Soil-Water Characteristic Curves for Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 255

5.12.2 Review of SWCC Estimation Procedures
from Grain-Size Distribution Curves
A number of methods have been proposed for the estimation
of SWCCs from grain-size distribution data. There are three
broad categories of estimation techniques based on: (i) sta-
tistical estimates of water contents at various soil suctions
(Gupta and Larson, 1979a), (ii) estimation of soil parameters
for an algebraic function for the SWCC (Rawls and Braken-
siek, 1985; Vereecken et al., 1989; Scheinost et al., 1997),
and (iii) physico-empirical models where a grain-size distri-
bution curve is used in the prediction of the SWCC (Arya
and Paris, 1981; Tyler and Wheatcraft, 1989; M.D. Fredlund
et al., 1997a).
Arya and Paris (1981) used a physico-empirical type
model for the estimation of the SWCC from grain-size
distribution curves. The procedure has become quite widely
used in agricultural disciplines. M.D. Fredlund et al.
(1997a) used the capillary model equation along with the
M.D. Fredlund et al. (1997a) equation for the grain-size
distribution curve to develop a new physico-empirical
equation for calculating the SWCC. Parametric studies were
performed using several SWCC data sets. A combination
of the physico-empirical model and the parametric study
information formed the basis for the M.D. Fredlund et al.
(1997a) estimation technique for the SWCC.

5.12.5 Description of Pedo-Transfer Functions
Two methodologies have been used to estimate the SWCC
from grain-size distribution curves: (i) the functional param-
eter regression methodology and (ii) the physico-empirical
methodology.

5.12.6 Functional Parameter Regression Method
The functional parameter regression method assumes that
parameters of the SWCC equation can be correlated to basic
physical properties. An example is the correlation between
the air-entry parameter of an SWCC equation and soil prop-
erties such as percent sand or porosity. Rawls and Braken-
siek (1985) presented regression equations for estimating the
parameters for the Brooks and Corey (1964) equations. The
regression equations estimated the air-entry pressure a aev
(i.e., bubbling pressure), the pore size index λ be , and the
residual water content w r for the Brooks and Corey (1964)
equation.
The Vereecken et al. (1989) method involved fitting a
data set of 40 Belgian soils with the van Genuchten (1980)
equation. A sensitivity analysis was performed on the opti-
mized parameters of the SWCC to assess the relative impor-
tance and uniqueness of the parameters. A principal factorial
analysis was used to examine the relationship between the
estimated SWCC and the basic measured soil properties.
It was concluded that the SWCC could be estimated to a
reasonable level of accuracy using soil properties such as
grain-size distribution, dry density, and carbon content. The
study focused mainly on the agricultural discipline where
organic soils were involved and the emphasis is on water
availability for plant growth.

5.12.3 Definition of Terms Associated with Estimation
Techniques
A few definitions are useful for describing the conceptual
models for the estimation of the SWCC:
1. A soil property function is a relationship between a phys-
ical soil property and either soil suction, the complete
stress state, or the volume-mass properties of a soil.
2. A pedo-transfer function , PTF (Bouma, 1989), is a
function that has as its arguments basic soil data such as
the grain-size distribution and dry density (or porosity)
and yields a soil property function.
3. An estimated SWCC is either:
i. a monotonic, single-valued function that yields
water content (i.e., volumetric or gravimetric) for
a given scale of soil suction or
ii. a relationship consisting of two functions including
a drying and wetting branch (Tietje, 1993). In other
words, the function has hysteresis and the drying
and wetting branches form limiting conditions.

5.12.7 Description of Modified Kovacs Model
(Aubertin et al., 2003)
The modified Kovacs (MK) model is a functional parameter-
type model developed for the estimation of SWCCs (or
WRCs) by Aubertin et al., (2003). The model has been found
to perform well for tailing materials as well as granular and
cohesive soils.
The MK model assumes that the amount of water held in
a soil is attributable to two primary mechanisms: (i) capil-
lary saturation S c and (ii) adhesive saturation S a . Capillary
saturation is believed to dominate water adsorption in the
low-suction range while adhesive saturation dominates in
the high-saturation range. The two components of saturation
are combined using the following equation:

5.12.4 Representation of Grain-Size Distribution
The presented PTF uses the M.D. Fredlund et al., (1997a)
unimodel (Eq. 2.1) and bimodal (Eq. 2.6) equations to repre-
sent the grain-size distribution (M.D. Fredlund et al., 2000a).
The unimodal and bimodal Fredlund (1997) grain-size dis-
tribution equations can be found in Chapter 2. Most PTFs
use grain-size distribution information in some form as the
basis for the estimation of the SWCC.

− 1 S a ( 1

θ
n =

S = 1 − − S c ) (5.81)

where:

S = any degree of saturation,

θ = any volumetric water content,

n = initial porosity of the soil,

S c = saturation associated with the capillary component,