A relation of hydraulic conductivity — void ratio for soils based on Kozeny-Carman equation

• Kozeny-Carman equation was improved by introducing a concept of effective void ratio.
• This paper presents a theoretical explanation for the failed applicability of the Kozeny-Carman equation in clayey soils.
• The proposed equation has the capability to predict hydraulic conductivity for both coarse- and fine-grained soils.

The relationship between hydraulic conductivity and void ratio is briefly reviewed. The classical Kozeny-Carman equation is known for its capacity to describe hydraulic conductivity of sandy soils, but unsuccessful applicability in clayey soils. To solve this problem, the concept of effective void ratio is introduced to derive a new hydraulic conductivity-void ratio relationship based on the Poiseuille's law. The proposed equation is evaluated by using experimental data from existing literature, and proved to have a satisfied capability to predict hydraulic conductivity for a wide range of soils, from the coarse-grained to the fine-grained. This paper presents a theoretical explanation for the failed applicability of the Kozeny-Carman equation in clayey soils: the existence of the voids that contain immobile water have no contribution to flow but have the same contribution to the total void ratio (used in the KC equation to predict hydraulic conductivity) as the voids with mobile water.