## 6 Verification of Formulas Using Additional Data  
This section presents additional verification of the formulas used in the study by comparing their predictive performance against the actual bearing capacity values obtained from the PDA (Pile Driving Analyzer) measurements. A total of 60 data points were used for verification, collected from 7 different sites (Table 3). Out of the 60 data points, 39 were collected from 4 different sites using 600 mm diameter PHC piles and 21 data points were collected from 3 other sites using 500 mm diameter PHC piles. The 500 mm diameter data were utilized to examine the sensitivity of the formulas to different pile diameters. The study results underwent verification using the same methods employed in earlier sections. The formulas under consideration include the Hiley, Original Gates, Gates (PHC), Gates (Coef), Gates (PHC Coef), Gates (Coef2), and Gates (PHC Coef2) formulas. The Danish formula was excluded from verification due to missing variables in the collected data. Figure 7 shows the comparison of the bearing capacity values obtained from 60 dynamic load tests with those calculated using the driving formulas, with the 500 mm diameter data marked in red and the 600 mm diameter data marked in blue. As shown in the figure, the Hiley formula demonstrates reasonable accuracy, while the original Gates formula tends to underestimate all values. Gates also shows a decline in accuracy beyond 3000 kN. The improved formulas, Gates (PHC), Gates (Coef), and Gates (PHC Coef), exhibit enhanced accuracy. The Gates (Coef2) and Gates (PHC Coef2) formulas also show improvement, but, similar to previous results, a gap was observed. Data obtained from the 500 mm diameter piles generally showed lower bearing capacity values compared to the 600 mm data due to the influence of pile size. Therefore, the Gates formula, which has high accuracy for bearing capacity calculations below 3000 kN, showed similar results to the bearing capacity values obtained from the PDA for the data acquired with the 500 mm diameter piles. Overall, no differences were found based on pile diameter. The statistical results are summarized in Tables 5-7 for detailed verification. The tables present the mean absolute error rates, standard deviations of absolute error rates, and mean error rates for each method. Table 6 shows the 21 data points for a 500 mm diameter, and Table 7 shows the combined 60 data points. Figure 7: Comparisons of bearing capacities (Qu) determined using 60 PDA data and bearing capacities calculated using pile driving formulas (**(a)**) Hiley, **(b)** Original Gates, **(c)** Gates, **(d)** Gates (PHC), **(e)** [PERSON] (Coef), **(f)** [PERSON] (PHC Coef), **(g)** Gates (Coef2), and **(h)** Gates (PHC Coef2)) for piles with diameters of 500 mm and 600 mm. Table 5 shows the statistical results using 39 data points for a 600 mm diameter PHC pile. Although the verification used a small dataset of 39 samples, the results showed that the Hiley formula achieved the highest accuracy, consistent with previous findings. The Gates (PHC) and Gates (PHC Coef) formulas demonstrated the highest accuracy among the improved Gates formulas. Specifically, the absolute mean error significantly dropped from 20% to around 10%. In contrast, the method employing optimal intervals and coefficients optimized using 242 data points showed lower accuracy than other improved Gates formulas, leading to negative results regarding its practicality during the verification stage. In contrast, Table 6, which uses data from 21 sets of 500 mm diameter PHC piles, shows results slightly different from previous findings. Compared to the analysis with the 600 mm diameter data, the Gates formula demonstrates much higher accuracy. The reason is that most of the data fall within the range of 3000 kN or less, where the Gates formula