Correlation between Coda Wave and Stresses in Uni-Axial Compression Concrete
Abstract
:1. Introduction
2. Correlation Model of Sound Velocity and Stress in Concrete
2.1. Sound Velocity in Concrete without Stress Action
2.2. Crack Deformation under Uni-Axial Stress
2.3. Sound Velocity Change Induced by Uni-Axial Stress
3. Experimental Investigation
3.1. Experimental System and Sensors
3.2. Specimen Arrangement
3.3. Propagating Regularity of the Coda Wave in Concrete
3.3.1. Frequency Effect
3.3.2. Influence of the Relative Position of Transmitters and Receivers
3.4. The Coda Wave Test under Uni-Axial Stress
3.4.1. CWI Analysis Method
3.4.2. Relation between Stress and Coda Wave Velocity
3.4.3. Data Processing and Parameter Fitting
4. Discussion
- Step 1.
- Conduction of field test or laboratory experiment on unloaded concrete to obtain the initial waveform of the coda wave;
- Step 2.
- Calibration or regression of the parameters in Equation (22);
- Step 3.
- Conduction of field test on loaded concrete structures to obtain the waveform of the coda wave;
- Step 4.
- Analysis of the obtained coda wave by the wave expansion method to determine the relative change between the sound velocity ;
- Step 5.
- Determine the stress (or stress increment ) using Equation (22) with calibrated parameters.
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
acoustic slowness; | |
sound velocity; | |
, and | velocity of the waves propagating in the elastic matrix, concrete with cracks, and air, respectively; |
, , and | acoustic slowness in the elastic matrix, concrete with cracks, and air, respectively; |
porosity of concrete; | |
stress in concrete under an applied load; | |
total deformation of concrete; | |
deformation of elastic concrete matrix; | |
closed deformation of microcracks; | |
extended deformation of microcracks; | |
elastic modulus of concrete; | |
shear modulus of concrete; | |
elastic constant of concrete, ; | |
Poisson’s ratio of concrete; | |
fracture toughness of concrete; | |
crack density parameter in unit volume concrete; | |
a0 | semi-major axis of concrete microcrack; |
b0 | semi-minor axis of concrete microcrack; |
and | orientation parameters of crack; |
critical stress of crack closure or expansion; | |
proportional to the stress ; | |
U | displacement of crack in the direction of the major axis; |
V | displacement of crack in the direction of the minor axis; |
displacement of point A in the direction of the major axis; | |
displacement of point B in the direction of the major axis; | |
displacement of point A in the direction of the minor axis; | |
displacement of point B in the direction of the minor axis; | |
displacement of point A in the direction of the y axis; | |
displacement of point B in the direction of the x axis; | |
closure displacement in the direction of the y axis; | |
closure displacement in the direction of the y axis; | |
expansion displacement in the direction of the x axis; | |
kN | intensity of crack in concrete without an applied load; |
closure deformation of concrete caused by stress σ; | |
expansion deformation of concrete caused by stress σ; | |
volume strain of the crack closure; | |
volume strain of the crack expansion; | |
ka, kb1 and kb2 | undetermined coefficients; |
density parameter of the horizontal equivalent cracks in concrete; | |
density parameter of the extended equivalent cracks in concrete; | |
a | semi-length of microcrack in concrete; |
b | semi-width of microcrack in concrete; |
increment of acoustic slowness caused by microcracks; | |
S1 | acoustic slowness caused by microcrack, when the sound wave passes through the element in the minor axis direction of the crack; |
S2 | acoustic slowness caused by microcrack, when the sound wave passes through the element in the major axis direction of the crack; |
increment of concrete acoustic slowness caused by a set of parallel cracks; | |
shape correction coefficient of an elliptical crack in a rectangular crack; | |
and | increment of the acoustic slowness caused by crack closure and expansion, respectively; |
ks | parameter related to the shape and density of crack, ; |
, , , , , and | undetermined parameters related to cracks, , , , , , ; |
increment of sound velocity; | |
i = 1, 2, … | denotes axial and horizontal directions. |
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Center Frequency (kHz) | Size (mm) | Weight (g) | Operating Temperature Range (°C) | Frequency Range (kHz) | Resonance Frequency (kHz) |
---|---|---|---|---|---|
300 | 8 × 8 | 2 | −65~177 | 150~400 | 300 |
150 | 23 × 19 | 27 | −45~125 | 50~200 | 150 |
50 | 23 × 19 | 33 | −45~125 | 35~80 | 50 |
Composition | Cement | Sand | Aggregate | Water | Admixture |
---|---|---|---|---|---|
Dosage per m3 (kg) | 420 | 622 | 1155 | 210 | 2.10 (1%) |
Model Parameter | Fitted Value | Correlation Coefficient R |
---|---|---|
6.314 × 10−3 | 0.9359 | |
2.395 × 10−4 | 0.9109 | |
5.454 × 10−7 | ||
10.77 |
Model Parameter | Fitted Value | Correlation Coefficient R |
---|---|---|
9.58 × 10−4 | 0.9237 | |
1.326 × 10−4 | 0.9915 | |
6.147 × 10−6 | ||
12.33 |
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Zhang, J.; Han, B.; Xie, H.-B.; Zhu, L.; Zheng, G.; Wang, W. Correlation between Coda Wave and Stresses in Uni-Axial Compression Concrete. Appl. Sci. 2018, 8, 1609. https://doi.org/10.3390/app8091609
Zhang J, Han B, Xie H-B, Zhu L, Zheng G, Wang W. Correlation between Coda Wave and Stresses in Uni-Axial Compression Concrete. Applied Sciences. 2018; 8(9):1609. https://doi.org/10.3390/app8091609
Chicago/Turabian StyleZhang, Jinquan, Bing Han, Hui-Bing Xie, Li Zhu, Gang Zheng, and Wenwu Wang. 2018. "Correlation between Coda Wave and Stresses in Uni-Axial Compression Concrete" Applied Sciences 8, no. 9: 1609. https://doi.org/10.3390/app8091609
APA StyleZhang, J., Han, B., Xie, H.-B., Zhu, L., Zheng, G., & Wang, W. (2018). Correlation between Coda Wave and Stresses in Uni-Axial Compression Concrete. Applied Sciences, 8(9), 1609. https://doi.org/10.3390/app8091609