | 180 | 60 |

Wave speed at uncracked (${\mathrm{V}}_{\mathrm{s}}$, mm/μs) | 4.3 | 3.7 |

Wave speed at cracked (${\mathrm{V}}_{\mathrm{d}}$, mm/μs) | 1.6 | 0.8 |

Crack depth evaluation result (t, mm) | 61.0 | 23.9 |

Measurement Distance (mm) | 60→240 | 120→180 |
---|---|---|

Distance of transducers (${\mathrm{X}}_{0}$, mm) | 180 | 60 |

Wave speed at uncracked (${\mathrm{V}}_{\mathrm{s}}$, mm/μs) | 41.5 | 16.4 |

Wave speed at cracked (${\mathrm{V}}_{\mathrm{d}}$, mm/μs) | 112.0 | 72.9 |

Crack depth evaluation result (t, mm) | 225.6 | 129.9 |

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**MDPI and ACS Style**

Kim, J.; Cho, Y.; Lee, J.; Kim, Y.H.
Defect Detection and Characterization in Concrete Based on FEM and Ultrasonic Techniques. *Materials* **2022**, *15*, 8160.
https://doi.org/10.3390/ma15228160

**AMA Style**

Kim J, Cho Y, Lee J, Kim YH.
Defect Detection and Characterization in Concrete Based on FEM and Ultrasonic Techniques. *Materials*. 2022; 15(22):8160.
https://doi.org/10.3390/ma15228160

**Chicago/Turabian Style**

Kim, Jeongnam, Younho Cho, Jungwon Lee, and Young H. Kim.
2022. "Defect Detection and Characterization in Concrete Based on FEM and Ultrasonic Techniques" *Materials* 15, no. 22: 8160.
https://doi.org/10.3390/ma15228160