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Closure to “Radial Consolidation Analysis Using Delayed Consolidation Approach” by Pankaj Baral, Cholachat Rujikiatkamjorn, Buddhima Indraratna, Serge Leroueil, and Jian-Hua Yin | Journal of Geotechnical and Geoenvironmental Engineering

The writers appreciate the discusser’s interest in this research and his comments and suggestions.

Clarification Regarding Analytical Models and Results

The writers confirm that only radial consolidation was considered in the original paper, while the vertical consolidation was ignored because the ratio between the length of vertical drain and equivalent unit cell diameter is more than 10 for all case studies (Rujikiatkamjorn and Indraratna 2007). The writers agree that the dissipation of excess pore water at the shallow depth would be influenced by vertical drainage, but this effect on overall consolidation is generally insignificant for long drains. Rates of settlement and excess pore pressure dissipation will be slightly faster when vertical drainage is considered at the shallow depth, if the drains are relatively short.

Clarification about Depth of Pore Water Pressure Measurement for Muar Embankment

Many thanks for pointing out the actual depth of pore water pressure measurement for the Muar clay embankment. It is indeed 11.2 m (Indraratna and Redana 2000), and it was mistakenly written in the figure caption as 3 m. The authors apologize for this error.

Clarification about Surface Settlement

Figs. 12(b) and 13 are from two different sites of Second Bangkok International Airport (SBIA), Thailand. The measured settlement of 1.25 m at the end of monitoring period in Fig. 12(b) is from the TS2 location, and in Fig. 13 is from the TS3 location. The subsurface settlement profiles were not available for TS2 and therefore TS3 was used to validate the subsurface settlement.

Clarification Regarding Hypothesis

As discussed by Indraratna (2017), various case studies have shown that excess pore water pressures do not always dissipate as quickly as one expects when vertical drains are installed, even when the load remains constant or removed. The Mandel-Cryer effect, high lateral yielding characteristic of most viscoplastic soils, strain rates, and chemical precipitation and bioclogging (bacterial) in the vicinity of piezometers can contribute to this phenomenon. In this paper an attempt was made to explain this phenomenon using the framework of Hypothesis B through (1) the increase in effective stress due to delayed consolidation caused by the viscosity of clay, and (2) the change in preconsolidation pressure due to strain rate as shown in Fig. 4 of the original paper. These are the key differences between the current model and those of Yin and Graham (1989) and Indraratna and Redana (2000). Although the settlement predictions are similar, the current model can simulate the retarded pore pressure dissipation much better, which has often been a trend observed in the field, yet not captured in many of the past studies adopting ideal drain conditions.

For the Ballina case study, the writers have similar opinions regarding the poor measurement of time-dependent pore pressure. Ballina is a town located on acid sulfate soils, i.e., there is oxidizable pyrite in the shallow ground leaching sulfuric acid catalyzed by certain bacteria strains thriving in the floodplains (high organic content). Indraratna et al. (2017) showed that partial clogging of piezometers with time caused by chemical precipitation (e.g., iron oxides), acidophilic anaerobic bacteria–induced gas bubbles (cavitation), acid corrosion of measuring tips, and growth of bio-slimes would inhibit the rate of pore pressure dissipation. In this regard, the measured results alone may not be sufficient to confirm the validity of the model.

For the SBIA and Muar clay embankment, although the differences in terms of excess pore pressure predictions among the three models are relatively small (less than 4 kPa), the current model still provides a significantly better agreement with the field measurements.

The discusser has provided some interesting case history data. The writers will attempt to analyze that data in a future publication, but it is certainly not within the scope of this closure.


Indraratna, B. 2017. “Recent advances in vertical drains and vacuum preloading for soft ground stabilisation.” In Proc., 19th ICSMGE, 141–166. London: International Society for Soil Mechanics and Geotechnical Engineering.
Indraratna, B., P. Baral, J. Ameratunga, and B. Kendaragama. 2017. “Potential biological and chemical clogging of piezometer filters in acid sulphate soil.” Aust. Geomech. J. 52 (2): 79–85.
Indraratna, B., and I. Redana. 2000. “Numerical modeling of vertical drains with smear and well resistance installed in soft clay.” Can. Geotech. J. 37 (1): 132–145.
Rujikiatkamjorn, C., and B. Indraratna. 2007. “Analytical solutions and design curves for vacuum-assisted consolidation with both vertical and horizontal drainage.” Can. Geotech. J. 44 (2): 188–200.
Yin, J. H., and J. Graham. 1989. “Viscous-elastic-plastic modelling of the time-dependent stress-strain behaviour of clays.” Can. Geotech. J. 26 (2): 199–209.

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