A review of different approaches to analytical modeling of soil-water retention curves

Soil-water retention curve describes the relationship between soil suction and soil water content. It has a wide range of applications from the predication of unsaturated shear strength to transient two-phase flow and stability analyses. All physically possible sets of retention curves for a soil with specified state parameters are bounded by the two main drying and wetting curves corresponding to the upper and lower bounds, respectively. As a result, the characterization of these two boundary curves as well as the hydraulic hysteresis is of great importance in problems related to both geo-environmental and hydro-geological fields of research. However, direct measurement of the soil-water retention curve requires advanced laboratory equipment and high expertise. In addition, the experimental output has discrete nature and is usually limited to low suction ranges compared with the theoretical full range. In other words, direct incorporation of experimental data to numerical flow and stability analysis becomes impossible; thus, continuous mathematical modeling is inevitable. Consequently, there has always been great interest in the analytical modeling of soil-water retention curves. No thorough study can be found in the literature so far to collect and revisit the pros and cons of various analytical modeling approaches to simulation of this key hydro-mechanical feature. Therefore, the main objective of the current study is to provide a comprehensive review of all available modeling philosophies with emphasis the capabilities and fundamental limitations of each approach. The paper is especially distinctive in classifying all current approaches under seven categories and in providing insights into the general framework of each one. Eventually, a discussion, highlighting the shortcomings and essential modelling needs, is provided to shed light on potential research directions in future.