Analytical Models of the SWCC

There is a number of parametric models that have been suggested in the literature for describing the matric potential’s dependency on water content (matric poten­tial being defined in Eq. 2.26). The models are all empirical and two frequently used are the power law model suggested by Brooks and Corey (1964) and the model suggested by van Genuchten (1980). For further details, see Fredlund and Rahardjo (1993), Fredlund and Xing (1994) and Apul et al. (2002).

The Brooks and Corey (1964) model is given as:

A

where the normalized water content, 0, is defined as:

The parameters вг and Srr are the irreducible (residual) volumetric water content and irreducible (residual) saturation respectively. The parameter Фь is the air entry value and the parameter A is called the pore size distribution index. The air entry value of the soil, Фь, is the matric suction at which air starts entering the largest pores in the soil (Fredlund et al., 1994). The parameter A characterizes the range of pores sizes within the soil, with larger values corresponding to a narrow size range and small values corresponding to a wide distribution of pore sizes.

The van Genuchten (1980) model relates the water content to the suction charac­teristics and is given as:

where a, N and M are experimentally determined parameters. Based on Mualem’s (1976) relative permeability model the parameters N and M are related as follows:

According to Fredlund and Xing (1994) this constraint between the parameters M and N reduces the flexibility of the van Genuchten model. They further claim that more accurate results can be achieved leaving the two parameters without any fixed relationship. Their model is a somewhat more general than the others and is based on the pore size distribution of the medium. It is given as:

M

where a, N and M are now different parameters to those of the van Genuchten model and also need to be estimated experimentally, but where n is the porosity and Ф is the matric potential in metres, as before (see Eq. 2.32). Figure 2.10 shows two typical soil water characteristic curves (SWCC) according to the van Genuchten model for coarse grained (unbroken line) and fine grained soils (dotted line) respec­tively. The parameters used for the two curves are given in Table 2.2.

Vol. water cont. Vol. water cont.

Fig. 2.10 Typical SWCC for a coarse (unbroken line) and fine grained (dotted line) soil using the van Genuchten’s model. The parameter used to plot the curves are given in Table 2.2