Theoretical Relationship between Saturated Hydraulic Conductivity and Air Permeability under Dry Conditions: Continuum Percolation Theory

Abstract

The saturated hydraulic conductivity, Ks, is a fundamental characteristic of subsurface flow and the hydrologic cycle. However, direct measurement of Ks is time consuming. Recently, air permeability measurements at 50 and 100 cm of H2O tension, a relatively dry condition in coarse and medium‐textured soils, have been used to estimate Ks. In this short communication, we present a theoretical framework for relating Ks to ka(ϕ), the air permeability as a function of porosity, ϕ, under completely dry conditions. We used power‐law scaling from continuum percolation theory to develop a theoretical relationship between Ks and ka(ϕ). Our result, similar in form to a published logarithmic equation with empirical coefficients, gives a physical interpretation to these empirical coefficients.