Permeability assessment of some granular mixtures

This note presents some constant-head permeability test results on 30 granular mixtures. These data are then interpreted using the grading entropy approach, as well as the ‘ Hazen ’ , ‘ Shepherd ’ , ‘ Kozeny – Carman ’ and ‘ Chapuis ’ models. The predictive power of each of the five methods is compared. A correlation between the normalised grading entropy coordinates and the coefficient of permeability is presented. Permeability zones on the normalised entropy diagram are identified.


Contribution by Brendan C. O'Kelly and Maria Nogal
As part of their paper (Feng et al., 2019), the authors presented the novel application of the grading entropy framework for hydraulic conductivity assessments, along with a model (Equation ( 27)), requiring only the normalised grading entropy coordinates A and B as inputs, for reliably predicting the permeability coefficient ( ) values of 30 compacted crushed basalt-gritstone gravel mixtures investigated.The discussers note that the gradation characteristics of these gravel mixtures were such that their B values negatively correlate with A (R 2 = 0.50), meaning that the values could also be reasonably predicted based entirely on their A values, or less reliably based solely on their B values (Equations ( 25) and ( 26), respectively).Further, considering all 30 gravel mixtures investigated, their reported values of void ratio (e) linearly correlate positively and negatively with A (R 2 = 0.64) and B (R 2 = 0.53), respectively.Importantly, the values of coefficients deduced for these various correlations are dependent on compaction level.As such, Equations ( 25)-( 27) would generally underestimate the actual values for the same gravel mixtures placed at lower densification levels (higher e values).In these instances, the inclusion of the e parameter in the model (Equation ( 27)) would seem appropriate, thereby extending its scope and reliability for other field applications (e.g.assessing the loosely placed materials as potential drainage/filter media).Therefore, the following regression model is proposed: where , , and are the fitting coefficients.Note that is expressed in the same units as , whereas the other coefficients are dimensionless.This avoids the mathematical and physical inconsistencies discussed in Castillo et al. (2014aCastillo et al. ( , 2014b)).
Towards demonstrating this point, the discussers performed multiple linear regression analysis for the proposed model (Equation ( 28)) utilising the listed A, B and e values for the various granular mixtures presented in Table 2. Compared to the authors" model (Equation ( 27 The discussers found that Equation ( 27) cannot reliably represent the described sandy soil dataset, with 90% of the Arshad et al. (2019) points falling outside the prediction intervals (alpha = 5%).Further, with fitting coefficient values deduced for the basalt-gritstone gravel mixtures as inputs, the proposed expanded model also cannot reliably represent the sandy soil dataset, with 95% of the Arshad et al. (2019) points falling outside the prediction intervals (alpha = 5%).In other words, it would appear that the deduced fitting coefficient values are specific to the particular test material under investigation.This is not unexpected, but consistent with the fact that the two samples (datasets) do not represent the same statistical population.
The discussers also performed multiple linear regression analysis of the dataset (n = 20) for the silty sand and sand materials to investigate the goodness of fit achieved for both prediction models.Compared to the model without the e parameter included (R 2 = 0.45, = 0.30, and p = 0.006 for = 0), the proposed model (Equation ( 28)) produced values of R 2 = 0.68, = 0.56 and p = 0.0003.That is, consideration of the e parameter significantly improves the fitting, with less than 50% of the variability of the data predicted by the two-variable model, whereas Equation (28) accounts for almost 70% of the variability of the model.Further, the values for these sandy soils were mostly captured by B and e, whereas A adjusts the final value (small value).
Compared to the basalt-gritstone gravel mixtures, the substantially different values of the deduced fitting coefficients and significantly lower values for the sandy soils may be explained by greater variation in their gradation characteristics (with B substantially independent of A), differences in shape factor for the solid particles and their significantly greater specific surface area (S s ), as well as possibly the relatively small sample size of this dataset.As with the evolution of conventional permeability models, the inclusion of a particle shape factor and the S s parameter in the formulation of the discussed models may further enhance their performance.
): R 2 = 0.90, n = 30, p < 0.0001), the analysis for the proposed expanded model with deduced fitting coefficients = 662.75mm/s, = 5.55, = -1.32 and = 4.58 resulted in a slightly better fit (R 2 = 0.96, n = 30, p < 0.0001).In terms of the adjusted R-squared, , which penalises the number of predictors employed in the model, the two-variable model exhibits a value of 0.88, compared to the proposed three-variable model value of 0.95, again indicative of the latter model"s better fit.In order to further test the advantage of the proposed expanded model for other soil types (classifications), the discussers employed the same investigative approach in considering the dataset comprising of A, B, e and values reported for 20 silty sand and sand materials in the paper byArshad et al. (2019).Compared to the gravel mixtures investigated by the authors (D 10 = 0.72-7.02mm, e = 0.51-0.85and = 4.19-561.20 mm/s), these sandy soils had particle shape classes varying from angular to sub-angular, D 10 = 0.01-0.50mm, e = 0.32-0.60 and substantially lower values of ranging 0.0007-3.50mm/s.Further, in terms of linear correlation, the B Downloaded by [ University of Bristol] on [30/07/19].Copyright © ICE Publishing, all rights reserved.Accepted manuscript doi: 10.1680/jgeot.19.d.005 values of these sandy soils only weakly correlated with their A values (R 2 = 0.27), such that when analysed independently, only weakly correlated with A and B. Overall, the same general trends are evident for both Arshad et al. (2019) and Feng et al. (2019) datasets, namely: correlates positively with and negatively with , while and e both correlate positively with A and negatively with B. In terms of the e relationship: for the Arshad et al. (2019) dataset, power fitting produced superior R 2 , whereas for the Feng et al. (2019) dataset, power and exponential fitting were found to produce comparable results (R 2 ≈ 0.86).