Simplified power law relationship in the estimation of hydraulic conductivity of unsaturated sands using electrical conductivity

Abstract

The unsaturated zone is a complex multiphase system, and modelling and prediction of flow and contaminant transport in this zone remain a challenge. In order to understand the mechanisms of fluid flow in unsaturated sands, an accurate and efficient approach to estimate unsaturated hydraulic conductivity (K) is essential. In this study, a power law relationship was derived from a combination of Archie's law and van Genuchten's model to relate bulk (apparent) electrical conductivity (ECa) with unsaturated K. The laboratory sandbox experiments were conducted first to delineate the soil water characteristic curves (SWCCs). Time domain reflectometry was used to simultaneously measure volumetric water content (theta) and ECa. Then, the experimental relationships of the effective saturation (S) and ECa and simulated S-K were combined to establish the relationship between ECa and unsaturated K. The developed power law relationships described the relative EC (ECr) and relative K (K-r) very well by just using one parameter, exponent beta. When fluid EC was low, the beta values for the drainage and wetting processes ranged within 2.09-2.74 and 2.50-3.79 respectively. The variations of beta values of homogeneous material were smaller that of heterogeneous material and the effect of hysteresis on the ECr-K-r relationship was observed. When pore space was filled with the high-EC solution, it easily mimicked the S-K-r relationship and resulted in a smaller beta value. The beta value acted as a lumped factor accounting for pore tortuosity, pore connectivity, shape of pore space, and fluid EC. The power law relationship of ECr-K-r developed in this study could lead to a direct estimation of the spatial and temporal variations of unsaturated K, once the measurements of SWCC are available from estimation of saturated K and combination of time-lapse ECa measurements. Accurate and efficient estimation of unsaturated K could improve the prediction of flow in the unsaturated zone and allow a comprehensive understanding of unsaturated zone processes.