Hydraulic conductivity of unsaturated porous media: Generalized macroscopic approach

The macroscopic approach which yields the power function relationship between the relative permeability and the effective saturation, Kr = Sen, is generalized to allow n to vary with the soil type. Theoretical analysis shows that n may receive values lower than 3.0 for granular porous media and higher than 3.0 for soils of fine texture. These findings are verified by using experimental data of 50 soils. The lower limit of n is found to be 2.5, while high values (up to n= 24.5) are found for the fine-textured soils. Statistical analysis of the measured data of the 50 soil samples shows a significant correlation between n and w which indicates the amount of work per unit volume of soil required to drain a saturated soil to the wilting point. By using the soil characteristics ψ − Θ an empirical formula is derived which relates n to w by n = 0.015w + 3.0. This proposed model is compared with the two previous versions of Averjanov (1950) and Irmay (1954) on the basis of the experimental data of the 50 soils. A very good agreement is found between the measured Kr − Θ curves and the theoretical ones, derived by the new model, for granular soils as well as for soils of fine texture where the other models very often fail. The accuracy of the new model is competitive with the best of the statistical models analyzed by Mualem (1976a). By this study the power function model gains a high degree of accuracy, which, compounded by its simplicity, produces an efficient tool for prediction of the hydraulic conductivity of unsaturated soils.

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