Hydro-Mechanical Properties of an Unsaturated Frictional Material

186 CHAPTER 9. NUMERICAL SIMULATION OF COLUMN TEST BY FEM
9.2 Model used for Numerical Investigation
Based on the suction-water content model developed by Parker & Lenhard (1987) numerical
investigation are carried out. The model is an empirical scaling hysteresis approach that can
produce a realistic representation of scanning curves and hysteresis loops. For prediction of
main drainage and main imbibition curve Parker & Lenhard (1987) used the suction-water
content model by van Genuchten (1980). Their concept introduces an apparent saturation in
order to account for the effect of residual trapped non-wetting phase saturation. Thus they
distinguish between the effective and the apparent wetting phase saturation. The effective
saturation ¯ Sw is considered as the mobile part of the phase. The apparent saturation ¯ Sw is
the sum of the effective saturation ¯ Sw and the trapped effective saturation ¯ Snt of the non-
wetting phase (see Fig. 9.1). If there is non-wetting phase entrapment ( ¯ S nr(i)), the soil-water
characteristic curve for drainage and imbibition do not form closed loops. The formation of
closed loops is possible by substitution of the effective by the apparent saturation (Fig. 9.1),
that also accounts for fluid entrapment. Consequently, hysteresis is formed by scaling the
apparent saturation. For example, saturation at point ζ that lies on an imbibition scanning
curve (see Fig. 9.1, right) can be scaled as follows:
¯Sw(ζ) =
¯S7 − ¯ S6
¯S5 − ¯ · (
S6
¯ S4 − ¯ S3) + ¯ S3. (9.1)
For simulation of flow in unsaturated porous media and considering hysteresis effect in
these simulations the model by Parker & Lenhard (1987) was implemented into MUFTE-
UG by Sheta (1999) and Papafotiou (2008).
Capillary Pressure
i
S w(i)
j
S nt(ij)
S w(j)
S w(j)
S nr
S nr(i)
Effective Saturation Apparent Saturation 1
Figure 9.1: Hysteresis and phase entrapment properties of the soil-water characteristic curve
Capillary Pressure
5
7
2
6
4
ζ ξ
3