Hysteretical models for prediction of the hydraulic conductivity of unsaturated porous media

A theory which permits a quantitative prediction of the actual phenomena of considerable hysteresis characterizing the hydraulic conductivity‐capillary head relationships, and the less significant hydraulic conductivity‐moisture content hysteresis, is proposed. The models used to represent capillary hysteresis are extended to permit the prediction of the hydraulic conductivity of unsaturated porous media for any continuous process of imbibition and drainage. The generalized models require the same amount of experimental data as the previous models with the addition of a measured value of the hydraulic conductivity at a definite point. For an incomplete measured θ(ψ) loop the knowledge of K at the minimum measured value of ψ can be used to improve prediction. The dependent domain model suggested by Mualem and Dagan (1975) is generalized by adding two functions KL(ψ) and KH(ψ) . All K(ψ) scanning curves are expressed with the aid of KL(ψ) and KH (ψ) by convenient compact formulation similar to that used to describe the θ(ψ) curves. The theory is verified by comparison with the detailed experimental data presented by Topp and Miller (1966). Very good agreement between theory and observations is found. The predicted K(ψ) hysteresis has all the experimentally observed features. The predicted K(θ) hysteretical loop almost shrinks to a unique curve, though the ψ(θ) loop, used as data, is of considerable extent.