Response to discussion: Observational techniques by curve fitting for predicting radial consolidation settlement

We appreciate the discusser’s view that the proposed methods differ in form from traditional procedures such as Asaoka’s method or the rectangular hyperbola method. However, we respectfully submit that the essence of our methods remains observational, as they rely entirely on field monitoring data of time settlement relationships rather than on laboratory-only parameters. The use of iterative optimisation algorithms or numerical integration is intended as an implementation tool to achieve a best-fit interpretation of the observational data, especially when data are missing, irregular, or unevenly spaced. In this regard, our approach adheres to the observational principle while extending its applicability to practical cases where field data are often less than ideal.

The discusser correctly notes that a number of classical procedures—including the square-root-of-time fitting method, log₁₀(de²/t) against U_r plots, the one-point method (Sridharan et al., 1996), and the log t fitting method (Prakash et al., 2011)—have been widely studied in the literature. We fully acknowledge the significance of these approaches, many of which are simple, user-friendly, and validated against extensive laboratory data. The scope of our study, however, was not to provide a comprehensive review of all existing techniques but rather to investigate curve-fitting approaches that can be applied consistently when dealing with field monitoring records. As the discusser has also noted, the simpler methods have not yet been validated with full-scale field monitoring data. In contrast, the present paper demonstrates that our proposed methods achieve excellent agreement with both CRS-R test results and embankment monitoring data, yielding R² values greater than 0.99. Thus, while we concur that the additional methods are of merit, the contribution of our study is to provide and validate practical alternatives that remain robust under actual site conditions.

The discusser raised a query regarding the apparent similarity of the reported coefficients of radial consolidation across depths. We would like to clarify that Table 1 contains a few typographical errors. The corrected values are C_r = 0.82 ± 0.07 m²/year (instead of 0.82 + 0.07 m²/year) for the proposed Method 1; 0.76 ± 0.05 m²/year (instead of 0.76 + 0.05 m²/year) for the proposed Method 2; and 0.83 ± 0.11 m²/year (instead of 0.83 + 0.11 m²/year) for the Asaoka method. These values represent the back-analysed results from the nine selected settlement plates, showing the variation of C_r at the final stress level. As explained in the paper, C_r values estimated at stress levels closer to the final vertical stress display smaller variations, which accounts for the observed consistency across depths. This consistency further supports the reliability of the proposed methods in comparison with both laboratory and field benchmarks.

We thank the discusser once again for drawing attention to additional techniques and for raising important questions. His observations have allowed us to clarify the scope and intention of our study. It is our view that the classical simple methods and the proposed curve-fitting procedures should be regarded as complementary, each offering benefits under specific conditions of practice. We hope this exchange contributes to a broader understanding of settlement prediction methods in radial consolidation and to their continuing development in geotechnical engineering.