## 4 Verification of the Applicability of the Unified Equation
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multirow{2}{*}{**No. **} & \multirow{2}{*}{**w/cem**} & \multirow{2}{*}{\ \begin{tabular}{c} **S/A** \\ **(\%)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **V\({}_{\text{paste}}\)** \\ **(\%)** \\ \end{tabular}  } & \multicolumn{6}{c}{**Mixture Proportion, kg/m3**} \\ \cline{5-10}  & & & & & & & & & \\ \hline PFC1 & 0.4 & & & 163 & 293 & 0 & 126 & 4.19 & & \\ PFC2 & 0.6 & & 42 & 30 & 195 & 229 & 0 & 98 & 0.82 & 750 & 1044 \\ PFC3 & 0.4 & & & 196 & 352 & 0 & 151 & 5.02 & & \\ PFC4 & 0.6 & & & 196 & 35  
Figure 9(a) presents a comparison between the UPV-based strength estimations of concrete at different ages and the strength measurements obtained from actual compression tests. Of the 203 entries of verification data, most achieved an error within \(\pm\)15%; only 27 entries (13.3%) had an error greater than 15%. To determine the possible cause of the relatively large error in prediction, another comparison chart, Figure 9(b), was created, which compares the estimation results of concrete among samples at 1\(\sim\)3 days old and among those at all ages. Figure 9(b) reveals that 21 entries (approximately 10.3%) with estimation errors greater than 15% were identified in the estimation results for concrete at ages within 3 days, and these errors were all relatively conspicuous. In other words, only 6 entries (3.0% of the total verification data) with prediction errors greater than 15% were identified for concrete samples at ages more than 3 days, and these errors were only slightly greater than 15%. This result indicates that using the proposed unified equation to estimate the strength of concrete at ages after 3 days can yield highly reliable estimations. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**Day 1**} & \multicolumn{2}{c}{**Day 3**} & \multicolumn{2}{c}{**Day 7**} & \multicolumn{2}{c}{**Day 14**} & \multicolumn{2}{c}{**Day 28**} & \multicolumn{2}{c}{**Day 56**} \\ \cline{2-13}  & **S** & **V** & **S** & **V** & **S** & **V** & **S** & **V** & **S** & **V** & **S** & **V** \\ \hline PFC1 & 17 & 3781 & 30 & 4261 & 36 & 4392 & 45 & 4465 & 47 & 4553 & 59 & 4660 \\ PFC2 & 6 & 3304 & 12 & 3859 & 17 & 4012 & 21 & 4150 & 26 & 4256 & 34 & 4426 \\ PFC3 & 16 & 3769 & 25 & 4154 & 36 & 4287 & 44 & 4378 & 47 & 4485 & 50 & 4547 \\ PFC4 & 5 & 3271 & 9 & 3607 & 14 & 3885 & 16 & 4023 & 22 & 4154 & 26 & 4324 \\ PFC5 & 15 & 3803 & 22 & 4217 & 35 & 4368 & 48 & 4464 & 58 & 4548 & 70 & 4641 \\ PFC6 & 3 & 2835 & 8 & 3563 & 13 & 3788 & 16 & 3915 & 21 & 4084 & 26 & 4239 \\ PFC7 & 13 & 3682 & 25 & 4156 & 32 & 4255 & 41 & 4388 & 43 & 4470 & 55 & 4531 \\ PFC8 & 4 & 2962 & 8 & 3632 & 12 & 3856 & 18 & 4009 & 21 & 4143 & 27 & 4278 \\ PSC1 & 14 & 3362 & 29 & 4194 & 41 & 4351 & 50 & 4466 & 51 & 4499 & 60 & 4624 \\ PSC2 & 2 & 2617 & 9 & 3590 & 16 & 3886 & 22 & 4143 & 25 & 4239 & 29 & 4343 \\ PSC3 & 5 & 3161 & 19 & 4005 & 29 & 4145 & 39 & 4296 & 44 & 4445 & 48 & 4523 \\ PSC4 & 2 & 2811 & 9 & 3543 & 15 & 3903 & 22 & 4076 & 26 & 4184 & 30 & 4328 \\ PSC5 & 8 & 3468 & 21 & 4151 & 41 & 4286 & 50 & 4414 & 56 & 4507 & 63 & 4645 \\ PSC6 & 3 & 2689 & 10 & 3585 & 18 & 3904 & 28 & 4137 & 34 & 4288 & 39 & 4418 \\ PSC7 & 4 & 3037 & 16 & 3960 & 29 & 4089 & 35 & 4297 & 44 & 4432 & 50 & 4536 \\ PSC8 & 2 & 2672 & 7 & 3520 & 14 & 3782 & 19 & 3998 & 27 & 4179 & 32 & 4272 \\ PPC2 & 14 & 3752 & 31 & 4172 & 46 & 4303 & 46 & 4440 & 54 & 4553 & 66 & 4592 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The measured UPV and strength data collected for pozzolanic concrete. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.