Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

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

  • 244 Accesses

  • 3 Citations


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.

This is a preview of subscription content, log in to check access.


  1. Abramowitz, M. and Stegun, I. A.: 1972:, Handbook of Mathematical Functions, Dover, New York.

  2. Bass, J.: 1968, Cours de mathematiques, Volume 1, Masson, Paris.

  3. Brooks, R. H. and Corey, A. T.: 1966, Properties of porous media affecting fluid flow, J. Irrig. Drain. Div. ASCE 92, 61–88.

  4. Brutsaert, W.: 1966, Probability laws for pore size distribution, Soil Sci. 101, 85–92.

  5. Brutsaert, W.: 1967, Some methods of calculating unsaturated permeability, Trans, ASAE 10, 400–404.

  6. Burdine, N.T.: 1953, Relative permeability calculation from size distribution data, Trans, AIME 198, 71–78.

  7. Childs, E. C. and Collis-Georges, N.: 1950, The permeability of porous material, Proc. R. Soc., London, A. 201, 392–405.

  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.

  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.

  10. Marshall, T. J.: 1958, A relation between permeability and size distribution of pores, J. Soil Sci. 9(1) 1–8.

  11. Millington, R. J. and Quirk, J. P.: 1961, Permeability of porous solids, Trans. Faraday Soc. 57, 1200–1206.

  12. Mualem, Y.: 1976, A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res. 12(3), 513–522.

  13. Mualem, Y.: 1978, Hydraulic conductivity of unsaturated porous media: generalized macroscopic approach, Water Resour. Res., 14(2), 325–334.

  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.

  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.

  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.

  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.

  18. Thony, J. L.: 1971, Etude experimentale des phenomenes d'hysteresis dans les écoulements en milieux poreux non saturés, PhD Thesis, Univ. Grenoble.

  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.

  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.

  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.

  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.

  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.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Tzimopoulos, C.D., Sakellariou-Makrantonaki, M. A new analytical model to predict the hydraulic conductivity of unsaturated soils. Water Resour Manage 10, 397–414 (1996). https://doi.org/10.1007/BF00452953

Download citation

Key words

  • hydraulic
  • conductivity
  • new analytical model
  • prediction