# Correlation between Coda Wave and Stresses in Uni-Axial Compression Concrete
## 3 Experimental Investigation
### The Coda Wave Test under Uni-Axial Stress
#### 3.4.2 Relation between Stress and Coda Wave Velocity  
Figure 9 illustrates the experimental curves of the relation between the relative variation of axial sound velocity and the stress on the specimen C-1-1. It was found that the axial sound velocity increases with the increase of stress in the process of loading from 0 MPa to 10 MPa. This is because the sound velocity in the pores is far less than that in the concrete matrix. Under the action of the stress, the microcracks in the concrete begin to close, resulting in the decrease of the porosity and the increase of the sound velocity. The sound velocity starts to decrease during the unloading process from 10 MPa to 0 MPa. After unloading completely, the sound velocity increases by approximately 2.15% compared to that at the initial time without loading. This is because the cracks are elastic, and in the process of unloading, the closed cracks start to recover and the sound velocity is reduced. When the specimen was unloaded to 0 MPa, a part of the closed cracks which did not have time to fully recover to the original state remained. Therefore, the corresponding wave velocity is larger than that at the initial time. Then, the specimen was loaded from 0 MPa until 32 MPa, approximately 75% of the concrete strength. In this process, after the maximum sound velocity increase by 7.35%, it begins to slow down, but the trend is not obvious, indicating that the cracks start to extend with the increase of stress, the porosity increases, and the wave velocity decreases. However, the secondary cracks generated by the crack growth form along the axial direction, and their influence on the horizontal sound velocity is large but the influence on the axial sound velocity is small, so the change of axial sound velocity is not obvious in the crack extended stage. Finally, the specimen was unloaded from 32 MPa to 0 MPa. In this process, the change of the axial sound velocity is not obvious, but still has a downward trend. This is because when the concrete is loaded at a high stress level, the cracks are in an unstable situation. After unloading, the cracks continue to extend. Therefore, the axial sound velocity has a downward trend. In the whole process, the maximum sensitivity is 1 MPa, and the change in the wave velocity (dV/V) is 0.00885.  
In Figure 10, the relation between the horizontal sound velocity and the stress on the specimen C-2-1 is shown. It was found that the horizontal sound velocity increases with the increase of stress in the process of loading from 0 MPa to 10 MPa, but the change is not obvious. This is because when the microcracks are in the closed stage, their lateral deformation is much smaller than their axial deformation. The closed cracks begin to recover during the unloading process from 10 MPa to 0 MPa. After unloading to 0 MPa, the sound velocity is increased by about 0.55% compared to that at the initial time without loading. This is also because a part of the closed cracks remains, as they may not have time to fully recover to the original state. Then the specimen was observed with loading from 0 MPa to 32 MPa. After the sound velocity reaches the maximum value, it begins to decrease sharply. The maximum sound velocity is about 1.21% larger than that at the initial time. This is  
Figure 9: Relation between the relative change of axial velocity and stress.  
because the cracks begin to extend as the stress increases. The secondary cracks are along the axial direction, which has a great influence on the horizontal sound velocity, so the horizontal sound velocity in the crack extended stage decreases sharply. Finally, the specimen was unloaded from 32 MPa to 0 MPa. In this process, the cracks are in an unstable extended stage. After unloading, the cracks will continue to extend and the horizontal sound velocity will continue to decrease. After unloading to 0 MPa, the sound velocity is about 6.75% lower than that at the initial moment. In the whole process, the maximum sensitivity is 1 MPa, and the change in the wave velocity (dV/V) is 0.00095.