Hydro-Mechanical Properties of an Unsaturated Frictional Material

2.5. CONSTITUTIVE MODELS FOR HYDRAULIC FUNCTIONS 45
smaller the transition zone and the residual suction. The parameter m influences the plateau
of the curve. With increasing m the lower plateau moves up in the residual zone.
- Feng & Fredlund (1999), Pham (2003)
An empirical model that takes hysteresis into account is that proposed by Feng &
Fredlund (1999). The relation utilizes the main drainage curve and two experimental
data on the main imbibition curve to predict the entire relation between water content
w and suction during imbibition (see Fig. 2.20):
w(ψ) = wubd + cψ dd
b + ψ dd
(2.13)
where: w is the water content, wu is the water content on the main drainage curve at
zero soil suction, c presents the water content at high soil suction and bd and dd are
curve-fitting parameters for the drainage curve. Pham et al. (2003) enhanced the above
written model and suggested the following equations to define two suction values along
the main drainage curve by using parameters derived from main imbibition curve fit:
� �1/dd bd
ψ1i ≈ ,
10
��bd(wu �1/dd − w1i)
ψ2i = ψ1i − 2
− b
w1i − c
1/dd
�
(2.14)
where: bd and dd are best-fit parameters from the main drainage curve using Eq. 2.13
and ψ1i, ψ2i and w1i, w2i are the water content and the suction values in the two points.
Knowing ψ1 and ψ2 and the measured water contents w1i and w2i the unknown curve
Water content (%)
40
30
20
10
0
w2i
ψ1i
ψ2i w1i
0.1 1 10 100
Suction (kPa)
Pham et al. (2003)
Figure 2.20: Soil-water characteristic curve including the two points used for estimation of
imbibition curve