# A Simple Model for Estimating the Hydraulic Conductivity of Unsaturated Soil
## 1 Introduction  
Geotechnical problems and geological hazards at the earth's surface are often closely related to water transport through soils, such as rainfall-induced settlements and landslides [1; 2; 3; 4]. The majority of the natural soils are generally unsaturated [5]. Hence, a reasonable description of the hydraulic conductivity of unsaturated soils is critical to accurately predicting the water movement [6; 7].  
A direct measurement of the unsaturated hydraulic conductivity is the most accurate method. The commonly used methods include horizontal infiltration, outflow, evaporation and instantaneous profile [8]. However, these methods are time-consuming and costly, especially for a low water content [9]. Therefore, numerous studies have proposed models for estimating the unsaturated hydraulic conductivity. The majority of these models (including empirical, macroscopic and statistical models) have been established by bridging the soil-water characteristic curve (SWCC) with the hydraulic conductivity curve [10]. The statistical models are the most widely used ones, being based on the capillary flow and free-associative pores [9; 11; 12]. [PERSON] and [PERSON] [13] proposed the Childs and Collis-George model in terms of the Kelvin capillary model and the Hagen-Poiseuille equation. Since then, various statistical models have been proposed [6; 14; 15; 16; 17; 18; 19; 20]. However, the construction of these models was based on the capillary flow in the low suction range. Thus, they cannot describe the situation where the adsorptive water film flow dominates for the high suction range [21; 22].  
To improve the estimation of the hydraulic conductivity, which is dominated by an adsorptive water film flow in the high suction range, [PERSON] [23; 24] derived a hydraulic conductivity model based on the planar thin film dynamics. Since this model has explicit physical meaning, many studies have combined it with statistical models to predict the hydraulic conductivity over a wide suction range [25; 26; 27; 28; 29; 30; 31]. [PERSON] and [PERSON] [25] adoptedthe Mualem model to account for the capillary flow, and constructed a new equation for calculating the adsorptive water flow which included the effects of ionic-electrostatic forces and molecular forces. [PERSON] et al. [26; 27; 28] used the hydraulic conductivity at the critical suction point as a reference in simplifying the model of water film flow, and they also used the Mualem model to calculate the capillary flow. [PERSON] et al. [31] proposed a more precise model accounting for the adsorptive water film based on micromechanics, and they used the Mualem model to predict the capillary flow as well. These models have a good ability to estimate the hydraulic conductivity over a wide suction range. However, the forms of these models are relatively complex. Additionally, these models used the Mualem model with scaling parameters, which need to be determined by the measured unsaturated hydraulic conductivity curve. These obstacles limit the application of these models in practice.  
This study aims to propose a simple and convenient hydraulic conductivity model for unsaturated soil. Firstly, the soil-water interaction mechanisms are explained, and accordingly, the soil-water characteristic curve and hydraulic conductivity curve are divided into three parts. Secondly, [PERSON] and [PERSON]'s equation is used to describe the soil-water characteristic curve. Thirdly, a simple piecewise function is proposed for estimating the hydraulic conductivity of unsaturated soil. Fourthly, a calibration approach for the model parameters is introduced. Finally, the performance of the proposed model is validated with experimental data from different soils.