## 7 Discussion and Conclusions  
Due to time savings and efficiency in construction, piles often rely on penetration amounts for the remaining piles after performing dynamic load tests (DLT). For these remaining piles, using pile driving formulas that consider penetration amount and driving energy, rather than solely relying on penetration amounts for construction quality control, enhances reliability. However, other pile driving formulas face reliability issues, except for the Hiley formula. Furthermore, a formula optimized for PHC piles, widely used in Asia, is required. Therefore, this study reviewed the applicability of representative existing pile driving formulas using 258 dynamic load test data points and further improved these formulas to increase their applicability to pile construction management. Finally, using an additional 60 dynamic load test data points, the findings of this study were verified, and a sensitivity analysis of pile diameter was conducted. The contents of the study are summarized as follows:  
1. The review of pile driving formulas included the Hiley, Gates, Danish, and original Gates formulas. The Hiley formula showed the highest accuracy with an average absolute error of about 12% compared to the dynamic load test. The high accuracy of the Hiley formula in this study resulted from using EMX and well-estimated rebound values obtained through the PDA. The Danish and Gates formulas showed similar trends to the dynamic load test but had an average absolute error of around 16%, indicating lower accuracy than the Hiley formula. The original Gates formula exhibited accuracy that was too low to be practical. 2. Although the Hiley formula demonstrated high accuracy, the rebound value, used as a variable in the formula, must be measured accurately, which is challenging. As an alternative, an improved formula based on the Gates formula was proposed, with easier variable acquisition. Specifically, the Gates formula showed results similar to the dynamic load test results for values below approximately 3000 kN. However, for values above 3000 kN, the calculated bearing capacity generally appeared lower, necessitating improvement. To make these improvements, 242 dynamic load test data points, excluding outliers, were used, and the optimal constants satisfying the data were derived through curve fitting. The enhanced Gates formula (Gates (PHC)) with new constants demonstrated significantly improved accuracy compared to the original Gates formula. 3. The Gates and Gates (PHC) formulas tend to underestimate bearing capacity as it increases due to the non-linear characteristics of the model. Therefore, different coefficients were applied for each segment of bearing capacity calculated from the Gates formula to overcome this shortcoming. Two approaches were used for applying coefficients: one approach (1) involved dividing the segments by 1000 kN and applying coefficients to each segment, and (2) the other involved determining the optimal segments and applicable coefficients through iteration. Both methods improved accuracy compared to the original Gates formula, but the iteration method created data gaps, making it insufficient for use. The study results showed that the Gates (PHC Coef) formula has high accuracy, but the definition of the interval range for this formula is not justified. Therefore, the Gates (PHC) formula is a safe choice, and considering the overall results, Gates (PHC Coef) is also worth considering. 4. To verify the results and conduct a sensitivity test on pile size, 60 additional data sets were used. The additional data consist of 39 data sets for 600 mm diameter piles and 21 data sets for 500 mm diameter piles. The verification results showed that, regardless of the presence of the 500 mm diameter data, both the Gates (PHC) and Gates (PHC Coef) formulas demonstrated higher accuracy compared to the initial study results, confirming the validity of the improved formulas. 5.