Enhancing Quality Management of PHC Piles through Improved Driving Formulas: A Comprehensive Review and Analysis

Comments:

The paper is a very interesting research work about the reliability of the use of driving formulas to estimate the bearing capacity of piles based on penetration depth data. It is also proposed slight changes in the formulas to improve their reliability based on the comparison of the values of the bearing capacity of 258 600mm diameter pre-stressed high-strength concrete piles obtained with theses formulas and those obtained with dynamic load tests. 

The text is well written and easy to follow. The introduction presents a good review of the literature. The conclusions are consistent with the obtained results, even though I think that the Gates (PHC) formula would be a better choice considering that the additional use of coefficients according to ranges of application in Gates PHC Coef formula is not justified by the difference in the reliability of the two formulas. Although the theme is highly studied, the work presents novelty. The contribution of the work is well established, and it is worth of investigation, but I think that using only 600mm diameter piles is a huge limitation of the study and I highly recommend the authors to include results with different diameters before publishing the paper.

Response:

Thank you for your insightful review.

First, as you pointed out, the Gates (PHC Coef) lacks sufficient justification for its range, so Gates (PHC) might be a safer choice. Therefore, we acknowledged this limitation and revised the paper's conclusion to state: (1) Gates (PHC) is a safe choice, and (2) considering the overall results, Gates (PHC Coef) is a choice worth considering.

Second, addressing the part concerning different pile diameters are discussed in below.

All data were collected from construction sites in South Korea. In South Korea, more than 90% of sites use PHC piles and drop hammers. To review the comments, an additional 21 data sets of 500mm diameter PHC piles were collected, and this was reflected in the final verification. The review results indicated that the effect of pile size was negligible or even showed improved accuracy, suggesting that this formula can be applied without diameter constraints. The impact of pile type is expected to be minimal, but further research is needed regarding the hammer type due to its relation to hammer efficiency.

In the additional study using the 21 data sets of 500mm diameter PHC piles, the accuracy ranking of the formulas differed from that with the existing 600mm diameter PHC piles. As the pile diameter decreased, the bearing capacity tended to be lower. Lower bearing capacity resulted in the Gates formula, which previously had low prediction accuracy, showing higher accuracy than the 600mm diameter PHC piles. The optimized Gates (Coef) showed the highest accuracy for the same reason.

Although this verification was based on a small data set of 21 samples, it led to the conclusion that using Gates (Coef) or Gates (PHC Coef) for PHC piles with a diameter of 500mm or less and Gates (PHC) or Gates (PHC Coef) for PHC piles with a diameter greater than 500mm would be more appropriate.

Thank you very much for the valuable feedback. We were able to conduct additional research, which led to this important conclusion. We appreciate the opportunity to strengthen our study by collecting more data on piles of various diameters in the future.

Response 1:

Thank you for the insightful feedback.

The 258 sets of dynamic load test data and the additional 39 sets of validation data used in this study did not include information about soil type, as obtaining soil type information during data collection was not possible in the actual construction site. Therefore, the effect of soil type on pile bearing capacity was not considered in this study. We acknowledge this limitation and appreciate the observation.

In practical applications of pile penetration and driving formulas, site managers or construction workers tend to focus more on the penetration depth and bearing capacity of the pile rather than the soil type. Managing piles in the field involves many complex factors, making it challenging to consider all soil conditions. Therefore, an indirect assessment through pile behavior is often preferred over considering soil conditions. The main objective of this study was to derive an empirical formula that can be applied to various soil types despite some constraints on the types of piles and hammers. Therefore, a large number of data was utilized to cover the various soil types.

In future research, priority will be given to including soil type data to conduct a more comprehensive analysis. This feedback will be considered to improve the robustness of future studies.

Comments 2: The "Gates(PHC Coef)" method mentioned in the study was determined to be the most accurate method. In what specific cases does this approach show greater accuracy than Hiley's formula? Are there any limitations or boundary conditions?

