## 4 Non-Destructive Test Results and Comparisons
### Comparison with Previous Equations  
To validate the accuracy of the formula suggested in this study, the estimated compressive strength of concrete results from the suggested formula were compared with those of other considered formulas for UPV or RH (as summarized in Tables 4 and 5). The expression types are classified as 1 st and 2 nd polynomial, power or exponential. The compressive strength of concrete ranged from 20 to 100 MPa, however, most of the tested strength is limited to high strength concrete exceeding 40 MPa. Figure 5 presents a summary of the test to predicted ratio for the average compressive strength of concrete. The results indicate that most of the considered formulas are conservative in their predictions of the compressive strength of high strength concrete, based on data from the UPV and RH methods. These results can give safer prediction but may be impractical with respect to the factor of safety resulting from the strength evaluation. Consequently, the formula suggested by the dual linear regression expression showed the best accordance with the test results. Tables 6 and 7 include the  
Figure 4: Relationship between tested compressive strength of concrete cylinder and predicted by the non-destructive test. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Experimental Results**} & \multicolumn{3}{c}{**Estimated Strength (MPa)**} \\ \cline{2-7}
**Specimen** & \(f_{c}\) **(MPa)** & \(v_{p}\) **(km/s)** & \(R_{0}\) & \multicolumn{2}{c}{**Single**} & \multicolumn{2}{c}{**Single**} & \multicolumn{2}{c}{**Dual Regression**} \\  & & & & & & **Regression by \(v_{p}\)** & **Regression by \(R_{\theta}\)** & **by \(v_{p}\) and \(R_{\theta}\)** \\ \hline
1-1 & 52.3 & 4.89 & 37.6 & 64.3 & 56.5 & 54.8 \\
1-2 & 53.8 & 4.73 & 38.4 & 63.3 & 57.7  
analysis results in terms of \(RMSE\). Figure 6 plots the entire comparison, revealing which formula has the smallest \(RMSE\), thus showing the highest accuracy in the prediction of the compressive strength of high strength concrete. With the exception of the formulas of [PERSON] and [PERSON], most of the considered formulas presented relatively large \(RMSE\). Consequently, the estimation equation suggested in this study showed the lowest \(RMSE\) among the considered formulas. This proves that the dual linear regression expression used in this study can give a good prediction for the strength evaluation of HSC by combining two significant influencing factors: measured UPV and RH. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**References** & **Test/Predicted** & **Standard Deviation** & **Root Mean Square * \\ \hline [PERSON] [4] & 1.6 & 0.13 & 23.6 \\ [PERSON] [34] & 2.4 & 0.21 & 37.5 \\ [PERSON] [10] & 1.5 & 0.21 & 22.4 \\ [PERSON] [35] & 1.0 & 0.08 & 5.1 \\ [PERSON] [36] & 1.1 & 0.11 & 8.7 \\ [PERSON] [37] & 1.3 & 0.12 & 15.9 \\ [PERSON] [13] & 1.6 & 0.13 & 24.6 \\ [PERSON] [38] & 1.2 & 0.09 & 12.4 \\ [PERSON] [39] & 1.7 & 0.16 & 25.9 \\ Dual linear & 1.0 & 0.08 & 4.9 \\ regression & & & \\ \hline \hline \end{tabular}  
* * calculated by using the results in Table 3.  
\end{table} 
Table 6: Comparison results of compressive strength of concrete by rebound hammer test.