Closed‐Form Expression for the Multi‐Modal Unsaturated Conductivity Function

Abstract

In this note we derive a closed‐form expression representing the hydraulic conductivity function for soils with a multi‐modal pore size distribution. By combining the multi‐modal representation of the retention function of Durner with the conductivity representation model of Mualem and following van Genuchten, we derive a simple analytical expression for the conductivity of soils with heterogeneous pore systems. Examples for the representation of bi‐modal and tri‐modal retention and corresponding conductivity curves demonstrate the applicability of the simple analytical expressions. It is concluded that the usefulness of the multi‐modal representation of retention functions is increased by providing an analytical expression to directly calculate unsaturated hydraulic conductivities.