## 4 Non-Destructive Test Results and Comparisons  
### Experimental Results and Strength Prediction of Concrete Cylinder  
After finishing water curing under a constant temperature and humidity for 28 days, the compressive strength tests were conducted using a 1000 kN UTM. The compressive strength of the concrete cylinder was measured by averaging nine separate cylinder specimens for each mix design (Table 2 summarizes the compressive strength results). The test results of mix 1 and mix 2 show a compressive strength of 53.1 and 66.2 MPa, respectively, and they exceeded their intended mixed design strength at 28 days. Mix 3, however, did not reach the intended mixed design strength of 100 MPa but stopped at 68.6 MPa, (a strength level of 69%). This phenomenon may be due to the pozzolanic reaction with high pozzolan ingredients; the strength occurrence was somewhat delayed until the full hydration reaction was completed. Figure 3 shows the relationship between the tested compressive strength and the strength predicted by the ultrasonic pulse velocity and rebound hammer tests. For high strength concrete, UPV ranged between 4.5 and 5.0, for a concrete with a compressive strength ranging from 50 to 80 MPa. The relatively high speed of the UPV is due to the high level of density in high strength concrete. The results of the rebound hammer test presented wider scatter of hammer values, even though the predicted strength range was same as that predicted by UPV. This discrepancy might be caused by predicting the compressive strength from the surface impact of the concrete specimen. This is because the surface is not regular and the impact test is largely depended on the testing workability. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Mix Types** & \(\mathbf{f_{c}^{\prime}}\) **(MPa)** & **Average (MPa)** \\ \hline Mix 1 & 52.3, 53.8, 52.2, 52.9, 54.5 & 53.1 \\ Mix 2 & 62.4, 70.4, 61.9, 73.8, 60.2, 65.7, 65.0, 69.8 & 66.2 \\ Mix 3 & 64.4, 65.3, 67.8, 66.2, 76.8 & 68.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Measured compressive strength of concrete cylinder according to the case of mix proportion. Figure 3: Relationship between tested compressive strength of concrete cylinder and predicted by the non-destructive test. For better accuracy and practicability, multivariable linear regression analysis (MRA) was employed as a statistical approach. MRA intends to simultaneously certify two or more independent influencing parameters. The general MRA equation is given in Equation (2), which the dependent variable being a linear equation of more than an independent variable. \[Y=a+b_{1}X_{i}+b_{2}X_{j}+\ldots b_{k}X_{n}\pm e \tag{2}\]  
where,  
\(Y=\) dependent variable  
\(a=\) Y intersect  
\(b_{1,2,\ldots k}=\) slopes related with \(X_{i,j,\ldots\ n}\)  
\(X_{i,j,\ldots\ n}=\) values of independent variables  
\(e=\) error  
In order to evaluate the degree of accuracy for the prediction equations, the root mean square error (\(RMSE\)) value was employed. When two data sets, for example, one set is from the observed or tested value and the other is the theoretical calculation or prediction, are compared, root means square can serve a measure how far on average the error is from 0. The standard deviation indicates the variability of the difference, where the \(RMSE\) is meaningful measure of the error. The common expression of \(RMSE\) is introduced in Equation (3). \[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(X_{i}-x_{i})^{2}} \tag{3}\]  
where,  
\(X_{i}=\) tested compressive strength of concrete (MPa)  
\(x_{i}=\) predicted compressive strength of concrete (MPa)  
\(n=\) number of specimens  
Based on a multiple regression analysis, this study suggests a dual variable regression equation for estimating the compressive strength of high strength concrete in practical applications (see Equation (4)). Table 3 summarizes the comparison results between the tested and predicted compressive strength of concrete obtained from single and dual linear regression expressions.