# Damage Detection at a Reinforced Concrete Specimen with Coda Wave Interferometry

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## Abstract

**:**

## 1. Introduction

## 2. Ultrasound Methods

#### 2.1. Basics

#### 2.2. Diffusion Approximation

^{2}/s.

#### 2.3. Sensitivity Kernel

#### 2.4. Imaging with an Inverse Problem

#### 2.5. Imaging with Influence Areas

## 3. Experiment

## 4. Results

#### 4.1. Decorrelation Investigations on Selected Measurement Pairs

#### 4.1.1. Pair 1 and 6

#### 4.1.2. Pair 3 and 4

#### 4.1.3. Pair 5 and 7

#### 4.2. CWI Damage Localization

#### 4.2.1. State 1: Uncracked

#### 4.2.2. State 2: Crack Formation

#### 4.2.3. State 3: Cracked

## 5. Discussion

#### 5.1. Overall Discussion with an Outlook to General Improvements

#### 5.2. Crack Detection and Related Challenges

#### 5.3. Comparison of Imaging Approaches

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CWI | Coda Wave Interferometry |

CC | Cross-Correlation Coefficient |

DC | Decorrelation coefficient |

FOS | Fibre Optic Sensor |

FE | Finite Elements |

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**Figure 1.**Example signal (60 kHz) with the used evaluation windows and envelope fitting with the solved diffusion equation.

**Figure 2.**Graphical explanation of the derivation of the influence areas with the help of a sensitivity kernel.

**Figure 3.**Dimensions of the test specimen with FOS in green and US transducers in blue. Results of the US transducer 16 proved to be erroneous and were not taken into account for the evaluation.

**Figure 4.**Strain results from 0 to 100 kN of the FOS. Due to the continuous measurement, the colors are referring to the load of the corresponding strain measurement.

**Figure 7.**Evaluation at load step 3 with 15 kN load applied with the two different methods of imaging from Section 2.4 and Section 2.5 shown in (

**a**,

**b**).

**Figure 8.**Evaluation at load step 4 with 20 kN load applied with the two different methods of imaging from Section 2.4 and Section 2.5 shown in (

**a**,

**b**).

**Figure 9.**Comparison of the damage localization with an inverse problem for 95 pairs (

**a**) and DC-based selected 61 pairs (

**b**) using the STIR method with ${m}_{max}=2.0$.

**Figure 10.**Evaluation of the change between load step 8 and 12 with the two different methods of imaging from Section 2.4 and Section 2.5 shown in (

**a**,

**b**).

**Figure 11.**Evaluation of the change between load step 27 and 30 with the two different methods of imaging from Section 2.4 and Section 2.5 shown in (

**a**,

**b**).

${\mathsf{f}}_{\mathrm{cm},\mathrm{cube}}$ | ${\mathsf{f}}_{\mathrm{ctm}}$ | ${\mathsf{E}}_{\mathrm{cm}}$ |
---|---|---|

$[\mathrm{N}/{\mathrm{mm}}^{2}]$ | $[\mathrm{N}/{\mathrm{mm}}^{2}]$ | $[\mathrm{N}/{\mathrm{mm}}^{2}]$ |

38.2 | 2.8 | 28,800 |

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## Share and Cite

**MDPI and ACS Style**

Grabke, S.; Clauß, F.; Bletzinger, K.-U.; Ahrens, M.A.; Mark, P.; Wüchner, R. Damage Detection at a Reinforced Concrete Specimen with Coda Wave Interferometry. *Materials* **2021**, *14*, 5013.
https://doi.org/10.3390/ma14175013

**AMA Style**

Grabke S, Clauß F, Bletzinger K-U, Ahrens MA, Mark P, Wüchner R. Damage Detection at a Reinforced Concrete Specimen with Coda Wave Interferometry. *Materials*. 2021; 14(17):5013.
https://doi.org/10.3390/ma14175013

**Chicago/Turabian Style**

Grabke, Stefan, Felix Clauß, Kai-Uwe Bletzinger, Mark Alexander Ahrens, Peter Mark, and Roland Wüchner. 2021. "Damage Detection at a Reinforced Concrete Specimen with Coda Wave Interferometry" *Materials* 14, no. 17: 5013.
https://doi.org/10.3390/ma14175013