## 6 Verification of Formulas Using Additional Data
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Formula**} & **Mean Error** & **Absolute Mean** & **Absolute Error** \\  & **(\%)** & **Error (\%)** & **Std. (\%)** \\ \hline Hiley & 7.20 & 11.82 & 8.10 \\ Original Gates & \(-\)39.59 & 39.59 & 4.26 \\ [PERSON] & \(-\)10.24 & 10.24 & 5.79 \\ [PERSON] (PHC) & 11.08 & 11.12 & 7.07 \\ [PERSON] (Coef) & \(-\)2.16 & 5.57 & 3.49 \\ [PERSON] (PHC Coef) & 4.67 & 10.59 & 6.69 \\ [PERSON] (Coef2) & \(-\)7.83 & 8.42 & 5.62 \\ [PERSON] (PHC Coef2) & 5.12 & 7.47 & 4.64 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of bearing capacity estimates using 8 different pile driving formulas and results from 21 PDA data points (mean error, absolute mean error, and standard deviation of absolute mean error) for piles with diameters of 500 mm. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Formula**} & **Mean Error** & **Absolute Mean** & **Absolute Error** \\  & **(\%)** & **Error (\%)** & **Std. (\%)** \\ \hline [PERSON] & 6.63 & 10.03 & 8.69 \\ Original Gates & \(-\)45.29 & 45.29 & 7.17 \\ [PERSON] & \(-\)17.08 & 17.08 & 9.87 \\ [PERSON] (PHC) & 2.83 & 10.46 & 6.65 \\ [PERSON] (Coef) & \(-\)5.90 & 9.11 & 6.53 \\ [PERSON] (PHC Coef) & 1.03 & 10.43 & 6.66 \\ [PERSON] (Coef2) & \(-\)8.12 & 11.05 & 6.61 \\ [PERSON] (PHC Coef2) & 4.65 & 11.37 & 7.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of bearing capacity estimates using 8 different pile driving formulas and results from 60 PDA data points (mean error, absolute mean error, and standard deviation of absolute mean error). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Formula**} & **Mean Error** & **Absolute Mean** & **Absolute Error** \\  & **(\%)** & **Error (\%)** & **Std. (\%)** \\ \hline Hiley & 6.32 & 9.06 & 8.95 \\ Original Gates & \(-\)48.36 & 48.36 & 6.54 \\ Gates & \(-\)20.76 & 20.76 & 9.69 \\ Gates (PHC) & \(-\)1.61 & 10.10 & 6.47 \\ Gates (Coef) & \(-\)7.91 & 11.01 & 7.02 \\ Gates (PHC Coef) & \(-\)0.93 & 10.35 & 6.73 \\ Gates (Coef2) & \(-\)8.27 & 12.47 & 6.73 \\ Gates (PHC Coef2) & 4.41 & 13.46 & 8.64 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of bearing capacity estimates using 8 different pile driving formulas and results from 39 PDA data points (mean error, absolute mean error, and standard deviation of absolute mean error) for piles with diameters of 600 mm. operates accurately. Among all formulas, the Gates (Coef) shows the highest accuracy. This is because the Gates (Coef) applies an optimized coefficient to the Gates formula for specific ranges, resulting in improved accuracy. Although their accuracy is relatively lower compared to other formulas, the previously recommended Gates (PHC) and Gates (PHC Coef) showed absolutely better accuracy than the results using 242 data points, confirming their successful verification. Lastly, the analysis using all data confirms that the Gates (PHC), Gates (Coef), and Gates (PHC Coef) formulas exhibit the highest accuracy (Table 7). The difference in the accuracy order of the formulas between the results using 60 data points and the previous 242 data points arises due to the data distribution. The previous dataset of 242 data points predominantly included the 600 mm diameter PHC pile data, with a significant proportion showing bearing capacities greater than 3000 kN. In contrast, the verification dataset had 30% of the data with bearing capacities of 3000 kN or less, which increased the accuracy of the Gates and Gates (Coef) formulas. Despite the difference in the accuracy order, the absolute mean error and absolute error standard deviation values showed better results, ultimately proving the validity of the formulas. Although the number of data points is limited, considering previous test results and verification results, the following conclusions can be suggested: (1) For PHC piles with a diameter of 500 mm or less, the Gates (Coef) or Gates (PHC Coef) formulas are recommended.