An Insight into the Projection Characteristics of the Soil-Water Retention Surface

The soil-water retention surface (SWRS), which describes the variation of the degree of saturation (S-r) with suction (s) and void ratio (e), is of crucial importance for understanding and modeling the hydro-mechanical behavior of unsaturated soils. As a 3D surface in the S-r -e-s space, the SWRS can be projected onto the constant S-r, constant s, and constant e planes to form three different 2D projections, which is essential for establishing the SWRS and understanding its various characteristics. This paper presents a series of investigations on the various characteristics of the three SWRS projections. For the S-r -s and S-r -e relationships, (i) a tangential approximation approach is proposed to quantitatively capture their asymptotes, and (ii) a new criterion is presented to distinguish the low and high suction ranges within which these two relationships exhibit different features. On the other hand, a modified expression is introduced to better capture the characteristics of the s-e relationships. The various projection characteristics and the proposed approaches are validated using a wide set of experimental data from the literature. Studies presented in this paper are useful for the rational interpretation of the SWRS and the hydro-mechanical coupling behavior of unsaturated soils.