Hydro-Mechanical Properties of an Unsaturated Frictional Material

46 CHAPTER 2. STATE OF THE ART
fitting parameters bi and di for imbibition curve can be calculated using:
� �
(w1i − c)(wu − w2i)
log
(wu − w1i)(w2i − c)
di =
, bi =
log(ψ2i/ψ1i)
(w1i − c)ψ di
1i
wu − w1i
(2.15)
The parameters bd and dd in Eq. 2.13 are replaced by the determined parameters bi
and di used for estimation of the main imbibition curve. Exemplary main drainage and
imbibition curve are given in Fig 2.20 for Hostun sand, where the additional two points
for deriving the main imbibition curve from the main drainage curve are included.
Physical Models
Domain models are based on physical properties of the soil. Domain models are divided into
independent domain models and dependent domain models. Based on Néel´s diagram (Néel
1942, 1943) or Mualem´s diagram (Mualem 1974), where the distribution of water in a soil
is defined during drainage and imbibition processes, the hysteresis was described by Everett
& Smith (1954), Everett (1955), Poulovassilis (1962), Philip (1964), Mualem (1974, 1984a),
Hogarth et al. (1988) (independent domain models) and Mualem & Dagan (1975), Mualem
(1984b), Topp (1971b), Poulovassilis & El-Gharmy (1978) (dependent domain models). De-
pendent models were derived from independent models and additionally consider the effect
of pore water blockage against the air-entry value and the water-entry value in a soil during
drainage and imbibition. Poulovassilis (1962) performed drainage-imbibition tests on glass
bead porous medium and was one of the first who applied the domain theory to hysteresis.
He obtained good agreement between predicted values and observed values. Further models
were suggested by Everett (1967), Topp (1971b). For these models a set of measured suction-
water content data at the scanning curves is required. To reduce the amount of required
experimental data Philip (1964), Mualem (1974) proposed similarity hypothesis. Based on
similarity hypothesis Mualem proposed several models (Mualem 1977, 1984b). These models
require boundary drainage curve for prediction.
The measurement of suction water content relationship in the field and also in the labo-
ratory is a time consuming procedure. Sometimes it is useful to estimate the suction water
content before. Physical models are capable to estimate the relation between saturation and
suction based on typical soil parameters as grain-size distribution or porosity. Physical models
based on soil parameters (e.g. grain-size distribution, void ratio) and/or pore geometry were
suggested amongst others by Arya & Paris (1981), Haverkamp & Parlange (1986), Fredlund
et al. (1997), Zapata et al. (2000), Aubertin et al. (2003), Zou (2003, 2004). These models
utilize soil properties as well as geometric properties to estimate the suction water content
relationship. Rojas & Rojas (2005) suggested a probabilistic model that is based on the phys-
ical description of a porous system. Therefore two different elements, the sites (cavities) and
bonds (throats) are considered each with a proper size distribution. Whereas most models