Hydro-Mechanical Properties of an Unsaturated Frictional Material

40 CHAPTER 2. STATE OF THE ART
2.5.1 Models for Soil-Water Characteristic Curve
The soil-water characteristic curve is the key function for estimation of unsaturated soil prop-
erties. Based on this relationship several other relations describing unsaturated soil behavior
are derived. Therefore it is important to establish a function, which relates the suction to
the water content. Numerous approaches, namely, empirical and physical models, have been
suggested for mathematical representation of the soil-water characteristic curve. Literature
regarding to this topic is presented in the next section.
Empirical Models
Empirical models (Brooks & Corey 1964, Gardner 1958, van Genuchten 1980, Fredlund &
Xing 1994) use statistical analysis to best fit experimental data to the selected equation.
However, the parameters have no physical meaning. A large number of empirical equations
have been proposed by different researchers to best fit experimental data of the soil-water
characteristic curve. Empirical models can be classified into models that do not consider
hysteretic behavior and into models that do consider hysteretic behavior in the soil-water
characteristic curve.
Equations including 2 parameters or 3 parameters were proposed for instance by Gardner
(1958), Brooks & Corey (1964), Campbell (1974), van Genuchten (1980), Fredlund & Xing
(1994). The parameters in the empirical equations are usually related to the air-entry value
and the rate of desaturation of the investigated soil. Equations proposed by Brooks & Corey
(1964), Farrell & Larson (1972), Williams (1982) are non-sigmoidal functions and equations
proposed by Gardner (1958), van Genuchten (1980), Fredlund & Xing (1994) are sigmoidal
functions. All these empirical equations can be used for the fit of either drainage curves or
imbibition curves. Hysteretic behavior is not taken into account. Detailed reviews and analysis
of empirical equations were summarized by several authors (Leong & Rahardjo 1997b, Singh
1997, Sillers & Fredlund 2001). Leong & Rahardjo (1997a) analyzed the effect of parameters
on the shape of the soil-water characteristic curve for several equations. Only few researchers
as for instance Hanks (1969), Dane & Wierenga (1975), Jaynes (1984), Pham et al. (2003)
presented empirical equations, which consider the hysteresis in soil-water characteristic curve.
Frequently used models are that by Brooks and Corey (1964), van Genuchten (1980) and
Fredlund & Xing (1994). The models are not capable to predict hysteresis or scanning curves
in the suction water content relationship. However, for each drainage or imbibition cycle
different set of parameters has to be provided. The above mentioned equations are explained
in the following and are used in the present investigation for analysis of the experimental
results of the soil-water characteristic curves.
- Brooks and Corey (1964)
One of the earliest equation was proposed by Brooks and Corey (1964). Brooks and
Corey (1964) suggested an power-law relationship for relating volumetric water content