On the use of the Kozeny–Carman equation to predict the hydraulic conductivity of soils

Abstract

The saturated hydraulic conductivity of a soil can be predicted using empirical relationships, capillary models, statistical models, and hydraulic radius theories. A well-known relationship between permeability and the properties of pores was proposed by Kozeny and later modified by Carman. The resulting equation is largely known as the Kozeny–Carman (KC) equation, although the two authors never published together. In the geotechnical literature, there is a large consensus that the KC equation applies to sands but not to clays. This view, however, is supported only by partial demonstration. This paper evaluates the background and the validity of the KC equation using laboratory permeability tests. Test results were taken from publications that provided all of the information needed to make a prediction: void ratio, and, either the measured specific surface for cohesive soils, or the gradation curve for noncohesive soils. The paper shows how to estimate the specific surface of a noncohesive soil from its gradation curve. The results presented here show that, as a general rule, the KC equation predicts fairly well the saturated hydraulic conductivity of most soils. Many of the observed discrepancies can be related to either practical reasons (e.g., inaccurate specific surface value; steady flow not reached; unsaturated specimens, etc.) or theoretical reasons (some water is motionless; hydraulic conductivity of soils is anisotropic). These issues are discussed in relation to the predictive capabilities of the KC equation.Key words: permeability, prediction, gradation curve, specific surface.