## 3 Results and Discussion
### Unconfined Compressive Strength and Curing Period
The most common measure is the coefficient of determination (R\({}^{2}\)) used in linear regression when conducting calibration experiments to quantify samples. In the linear context, this measure is very intuitive, as values between 0 and 1 give a quick interpretation of how much of the variance in the data is explained by the fit [17]. Although has been known for some time that R\({}^{2}\) is an inadequate measure for nonlinear regression, many scientists, as well as reviewers, insist that it is supplied in papers dealing with nonlinear data analysis. It is observed that R\({}^{2}\) is still frequently being used in the context of the performance or validity of a model when fitting to nonlinear data. [PERSON] and [PERSON] [17] pointed out the low performance of R\({}^{2}\) and its inappropriateness for nonlinear data analysis by basing their analysis on an extensive Monte Carlo simulation approach. From this point of view, some new figures of merit, such as the mean absolute error (MAE) and root mean square error (RMSE), were used in this study to demonstrate and supplement the performance of the polynomial regression model. The maxima and minima concepts were applied to estimate the maximum UCS and the corresponding optimum curing period for soil and the soil-fly ash mixtures using the trend lines in Figure 7. The corresponding estimated data are presented in Table 3. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Fly Ash**} & **Fitted** & & & & & & x = Optimum & y = Max \\  & **Polynomial** & **dy/dx = 0** & **d\({}^{2}\)y/dx\({}^{2}\)** & **R\({}^{2}\)** & **RMSE** & **MAE** & **Curing** & **UCS** \\  & **Equation** & **(y = \(f\)(x))** & & & & & & **Period (day)** & **(kPa)** \\ \hline \multirow{2}{*}{0\%} & As shown in & \(-7.4432\times\) & \multirow{2}{*}{\(-7.4432\times\) +} & \multirow{2}{*}{\(0.6256\)} & \multirow{2}{*}{\(712.33\)} & \multirow{2}{*}{\(627.80\)} & \multirow{2}{*}{\(19\)} & \multirow{2}{*}{\(1707\)} \\  & Figure 7 & & & & & & & & \\ \hline \multirow{2}{*}{40\%} & As shown in & \(-13.0382\times\) & \multirow{2}{*}{\(-13.0382\times\)} & \multirow{2}{*}{\(-13.0382\times\)} & \multirow{2}{*}{\(0.8374\)} & \multirow{2}{*}{\(1140.17\)} & \multirow{2}{*}{\(1037.47\)} & \multirow{2}{*}{\(16\)} & \multirow{2}{*}{\(2329\)} \\  & Figure 7 & & & & & & & & \\ \hline \multirow{2}{*}{50\%} & As shown in & \(-14.630\times\) & \multirow{2}{*}{\(-14.6300\times\)} & \multirow{2}{*}{\(0.6453\)} & \multirow{2}{*}{\(1464.32\)} & \multirow{2}{*}{\(1310.12\)} & \multirow{2}{*}{\(17\)} & \multirow{2}{*}{\(2815\)} \\  & Figure 7 & & & & & & & & \\ \hline \multirow{2}{*}{60\%} & As shown in & \(-6.893\times\) & \multirow{2}{*}{\(-6.8930\times\)} & \multirow{2}{*}{\(-6.8930\times\)} & \multirow{2}{*}{\(0.7330\)} & \multirow{2}{*}{\(776.89\)} & \multirow{2}{*}{\(705.90\)} & \multirow{2}{*}{\(18\)} & \multirow{2}{*}{\(1470\)} \\  & Figure 7 & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Estimated optimum curing period and maximum UCS from the trend lines. Figure 7: Variation of UCS with curing period with trend lines. From Figure 7 and Table 3, it was seen that the optimum curing period varied from 16 to 19 days based on the fly ash content, which is a very narrow range. Since 50% fly ash content showed the maximum UCS of 2815 kPa for a curing period of 17 days, it is reasonable to conclude that an optimum curing period could be 17 days. The variations of UCS with fly ash content for different curing periods are shown in Figure 8. It is seen in Figure 8 that the UCS showed a peak for 50% fly ash content for all curing periods, except for day 0. It makes sense that no strength was gained right after mixing and that strength increased with time. A soil mixture with 50% fly ash content appeared to be the optimum to provide maximum strength. However, due to a narrow variation of UCS between 40% and 50% fly ash content, a soil mixture with 40% fly ash content can also be considered as an alternative option.