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 (EC_a) 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 (θ) and EC_a. Then, the experimental relationships of the effective saturation (S) and EC_a and simulated S–K were combined to establish the relationship between EC_a and unsaturated K. The developed power law relationships described the relative EC (EC_r) and relative K (K_r) very well by just using one parameter, exponent β. When fluid EC was low, the β values for the drainage and wetting processes ranged within 2.09–2.74 and 2.50–3.79 respectively. The variations of β values of homogeneous material were smaller that of heterogeneous material and the effect of hysteresis on the EC_r–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 β value. The β value acted as a lumped factor accounting for pore tortuosity, pore connectivity, shape of pore space, and fluid EC. The power law relationship of EC_r–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 EC_a 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.

非饱和区是一个复杂的多相系统，在该区中对流量和污染物运移进行建模和预测仍然是一个挑战。为了理解非饱和砂岩中流体流动的机理，估算非饱和水力传导率（K）的准确而有效的方法至关重要。在这项研究中，幂定律关系是由阿奇定律和van Genuchten模型的组合得出的，该模型将体（表观）电导率（EC _a）与不饱和K关联起来。首先进行了实验室沙箱实验，以描绘土壤水分特征曲线（SWCC）。使用时域反射仪同时测量体积水含量（θ）和EC _a。然后，将有效饱和度（S）和EC _a与模拟的S - K的实验关系结合起来，以建立EC _a与不饱和K的关系。所建立的幂律关系仅通过使用一个参数β就很好地描述了相对EC（EC _r）和相对K（K _r）。当流体EC低时，排水和润湿过程的β值分别在2.09-2.74和2.50-3.79之间。β的变化均质材料的值小于异质材料的值，并且观察到磁滞对EC _r - K _r关系的影响。当孔隙空间充满高EC溶液时，它很容易模仿S – K _r关系并导致较小的β值。的β充当集总因子占孔隙曲折度，孔隙连通性，孔隙空间的形状，并且流体EC值。在这项研究中开发的EC _r - K _r的幂定律关系可能导致对不饱和K的时空变化的直接估计。，一旦从饱和K的估计值和延时EC _a测量值的组合中就可以获得SWCC_的测量值。准确而有效地估算不饱和钾可以改善对不饱和带流动的预测，并可以全面了解不饱和带过程。