Using the Effective Void Ratio and Specific Surface Area in the Kozeny–Carman Equation to Predict the Hydraulic Conductivity of Loess

Bo Hong,Xi’An Li,Li Wang,Lincui Li,Quan Xue,Jie Meng

doi:10.3390/w12010024

Abstract

Many modified Kozeny–Carman (KC) equations have been used to predict the saturated permeability coefficient (Ks) of porous media in various fields. It is widely accepted that the KC equation applies to sand but does not apply to clay. Little information is available to clarify this point. The effectiveness of the KC equation will be evaluated via laboratory penetration tests and previously published data, which include void ratio, specific surface area (SSA), liquid limit (LL), and permeability coefficient values. This paper demonstrates how to estimate the SSA of cohesive soil from its LL. Several estimation algorithms for determining the effective void ratio (ee) of cohesive soil are reviewed. The obtained results show that, compared to the KC equation based on porosity and geometric mean particle size (Dg), the KC equation based on the SSA and the ee estimation algorithm can best predict the Ks of remolded loess. Finally, issues associated with the predictive power of the KC equation are discussed. Differences between measured and the predicted Ks values may be caused by the uniformity of the reconstructed specimen or insufficient control of the test process and errors in the SSA and ee.

Highlights

The saturation permeability coefficient (Ks ) is an important parameter in hydrogeology and environmental geological fluid flow calculations, and has important implications for a wide range of fields such as hydrogeology and engineering geology [1,2]
Carman [11] implicitly considered the role of effective pores in the derivation process, but embodied effective pores in the definition of the hydraulic radius and did not define effective pores
Effective porosity can be obtained by using other measurement parameters, e.g., by defining effective porosity as the feed water, total porosity minus the water holding capacity or residual water content

Summary

Introduction

The saturation permeability coefficient (Ks ) is an important parameter in hydrogeology and environmental geological fluid flow calculations, and has important implications for a wide range of fields such as hydrogeology and engineering geology [1,2]. Scientists in the engineering and Earth sciences fields have been looking for alternative methods to estimate the hydraulic conductivity from the physical properties of porous material matrices and fluid for a long time [7,8,9]. Many equations have been proposed to predict the Ks of porous materials Examples of these proposals are empirical/semiempirical relations, capillary models, statistical models and the hydraulic radius theory. The most widely used prediction relation of Ks is based on the hydraulic radius theory. Effective porosity can be obtained by using other measurement parameters, e.g., by defining effective porosity as the feed water, total porosity minus the water holding capacity or residual water content. Bear [13] defines effective porosity as the water supply or total porosity minus field capacity. Ahuja et al [3] makes a similar definition

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Discussion

Conclusion