Soil-Water Characteristic Curves for Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 257

desorption SWCC and that this curve represents conditions
indicative of an initially slurry soil.

10000

1

11

1000

5.12.10 M.D. Fredlund (2000) Model to Predict SWCC
The M.D. Fredlund (2000a) unimodal and bimodal equations
(see Chapter 2) can be used to best fit grain-size distribu-
tion data. The M.D. Fredlund (2000) grain-size equations
provide a continuous fit of the entire grain-size distribution
curve, including the coarse and fine extremes (M.D. Fred-
lund et al., 2000a). The mathematical fit of the grain-size dis-
tribution data provides the basis for developing an algorithm
to predict the SWCC. The predictive model makes use of a
combination of the capillary model and an understanding of
changes in SWCCs associated with particle sizes. Volume-
mass properties and grain-size distribution data form the
basic information required for the estimation of the SWCC.
The methodology behind the M.D. Fredlund (2000)
method can be expressed in terms of a series of theorems:

100:1

100

10

1

0.1

0.01

0.01 0.1 1 10 100 1,000 10,000

a f , kPa

Figure 5.100 Relationship between AEV obtained using Fred-
lund (1997b) construction and parameter a f from Fredlund and
Xing (1994) equation for 311 soils.

Theorem 1—A soil composed entirely of uniform, homo-
geneous particle sizes has a unique drying (or desorp-
tion) SWCC.
Theorem 2—The capillary model can satisfactorily esti-
mate the air-entry value of each collection of uniform,
homogeneous particle sizes.
Theorem 3—The SWCC for soils composed of more than
one particle size can be represented as the summation
of the SWCCs for each of the individual particle sizes.

where:

T s = surface tension of water,

α 1 = contact angle,

ρ w = density of water,

g = acceleration due to gravity,

r = pore radius, and

ψ = soil suction.

An approximate shape for the SWCC can be computed
for each particle size. Estimating the shape for coarse sand
or fine silt can be accomplished with reasonable certainty.
Measured SWCCs for glass beads of various sizes were used
as a reference (Nimmo, 1997). The SWCC for a fine-grained
material was estimated from the results of soils with increas-
ing clay content. The glass beads and the clay soil provide
limiting values for groups of soils consisting of uniformly
sized particles (Fig. 5.102).
Typical SWCCs for uniform particle-size materials rang-
ing from coarse sand to clay-sized particles were computed
by incrementally altering the parameters of the Fredlund and
Xing (1994) equation. The n f and m f soil parameters for
the Fredlund and Xing (1994) equation are also required for
each uniform collection of particle sizes. A data set involv-
ing soils from Rawls et al., (1992), Sillers (1997), and the
Cecil soil survey (Bruce et al., 1983) was used to determine
approximate trends in the n f and m f parameters.
The grain-size distribution curve was divided into small
uniform soil divisions. A packing porosity n p was estimated,
starting with the smallest particle divisions (Harr, 1977) and
computing an SWCCs, as illustrated in Fig. 5.103. The divi-
sional SWCCs were then summed starting from the smallest
particle sizes and continuing until the volume of the pore
space was equal to that of the combination of all particle
sizes. The end result is an estimation of a predicted SWCC
representative of the desorption curve for a slurry soil.

The above theorems form the basic information for the
method based on the capillary model and the packing of
each uniform particle-size range. The Fredlund and Xing
(1994) equation was used to model SWCCs typical of each
range of soil particle sizes. The a f fitting parameter (i.e.,
a f is the inflection point on the SWCC) in the Fredlund
and Xing (1994) equation can be loosely related to the air-
entry value of the soil. Figure 5.100 shows the relationship
between the air-entry value of many soils and the a f fitting
parameter. A data set was used to “train” the proposed pedo-
transfer function. The a f parameter is typically higher than
the actual (or construction-based) air-entry value. The a f
parameter is the primary variable that represents the lateral
position of the SWCC.
The variation of the Fredlund and Xing (1994) equation
is shown in Fig. 5.101 for a range of n f and m f parameters
when the a f parameter is held constant at 100 kPa. The
representative SWCC can be shifted laterally for other
values of a f . An equivalent air-entry value (i.e., soil
suction) can be calculated based on the capillary model
when the pore radius between the soil particles is known.
The soil suction corresponding to the equivalent air-entry
value for a soil with uniform particle sizes can be written
as follows:

cos α 1
ρ w gr

ψ = 2 T s (5.92)