## 3 Experimental Verification
### Experimental Results during the Post-Tensioning Process
#### 3.3.2 Discussions
A 10% variation in the value of the elastic modulus of concrete can result in an error of more than 10%, based on measured strains on S2, and more than 20%, based strains on S3. This means that the used value of the elastic modulus of concrete can result in a significant variation in the predicted prestress forces, and using strains measured on S2 always yields better results than those on S3. This is because strains on S3 were placed closer to the segment joints, where the deformation over the cross-section is not linear. More discussions on this are presented in Section 5.4. These results demonstrate the influence of the elastic modulus of the concrete on the prestress force estimations, and ideally the elastic modulus of concrete should be directly measured from the tested structure. Otherwise, the range of the identified prestress force can be determined by considering the possible variations in the concrete elastic modulus. The second factor that could lead to an error between the theoretically predicted result and experimentally measured prestress force is related to the measurement error in the strain gauge values. Since any data acquisition system has a certain level of inaccuracy and is affected by measurement noise, the errors in the strain gauges can potentially affect the theoretical calculation results. Therefore, an error analysis of the effect of the strain gauge measurement accuracy on the prestress force identification is conducted, and the error of the strain measurement values is assumed to be at three different levels, namely, 2%, 5%, and 8%. The four strain gauges as shown in Figure 6 are considered to have these three different error levels, respectively. Random numbers from the standard normal distribution with a mean value of 0 and different standard deviation values (i.e., with different error levels) are added onto the experimental strain data. The relative errors in the calculated prestress force under different error levels in the measured strains are listed in Table 4.  
Table 4 indicates that increasing the strain measurement errors from 2% to 8% does not significantly change the estimated prestress force, with the errors remain at the similar level. This is because the errors in measured strains affect the positive and negative forces from both the concrete and reinforcements over the cross-section, which cancel out the error influences on the prestress force. Although both the strain and elastic modulus are linearly proportional to the force, i.e., E\(\varepsilon\), an error in the concrete elastic modulus has more significant effect on the estimated prestress force since it only affects the concrete force over the cross-section. These results indicate that the reliability of the equipment and measurement noise in strain data would also influence the theoretical calculation results, but are less significant as compared to that owing to the error in concrete elastic modulus. The experimental verification of using the proposed approach for quantifying the prestress force based on the neutral axis location shows that the predicted results have certain differences, when compared with the experimental measured result. This may be attributed to the uncertainty of the estimated elastic modulus or strain gauge measurements. However, the proposed approach can identify the prestress force variation. Therefore, the method can be used to identify the change in prestress force, and also approximately \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Uncertainty Error Level**} & \multicolumn{2}{c}{**S2**} & \multicolumn{2}{c}{**S3**} \\ \cline{2-5}  & **RE\({}_{\_62}\) (\%)** & **RE\({}_{\_107}\)** (\%)** & **RE\({}_{\_62}\) (\%)** & **RE\({}_{\_107}\) (\%)** \\ \hline
2\% & 2.84 & 1.38 & 12.68 & 11.44 \\
5\% & 2.76 & 1.25 & 12.56 & 11.28 \\
8\% & 2.43 & 1.05 & 12.24 & 10.99 \\ Original & 3.06 & 1.48 & 13.72 & 11.77 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Error analysis on the effect of strain measurement accuracy.