A New Method for Developing Equations Applied to the Water Retention Curve

Abstract

The soil water retention curve (WRC) represents the relationship between soil suction and water content. Previous equations for representing the WRC do not include a direct relationship between features of the curve and equation fitting parameters. We present a new method for developing equations for representing empirical data that ensures that features of the curve are directly related to fitting parameters in the equation. The method also ensures that the equation has a simple derivative and is readily integrated, an important property if the equation is to be used as part of a numerical model. This method has been applied to the WRC, producing a new equation that is able to accurately represent the entire WRC using a single equation. The direct relationship between the main features of the curve and fitting parameters ensures that the fitting parameters have clear theoretical meaning. Additionally, this direct relationship allows fitting parameters, such as the air-entry value, to be calculated using pedotransfer functions. The equation has been fitted to a wide range of experimental data and has been demonstrated to achieve an excellent fit for sand, silt, and clay soils across the entire suction range from the minimum measured suction value to 10^ kPa.Abbreviations: WRC, water retention curve.

Matric Suction in Recycled Unbound Granular Materials

“…Of the fitting models, the van Genuchten (1980) and Fredlund and Xing (1994) models appeared to provide SWCCs, which best followed the trends of the measured suction data. The Gould et al (2012) model demonstrated a high value of R 2 for all blends when compared with either the van Genuchten (1980) or the Fredlund and Xing (1994) model. The latter models are simple in their application for prediction of the SWCC, requiring little measured data, when compared with the model of Gould et al, which requires special testing techniques to obtain data for the wet end of the SWCC.…”

“…Gravimetric water content is displayed on the primary vertical axis for the Fredlund and Xing (1994) and Gould et al (2012) models. The degree of saturation is shown on the secondary vertical axis for the van Genuchten (1980) model and the predictive model of Houston et al (2006).…”

“…Regression parameters and correlation coefficients (R 2 ) of each model for each blend are presented in Table 4. It should be noted that the minimum suction was set as 1 kPa for all materials when applying the Gould et al (2012) model. It is evident from Table 4 and Figure 2 that the Gould et al (2012) model provided the best matching of the experimental data as it is based on the trend of the suction data; it is not predictive.…”

“…It should be noted that the minimum suction was set as 1 kPa for all materials when applying the Gould et al (2012) model. It is evident from Table 4 and Figure 2 that the Gould et al (2012) model provided the best matching of the experimental data as it is based on the trend of the suction data; it is not predictive. Of the fitting models, the van Genuchten (1980) and Fredlund and Xing (1994) models appeared to provide SWCCs, which best followed the trends of the measured suction data.…”

“…The SWCC data were less clear for the 30% RCO blend as the residual suction was not evident and had to be set equal to the maximum suction (10 6 kPa) to remove the second bending point from the SWCC, as suggested by Gould et al (2012).…”