Correlation of Load-Bearing Behavior of Reinforced Concrete Members and Velocity Changes of Coda Waves
Abstract
:1. Introduction
2. Methods
2.1. Sensing Structures with Ultrasound
2.1.1. General Aspects
- 1
- The low frequency range and stationary wave regime, where the wavelength is greater than the specimen itself. This regime is typically limited to .
- 2
- The single scattering regime where the wavelength is longer than the grains but smaller than the macroscopic size of the structure (). In this regime and , intrinsic absorption can be neglected since .
- 3
- The multiple scattering regime ( where but intrinsic absorption does not dominate signal spreading).
- 4
- The attenuative regime with where scattering and intrinsic absorption prevent elastic waves from significant spreading.
2.1.2. The CWI-Method
2.2. Load-Bearing Behavior of Flexural RC Members
2.2.1. Phenomenological Characterization of RC
2.2.2. Intermediate Resume
2.2.3. Computational Approach
3. Experiments
3.1. Experimental Setup
3.2. Placement of Measuring Equipment
3.3. Concreting and Curing
3.4. Load Control
3.5. Proof of Concept
4. Results and Discussion
4.1. Development of the Relative Velocity Change with Time and Load
- 1
- Cracking strongly affects the US signal and the key quantities computed with CWI, the correlation coefficient and the relative velocity change .
- 2
- The relative velocity change is always negative.
- 3
- Characteristic points associated with significant changes in the material response and can be identified in the F- relation, too.
- 4
- A fundamental change of the load-bearing behavior happens in the range of cracking ➁ and is also predicted by the F- relation.
- 5
- In agreement with the decreasing slope of the - relation, the slope of the F- relation decreases in transition from the non-cracked to the cracked state.
- 1
- The closer a sensor pair is located to the tensile zone, the more the relative velocity change drops.
- 2
- With load increase, cracks gradually grow towards the compressive zone at top. This is well-reflected by the trend of the central axis’ gradient towards the tensile one. As the cracks approach the centerline transducers, the US signal is affected more like the signal in the tensile zone.
- 3
- Not even in the non-cracked state with linear elastic material behavior, the central trend is the average of compressive and tensile trends. Thus, the relative velocity change develops non-linear with the load.
4.2. Establishing a Correlation Function
4.3. Impact of the Transducer Distance
5. Conclusions
- For the first time, a correlation between a key parameter of ultrasound and a structural state variable is established that covers 90% of the complex load-bearing behavior of RC members. It integrates load-dependent stiffness and concrete cracking.
- For the beam and a sensor distance of 30 cm, a linear model is established with great confidence: with: strain.
- Tripled sensor distances do not impair the proposed correlation function much.
- Whether in compression or tension, obtained from step-wise CWI is found to be negative throughout.
- The closer a sensor pair is located to the tensile zone, the more drops.
- Although always integrates elastic effects as well as micro- and macro-cracking, the latter seems to dominate. Compared to the compressive zone, is more sensitive to changes in the tensile zone.
- Conversely, changes in the compressive zone are more difficult to detect because they are easily superimposed by tension.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
FOS | Fiber Optic Sensor |
US | Ultrasonic |
RC | Reinforced Concrete |
NDT | Non-Destructive Testing |
CWI | Coda Wave Interferometry |
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Clauß, F.; Epple, N.; Ahrens, M.A.; Niederleithinger, E.; Mark, P. Correlation of Load-Bearing Behavior of Reinforced Concrete Members and Velocity Changes of Coda Waves. Materials 2022, 15, 738. https://doi.org/10.3390/ma15030738
Clauß F, Epple N, Ahrens MA, Niederleithinger E, Mark P. Correlation of Load-Bearing Behavior of Reinforced Concrete Members and Velocity Changes of Coda Waves. Materials. 2022; 15(3):738. https://doi.org/10.3390/ma15030738
Chicago/Turabian StyleClauß, Felix, Niklas Epple, Mark Alexander Ahrens, Ernst Niederleithinger, and Peter Mark. 2022. "Correlation of Load-Bearing Behavior of Reinforced Concrete Members and Velocity Changes of Coda Waves" Materials 15, no. 3: 738. https://doi.org/10.3390/ma15030738