Response 2:

In this study, the Hiley formula was calculated using highly accurate EMX and rebound values obtained through DMX from the PDA (Pile Driving Analyzer). Consequently, the accuracy of the Hiley formula used in this study remains very high. Generally, PDA applies to only a few piles among the total number of piles for management purposes. Therefore, EMX and DMX values generally cannot be utilized in the actual field. Furthermore, an accurate rebound value, especially in field conditions, is difficult to measure. Thus, the Hiley formula, while accurate, faces practical limitations due to the challenges of obtaining precise input variables. Therefore, in practice, the accuracy of the Hiley formula derived from this study is expected to be much lower than the accuracy calculated in this study.

In contrast, the Gates (PHC Coef) method proposed in this study consists of variables that are relatively easier to obtain. Therefore, it does not have the same constraints as the Hiley formula. This paper mentions that the use of EMX increases the accuracy of the Hiley formula, but this point should have been discussed in more detail. Additionally, the paper does not mention the high accuracy of rebound values obtained through DMX. These points are crucial for deriving the results of the study. Therefore, the paper has been revised to reinforce these points in the main text and the conclusion.

Thank you for the valuable question, which has allowed us to enhance the clarity and completeness of our study.

Comments 3: As mentioned in the study, the use of data and conditions is limited to drop hammer, PHC post and 600 mm diameter. Does this mean that the findings may not apply to other types of piles or different diameters?

Response 3:

All data were collected from construction sites in South Korea. In South Korea, more than 90% of sites use PHC piles and drop hammers. To review the comments, an additional 21 data sets of 500mm diameter PHC piles were collected, and this was reflected in the final verification. The review results indicated that the effect of pile size was negligible or even showed improved accuracy, suggesting that this formula can be applied without diameter constraints. The impact of pile type is expected to be minimal, but further research is needed regarding the hammer type due to its relation to hammer efficiency.

In the additional study using the 21 data sets of 500mm diameter PHC piles, the accuracy ranking of the formulas differed from that with the existing 600mm diameter PHC piles. As the pile diameter decreased, the bearing capacity tended to be lower. Lower bearing capacity resulted in the Gates formula, which previously had low prediction accuracy, showing higher accuracy than the 600mm diameter PHC piles. The optimized Gates (Coef) showed the highest accuracy for the same reason.

Although this verification was based on a small data set of 21 samples, it led to the conclusion that using Gates (Coef) or Gates (PHC Coef) for PHC piles with a diameter of 500mm or less and Gates (PHC Coef) for PHC piles with a diameter greater than 500mm would be more appropriate.

Thank you very much for the valuable feedback. We were able to conduct additional research, which led to this important conclusion. We appreciate the opportunity to strengthen our study by collecting more data on piles of various diameters in the future.

Comments 4: The authors refer to the process of verifying and improving the Hiley, Gates and Danish formulas. In addition to curve fitting and the application of segment-based coefficients, are there any other methods used to improve the accuracy of the Gates formula?

Response 4:

Thank you for the opportunity to enhance the background study of the paper. Here are the existing studies aimed at improving the accuracy of the Gates formula.

The first study is the modified formula proposed by Olson and Flaate in 1967. This study suggested four formulas suitable for various types of piles (timber, concrete, steel, and all types). However, this formula has not been converted to SI units, so it was not included in the main text.

The second study is the method recommended by FHWA in 2001. This method, proposed by Long, aimed to improve the Gates formula by addressing its tendency to underestimate bearing capacity. The approach involves multiplying the original Gates formula by 0.25 and then raising it to the power of 1.35, as shown below:

Subsequent research led to the version recommended by FHWA in 2006, which is the Gates formula used for comparison in this study and is currently the most widely used version. This paper addresses both the original version and the most widely used latest version.

The relevant details were supplemented in Section 3.2 when introducing the Gates formula. Thank you for your comments, which allowed for a more robust background study.