EJSS ejss_12152
B
Dispatch: April 25, 2014 Journal: EJSS CE:
Journal Name Manuscript No. Author Received: No of pages: 10 TS:
European Journal of Soil Science, 2014, 0, 000–000 doi: 10.1111/ejss.12152
A new equation for the soil water retention curve
X. Kuang & J. J. Jiao
Department of Earth Sciences, The University of Hong Kong, Pokfulam Road, Hong Hong, China
Summary
The soil water retention curve is a fundamental characteristic of unsaturated zone low and transport properties.
Recent studies show that an air-entry value is needed in a soil water retention equation in order to provide a
better prediction of relative hydraulic conductivity. A new equation considering the air-entry value is proposed
to describe the soil water retention curve. The performance of the proposed equation is contrasted with a
well-supported equation by comparing the measured and calculated data for 14 soils, representing various
soil textures, which range from sandstone to clay. Results show that the proposed equation provides adequate
characterization of the soil water retention curves. The equation for predicting relative hydraulic conductivity is
derived from the proposed soil water retention equation. An empirical equation for relative hydraulic conductivity
is also used. Our results show that the agreement between the predicted and measured relative hydraulic
conductivities is improved by the combinations of the proposed equation and the relative hydraulic conductivity
equations. The proposed equation is mathematically simple and it can easily be implemented in unsaturated low
and multiphase low numerical models.
Introduction
The water retention curve is the functional relationship between the
volumetric water content and the water pressure head of soils. It is
AQ1
usually used to predict other unsaturated soil hydraulic properties,
such as relative hydraulic conductivity and soil water diffusivity.
Therefore the soil water retention curve has been considered
to be one of the most fundamental hydraulic properties of a
soil (Assouline et al., 1998). It is therefore important to have a
model that can provide an accurate characterization of the soil
water retention curve. Numerous equations have been proposed by
researchers (Brooks & Corey, 1964; Farrell & Larson, 1972; van
Genuchten, 1980; Fredlund & Xing, 1994; Kosugi, 1994; Assouline
et al., 1998). Most of the proposed equations are empirical functions
(Fredlund & Xing, 1994; Leong & Rahardjo, 1997). Comprehensive
reviews of the equations have also been conducted (Leij et al., 1997;
Leong & Rahardjo, 1997; Sillers et al., 2001; Cornelis et al., 2005).
When a soil water retention equation is substituted into a capillary
model (Burdine, 1953; Mualem, 1976), a closed-form expression
for relative hydraulic conductivity may be obtained by integration.
The van Genuchten-Mualem (VGM) model (Mualem, 1976; van
Genuchten, 1980) is the most popular among these expressions.
It has the advantages of being a smooth soil water retention
curve and closed-form equation for relative hydraulic conductivity.
Recent studies show that it tends to under-estimate the relative
hydraulic conductivity, especially for relatively ine-textured soils
Correspondence: J. J. Jiao. E-mail: jjiao@hku.hk
Received 16 September 2013; revised version accepted 29 March 2014
(van Genuchten & Nielsen, 1985; Vogel et al., 2001; Ippisch et al.,
2006; Touma, 2009).
Many studies have been conducted to improve the VGM model.
Van Genuchten & Nielsen (1985) derived the general VGM model.
Vogel & Cislerova (1988) and Vogel et al. (2001) introduced
a minimum capillary height in the van Genuchten (1980) soil
water retention equation. Schaap & Leij (2000) found that the
parameter accounting for pore tortuosity and connectivity in the
relative hydraulic conductivity function of the VGM model is
predominantly negative. Schaap & van Genuchten (2006) intro-
duced a small air-entry value into the soil water retention curve
and used a pressure-dependent piece-wise linear correction to rel-
ative hydraulic conductivity near saturation. Furthermore, some
researchers have suggested using a value smaller than the saturated
hydraulic conductivity as the match point for unsaturated hydraulic
conductivity prediction (van Genuchten & Nielsen, 1985; Luckner
et al., 1989; Schaap & Leij, 2000). The validity of the VGM model
has been examined by Fuentes et al. (1992) and Ippisch et al.
(2006). Because of the limitation of the VGM model, Ippisch et al.
(2006) suggested that an alternative model including an air-entry
value should be used.
There are already equations for describing the soil water retention
curve that include an air-entry value (Brooks & Corey, 1964; Farrell
& Larson, 1972; Clapp & Hornberger, 1978; Kosugi, 1994), which
has been deined, for example, by Brooks & Corey (1964), Fredlund
& Xing (1994), Assouline et al. (1998) and Ippisch et al. (2006).
Among these equations, the Brooks & Corey (1964) equation is
the most popular because it is easy to use and numerous statistical
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© 2014 British Society of Soil Science 1