# Assessment of Strength Development at Hardened Stage on High-Strength Concrete Using NDT
## 3 Results and Discussion
### Discussion on Regression Equation of Concrete Strength Based on NDT  
Figure 9 shows the relation between the rebound value and ultrasonic pulse velocity of concrete. The rebound value and ultrasonic pulse velocity exhibited a nonlinear relation. The rebound value showed a tendency to significantly increase as the ultrasonic pulse velocity exceeded 4.2 km/s, which corresponds to core compressive strengths of 35 MPa or higher. Figure 10 shows the relation between core and cylinder holds on ultrasonic pulse velocity. As mentioned above, the cylinder holds exhibited higher ultrasonic pulse velocities than the core specimens. In this study, we found large differences in the ultrasonic pulse velocity depending on the rebound value and curing method. This result implies that the reliability of NDT may significantly vary depending on the surface condition and internal structure of the specimen undergoing testing [33; 44]. In this context, [PERSON] et al. have reported the effects of the surface hardening of concrete and the temperature on the ultrasonic pulse velocity with the curing method [45; 46]. Furthermore, factors such as the amount of aggregate and the aggregate-cement paste interface condition may also affect the ultrasonic pulse velocity [32; 33]. Considering that the correlation between the rebound value and the ultrasonic pulse velocity is not high (R\({}^{2}\) = 0.68) within the scope of this study, we proposed a regression equation for each NDT method. Figure 11 compares the various regression equation of the compressive strength of concrete based on the rebound value. Although many studies have been conducted on the rebound value,  
Figure 10: Relation between core and cylinder holds of ultrasonic pulse velocity. Figure 9: Relation between rebound value and ultrasonic pulse velocity of concrete. no satisfactory results have been reported with regard to its reliability. Meanwhile, the US Army Laboratory and JASS 5 [8] proposed a model to estimate the compressive strength of concrete using the rebound value by comparing with the experiment results. The proposed regression equation of previous studies can meet the \(\pm 20\%\) error range for compressive strengths of \(<\)40 MPa, but the model reliability significantly drops for higher compressive strengths over 40 MPa. In the region of high-strength concrete of 40 MPa or more, the value by the existing estimation formula was confirmed to be a value less than 70% compared to the actual compressive strength, and the tendency was confirmed to increase with increasing strength. Therefore, a regression equation that can predict up to a range of high-strength concrete of 40 MPa or more should be considered. Next, we proposed a regression equation of the compressive strength of concrete as per the experimental rebound values using Equation (5). \[\text{US Army: F}_{\text{R,\,etm}}=(0.0932\text{R}^{2}+8\text{R}-120.6)/10.2 \tag{3}\]  
\[\text{JASS 5: F}_{\text{R,\,etm}}=(7.3\text{R}+100)/10.2 \tag{4}\]  
\[\text{Proposed regression equation based on this study: F}_{\text{R,\,etm}}=3.12\text{R}-79.33 \tag{5}\]  
where F R, etm denotes the estimated compressive strength according to the rebound value (MPa) and R the rebound value. Figure 12 compares the regression equation of the compressive strength of concrete as per the ultrasonic pulse velocity. The model results include those of studies by JASS 5 [8], [PERSON] [47], [PERSON] [48], and [PERSON] [49]. It is confirmed that the existing compressive strength models based on the ultrasonic pulse velocity have low reliability, beyond the error range of \(\pm\) 20%, similar to the case of the analysis results based on the rebound value. When the existing estimation formula is used, it is confirmed that the difference between the compressive strength value and the measured value increases based on the ultrasonic speed of 4.1 km/s. In addition, in the range of concrete compressive strength of 40 MPa or more, the tendency gradually increases, and it is confirmed that the value is less than 70% at 60 MPa.