Investigation of Empirical Models for Hydraulic Conductivity from Grain-size Distribution

Abstract

Seven empirical models for calculating hydraulic conductivities in soils based on grain-size
distribution were investigated in this study. The results were compared with hydraulic
conductivity of soils computed using the constant head permeability test. Three samples were
collected from three trial pits in different locations along the bank of the stream located
downstream of National Root Crops Research Institute's earth dam Umudike, Abia state Nigeria.
The samples were subjected to sieve analysis and the constant head permeability tests using
standard methods. Hydraulic conductivities in soils computed from the empirical formulae were
each compared with hydraulic conductivity calculated using the constant head formula. Results
showed that mean hydraulic conductivities for constant head, Hazen, Breyer, Kozeny-Carman,
USBR, Kozeny, Terzaghi and Slitcher models were 18.16 m/d, 35.52 m/d, 34.80 m/d, 30.50 m/d,
25.86 m/d, 19.08 m/d, 15.66 m/d and 10.86 m/d respectively. ANOVA results for pairwise
comparison indicated that Kozeny formula gave the best performance with a p-value of 0.78 at
0.05 critical value. This was followed by Terzaghi, USBR and Slitcher with p-values of 0.44,
0.11 and 0.059 respectively, while the Kozeny-Carman, Hazen and Breyer performed poorly
with p-values of 0.03, 0.008 and 0.007 respectively. Confirmatory test using the Dunnett
simultaneous tests for level mean - control mean, computed adjusted p-value was highest at
1.000 for Kozeny model. In all the tests, Kozeny, Terzaghi, Slitcher and USBR performed well
with p-values 1.000, 0.923, 0.117, and 0.092 above the critical value of 0.05, while the Breyer,
Hazen, and Kozeny-Carman performed poorly with p-values 0.000, 0.000 and 0.004 below the
same critical value. Further research is recommended to address the contradictory results from
various researchers.