Hydro-Mechanical Properties of an Unsaturated Frictional Material

52 CHAPTER 2. STATE OF THE ART
Degree of saturation Sr0 for (ua − uw) ≈ 0: During the imbibition process of a soil some
air bubbles can be occluded in the pore water. If the ratio of the net volume of pore
water to the total volume of pore water (including the volume of the closed air bubbles)
during the imbibition process is assumed to be constant, then the ratio is just the degree
of saturation Sr0 for (ua − uw) ≈ 0. The parameter Sr0 influences mainly the saturated
zone and thus influences the air-entry value ψaev.
Various hysteresis models for calibrating the soil-water characteristic curve were compared to
each other by several authors Jaynes (1984), Viaene et al. (1994), Pham et al. (2005). Jaynes
(1984) compared the so called point method (Dane & Wierenga 1975), the slope method that
is a modified point method, the linear method (Hanks 1969) and the domain model (Mualem
1974). While the last two models predicted the best shape, the linear method was sug-
gested to use for numerical simulation of hysteretic flow because of its simplicity. A statis-
tical analysis of 6 hysteresis soil-water characteristic curves was carried out by Viaene et al.
(1994). The authors considered empirical models (Hanks 1969, Scott et al. 1983) as well as
independent (Mualem 1974, Parlange 1976) and dependent (Mualem 1984a) domain models.
Best agreement between observed and measured data was found when using both models of
Mualem, which are not trivial to use. When applying the empirical model by Scott et al.
(1983) good agreement was found. They confirmed that neglecting the hysteresis behav-
ior when describing drainage and imbibition path results in significant errors. In a recent
study Pham et al. (2005) compared 2 empirical models with 6 domain models on 34 soils
different of type. For the prediction of drainage and imbibition curves the empirical model
by Feng & Fredlund (1999) was suggested. For predicting scanning curves the domain model
by Mualem (1974) seemed to be the most accurate.
Discussion on soil-water characteristic curve as expressed by linearized functions and es-
sentially non-linear functions have been presented by Stoimenova et al. (2003a,b, 2005). The
methodology to assess the quality of the curve fitting through statistical analysis is also ad-
dressed. Agus et al. (2003) assessed three statistical models (Childs and Collis-George model
(1950), Burdine model (1950), Mualem model (1976)) with different soil-water characteristic
curves (Gardner 1958, van Genuchten 1980, Fredlund & Xing 1994).
2.5.2 Models for Unsaturated Hydraulic Conductivity
Unsaturated hydraulic conductivity functions can be calculated using either an indirect
method or a direct method. A variety of indirect methods can be used to determine the
unsaturated hydraulic conductivity function, namely, empirical models, macroscopic models
and statistical models (Leong & Rahardjo 1997a).