Estimation of hydraulic conductivity by the modified Kozeny–Carman equation considering the derivation principle of the original equation

The Kozeny–Carman (K–C) equation based on Poiseuille’s law is an efficient theoretical equation predicting hydraulic conductivity. Some modified K–C equations were proposed focusing on obtaining the uncertainty parameters in the original K–C equation. However, assumptions of some modified K–C equations are inconsistent with Poiseuille’s law. This study proposes a new modified K–C equation considering the derivation principle of the original K–C equation. By applying Poiseuille’s law in porous media, the concept of 2D porosity (ε) and a correction coefficient for permeation (f) are presented. During the derivation process, each section’s void distribution is assumed to be similar, and void pipes in various directions share similar characteristics, because the effective porosity (ne) is approximately equal to ε only when the change in the cross-section in porous media is small. The parameters in the new modified K–C equation include specific surface area (S0), tortuosity (1/cosθ), and ne. The prediction formulas of ne are presented according to the soil mineral and bound water features. The prediction formulas for S0 and 1/cosθ are deduced and verified by comparing them with established formulas proposed by other researchers and experimental data. The new modified K–C equation is adequate for predicting hydraulic conductivity for clay and sand by comparing it with the experimental value and theoretical equations, including the original and other established modified K–C equations.