# Detection and Identification for Void of Concrete Structure by Air-Coupled Impact-Echo Method

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## Abstract

**:**

## 1. Introduction

## 2. Theory

#### 2.1. Theory of Void Damage Model

#### 2.2. Acoustic Modal Theory

#### 2.3. Quantitative Index

## 3. Finite Element Model (FEM) for Concrete Void

#### 3.1. Parameters of FEM

#### 3.2. Sound Field Analysis of the FEM

#### 3.2.1. Analysis for the Influence of Width on Sound Field

#### 3.2.2. Analysis for the Influence of Depth on Sound Field

#### 3.3. Frequency-Domain Analysis of the FEM

#### 3.3.1. The Influence of Different Excitation Positions

#### 3.3.2. The Influence of Different Void Sizes

## 4. Experimental Verification

#### 4.1. Experiment

#### 4.2. Frequency-Domain Analysis of Experiment

## 5. Result Analysis and the Identification Method

#### 5.1. Result Analysis of Experiment and FEM

#### 5.2. The Method and Effect of Identification

## 6. Discussion

## 7. Conclusions

- (1)
- In this paper, numerical simulation and experiments are described for a void depth of less than 0.4 m. The results show that, compared with the void depth, the influence of the width on peak frequency increases significantly. When the void width is greater than 0.30 m, the peak frequency decreases with the increase in void width, and the change is obvious.
- (2)
- It is found that the acoustic peak frequency can effectively judge a concrete void depth of less than 0.4 m by numerical simulation. The method of peak frequency can be used identify a void with a width greater than 0.3 m in a concrete structure.
- (3)
- The main engineering value of this study is that the threshold value can be used to quickly judge whether there is a void in a concrete structure through single-point excitation. When multipoint scanning is used, the void range can be quickly estimated.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Finite element model (FEM) of concrete structure with void. (

**a**) The FEM; (

**b**) the impact force.

**Figure 3.**Sound field distribution map at t = 2 ms. (

**a**) c = 50 cm, h = 10 cm; (

**b**) c = 50 cm, h = 20 cm; (

**c**) c = 50 cm, h = 30 cm; (

**d**) c = 50 cm, h = 40 cm.

**Figure 4.**Sound field distribution map at t = 2 ms. (

**a**) h = 10 cm, c = 0 cm; (

**b**) h = 10 cm, c = 10 cm; (

**c**) h = 10 cm, c = 20 cm; (

**d**) h = 10 cm, c = 30 cm; (

**e**) h = 10 cm, c = 35 cm; (

**f**) h = 10 cm, c = 40 cm; (

**g**) h = 10 cm, c = 50 cm; (

**h**) h = 10 cm, c = 60 cm.

**Figure 6.**The void of concrete. (

**a**) The void depth h = 0.1 m. (

**b**) The void depth h = 0.2 m. (

**c**) The void depth h = 0.3 m. (

**d**) The void depth h = 0.4 m. (

**e**) Line chart of peak frequency.

**Figure 7.**Experiment design (

**a**) Model A: h = 10 cm, C = 20 cm; (

**b**) Model B: h = 6 cm, C = 35 cm; (

**c**) Model C: h = 10 cm, C = 45 cm; (

**d**) grid line layout; (

**e**) schematic plot; (

**f**) experiment.

**Figure 8.**Frequency-domain analysis of Model A. (

**a**) Grid lines; (

**b**) peak frequency of excitation points a, b, c; (

**c**) peak sound pressure of excitation points a, b, c.

**Figure 9.**Frequency-domain analysis of Model B. (

**a**) Grid lines; (

**b**) peak frequency of excitation points a

_{1}, b

_{1}, c

_{1}; (

**c**) peak sound pressure of excitation points a

_{1}, b

_{1}, c

_{1}.

**Figure 10.**Frequency-domain analysis of Model C. (

**a**) Grid lines; (

**b**) peak frequency of excitation points a

_{2}, b

_{2}, c

_{2}and d

_{2}; (

**c**) peak sound pressure of excitation points a

_{2}, b

_{2}, c

_{2}and d

_{2}.

Materials | Velocity of Sound (m/s) | Density (kg/m^{3}) | Elastic Modulus (Pa) | Poisson Ratio |
---|---|---|---|---|

Concrete | 4000 | 2500 | 3.0 × 10^{10} | 0.2 |

Air | 343 | / | / | / |

f | Theory | FEM | Experiment |
---|---|---|---|

Model B | 1862 Hz | 1892 Hz | 1860 Hz |

Model C | 1551 Hz | 1354 Hz | 1442 Hz |

Δf (Hz) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|---|

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

2 | 0 | 0 | 0 | 20 | 0 | 0 | 0 | 0 |

3 | 0 | −220 | −1320 | −1320 | −1320 | 0 | 0 | 0 |

4 | 0 | −220 | −1320 | −1320 | −1320 | −1320 | −200 | 0 |

5 | 0 | −220 | 0 | 0 | 0 | −220 | 0 | 0 |

6 | 0 | −220 | 0 | 160 | −1040 | −220 | 0 | 0 |

7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Δf (Hz) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|---|

0 | −29 | 86 | −100 | −86 | −86 | −57 | 86 | 129 | 71 |

1 | 43 | −71 | 57 | −43 | 71 | 100 | 86 | −57 | −57 |

2 | −43 | 0 | 14 | −129 | 57 | 86 | 100 | −114 | 114 |

3 | 157 | 129 | 0 | 71 | −957 | −970 | 57 | −43 | 171 |

4 | −57 | −100 | −86 | −957 | −957 | −957 | −957 | −43 | −86 |

5 | −43 | −57 | 14 | 71 | −957 | −957 | 143 | −100 | −71 |

6 | −43 | −29 | 71 | 86 | 57 | 71 | −171 | 71 | −57 |

7 | −57 | 129 | 86 | 14 | −157 | −14 | 100 | 100 | 29 |

8 | 14 | 114 | −57 | 100 | 29 | −14 | −157 | −143 | −176 |

Width of Void | Depth of Void | k | |
---|---|---|---|

Model A | 0.45 m | 0.10 m | 39.5% |

Model B | 0.35 m | 0.06 m | 57.1% |

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## Share and Cite

**MDPI and ACS Style**

Ju, J.; Tian, X.; Zhao, W.; Yang, Y.
Detection and Identification for Void of Concrete Structure by Air-Coupled Impact-Echo Method. *Sensors* **2023**, *23*, 6018.
https://doi.org/10.3390/s23136018

**AMA Style**

Ju J, Tian X, Zhao W, Yang Y.
Detection and Identification for Void of Concrete Structure by Air-Coupled Impact-Echo Method. *Sensors*. 2023; 23(13):6018.
https://doi.org/10.3390/s23136018

**Chicago/Turabian Style**

Ju, Jinghui, Xiushu Tian, Weigang Zhao, and Yong Yang.
2023. "Detection and Identification for Void of Concrete Structure by Air-Coupled Impact-Echo Method" *Sensors* 23, no. 13: 6018.
https://doi.org/10.3390/s23136018