Modified Kozeny-Carman equation for estimating hydraulic conductivity in nanoscale pores of clayey soils with active surfaces

Hydraulic conductivity is a critical parameter for studying the behavior of clay-water systems. However, accurately estimating saturated hydraulic conductivity k in clayey soil by using the Kozeny-Carman (KC) equation is challenging due to the neglect of its active surface properties and nanoscale pores. Clay surfaces can have diverse characteristics resulting from various physicochemical processes such as isomorphous substitution and are typically characterized by the Cation Exchange Capacity (CEC). These properties can significantly impact fluid transport through the clay matrix. To address this issue, this study modifies the KC equation by incorporating an adsorbed water proportion φ that considers the occurrence state of pore water and its correlation with pore diameter, making it applicable to clayey soils. Molecular dynamics (MD) models are established to investigate the influence of surface interaction (CEC) and nanopore size (r) on saturated hydraulic conductivity k of seepage flow in clayey soils. Based on the MD results, a specific function is proposed to quantify the adsorbed proportion φ, which is linearly related to the root of CEC and reciprocal of pore size (r), and then incorporated into a proposed hydraulic correction ratio k* to modify the classical KC equation. The modified KC equation is validated using experimental data from literature, showing a high R² value of 0.96. This result demonstrates that the proposed correction ratio k* can extend the application scope of the classical KC equation to clayey soils.