Water Resources Management

, Volume 10, Issue 5, pp 397–414 | Cite as

A new analytical model to predict the hydraulic conductivity of unsaturated soils

  • C. D. Tzimopoulos
  • M. Sakellariou-Makrantonaki


A new analytical model is presented for the prediction of hydraulic conductivity. The new model is based on the Brutsaert characteristic curve ψ(θ) and the Mualem integral relation. It is presented by a series expansion of the effective saturation (Θ) power and given in a simple algebraic relation. For checking the new model, twelve soils were selected from the available literature and a comparison was made between the new model, the experimental curve and the van Genuchten model as well. The suggested model is very close to the van Genuchten model in all cases except one and it exhibits hysteresis, due to the different values of the parameter b of Brutsaert equation for the wetting and drainage curves. Also a second model is presented, based on the Burdine integral relation.

Key words

hydraulic conductivity new analytical model prediction 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abramowitz, M. and Stegun, I. A.: 1972:, Handbook of Mathematical Functions, Dover, New York.Google Scholar
  2. Bass, J.: 1968, Cours de mathematiques, Volume 1, Masson, Paris.Google Scholar
  3. Brooks, R. H. and Corey, A. T.: 1966, Properties of porous media affecting fluid flow, J. Irrig. Drain. Div. ASCE 92, 61–88.Google Scholar
  4. Brutsaert, W.: 1966, Probability laws for pore size distribution, Soil Sci. 101, 85–92.Google Scholar
  5. Brutsaert, W.: 1967, Some methods of calculating unsaturated permeability, Trans, ASAE 10, 400–404.Google Scholar
  6. Burdine, N.T.: 1953, Relative permeability calculation from size distribution data, Trans, AIME 198, 71–78.Google Scholar
  7. Childs, E. C. and Collis-Georges, N.: 1950, The permeability of porous material, Proc. R. Soc., London, A. 201, 392–405.Google Scholar
  8. Giakoumakis, S.: 1987, Effets de la temperature sur les characteristiques hydrodynamiques de deux sols non saturés, indeformables, Contribution á l'étude de la propagation du gel, These de Docteur de l'INPG, Grenoble.Google Scholar
  9. Kunze, R. J., Vehara, G. and Graham, K.: 1968, Factors important in the calculation of hydraulic conductivity, Soil Sci. Soc. Am. J. 32, 760–765.Google Scholar
  10. Marshall, T. J.: 1958, A relation between permeability and size distribution of pores, J. Soil Sci. 9(1) 1–8.Google Scholar
  11. Millington, R. J. and Quirk, J. P.: 1961, Permeability of porous solids, Trans. Faraday Soc. 57, 1200–1206.Google Scholar
  12. Mualem, Y.: 1976, A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res. 12(3), 513–522.Google Scholar
  13. Mualem, Y.: 1978, Hydraulic conductivity of unsaturated porous media: generalized macroscopic approach, Water Resour. Res., 14(2), 325–334.Google Scholar
  14. Mualem, Y. and Dagan, G.: 1976, Development of methods, tools and solution for unsaturated flow with application to watershed hydrology and other fields. Research supported by a grant from the U.S.-Israel Binatl. Sci. Found., Res. Proj.Google Scholar
  15. Sakellariou-Makrantonaki, M., Tzimopoulos, C., and Gouliaras, D.: 1987, Analysis of a closed form analytical model to predict the hydraulic conductivity function, J. Hydrol. 92, 289–300.Google Scholar
  16. Sismanis, S.: 1992, Experimental ponding time during infiltration in unsaturated soils and numerical simulation. Application in homogeneous and layered soils, PhD Thesis, University of Thessaloniki, Department of Rural and Surveying Eng., Thessaloniki, Greece.Google Scholar
  17. Stephens, D. B., and Rehfeldt, K. R.: 1985, Evaluation of closed form analytical models to calculate conductivity in a fine sand, Soil Sci. Soc. Am. J. 49(1), 12–19.Google Scholar
  18. Thony, J. L.: 1971, Etude experimentale des phenomenes d'hysteresis dans les écoulements en milieux poreux non saturés, PhD Thesis, Univ. Grenoble.Google Scholar
  19. Topp, G. C.: 1969, Soil hysteresis measured in sandy loam and compared with the hysteretic domain model, Soil Sci. Soc. Am. Proc. 33, 645–651.Google Scholar
  20. Touma, J.: 1984, Etude critique de la caracterisation des sols non saturés: rol de l'air influence de l'écoulement multidimensionnel de l'eau, PhD Thesis Univ. Grenoble.Google Scholar
  21. Tzimopoulos, C., Sakellariou-Makrantonaki, M., Panoras, A., and Hadjigiannakis. S.: 1992, A hydraulic conductivity predictive model, with application in Sindos, near Thessaloniki. 5th Greek Congr. Water Resour., Larissa, Greece, pp. 21–29.Google Scholar
  22. van Genuchten, R.: 1978, Calculating the unsaturated hydraulic conductivity with a new closed-form analytical model, Water Res. Program, Princeton Univ., Princeton, N.J.Google Scholar
  23. van Genuchten, M. Th. and Nielsen, D. R.: 1985, On describing and predicting the hydraulic properties of unsaturated soils, Ann. Geophys. 3(5), 615–628.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • C. D. Tzimopoulos
    • 1
  • M. Sakellariou-Makrantonaki
    • 2
  1. 1.Department of Rural EngineeringAristotle University of ThessalonikiThessalonikiGreece
  2. 2.Department of AgronomyUniversity of ThessaliaVolosGreece

Personalised recommendations