Soil-Water Characteristic Curves for Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 270

SWCC, along with the saturated soil properties (Fredlund
and Rahardjo, 1993a; Vanapalli et al., 1996a; Barbour,
1998; D.G. Fredlund, 2000a; Fredlund et al., 2003). The
SWCC is relatively easy to measure and has become the
key unsaturated soil information for obtaining unsaturated
soil property functions. Various empirical procedures have
been proposed and tested for the estimation of essentially
all unsaturated soil property functions (e.g., permeability,
shear strength, volume change, and others). In each case,
the estimation procedure involves the use of the saturated
soil properties in conjunction with the SWCC.
Numerous estimation procedures have been proposed for
the water permeability function (Fredlund et al., 1994b).
The procedures differ primarily in the basic assumptions
involved in the development of the proposed model and
the mathematical manner (e.g., method of integration), by
which the SWCC is used in conjunction with the saturated
soil properties. As an example, several permeability func-
tions have been proposed, each one using the SWCC in a
somewhat different manner.
Constitutive relations for unsaturated soils can be written
using the SWCC equation. The SWCC is also dependent
upon the total stress state; however, in most cases the con-
stitutive equations for an unsaturated soil are sufficiently
accurate when written simply as a function of soil suction.
The development of unsaturated soil property functions has
made it possible to perform numerical modeling studies in
application areas such as seepage, shear strength, and volume
change (M.D. Fredlund, 2000). Even though the unsaturated
soil property functions are not measured, it is still possible to
estimate reasonable soil properties and then observe antici-
pated soil-structure interactions. The numerical modeler can
ask a series of plausible, “What if ... .?” questions and thereby
observe a range of possible responses. An understanding of the
statistical variability associated with the SWCC likewise pro-
vides an indication of the variability that might be anticipated
in the unsaturated soil property functions.

1999). Therefore, the angle of internal friction with respect
to soil suction tends to zero at residual soil suction.
The shrinkage curve for a soil indicates that the change in
void ratio tends toward zero at high soil suctions. It would
appear that the residual soil suction of a soil is closely related
to the shrinkage limit of a soil. The volume change function
(i.e., change in void ratio or specific volume) is equal to the
compressibility of the saturated soil up to the air-entry value.
The compressibility of the soil then decreases throughout
the transition zone becoming zero as residual soil suction
conditions are exceeded.

5.15.2 Important Role of SWCC
The unsaturated soil property functions can be related to the
SWCC because variations in the unsaturated soil properties
are primarily a function of the amount of water in the soil.
For some unsaturated soil properties it would appear that the
unsaturated soil property functions are primarily related to the
amount of water on an unbiased plane passing through the soil.
The coefficient of permeability of an unsaturated soil is a func-
tion of the volume of water in the soil while the shear strength
and volume change behavior is primarily a function of the area
of water on an unbiased cross section. The area of water on an
unbiased plane should be the same as the volume of water in a
representative elemental volume (Fung, 1965). Figure 5.123
illustrates the comparison between the volumetric and area
representations of the amount of water in a soil.

5.15.3 Application of Hysteretic SWCC in
Geotechnical Engineering
Geotechnical engineers have attempted to use the SWCC to
obtain an estimate of the in situ soil suction. In taking this

5.15.1 Unsaturated Soil Properties When Soil Suction
Exceeds Residual Suction
There is limited information on the form of the classic con-
stitutive relations for an unsaturated soil as residual suction
is exceeded. There is little experimental evidence related to
the coefficient of permeability of a soil as residual suction is
exceeded. However, the coefficient of permeability is known
to become extremely low and hydraulic flow would appear
to essentially cease near residual conditions, giving way to
vapor flow. In other words, there appears to be a change from
liquid flow to vapor flow as residual suction is exceeded.
The effective angle of internal friction can be applied
to a soil up to the air-entry value. The friction angle then
decreases until it becomes essentially zero at soil suctions
exceeding residual soil suction. Recent research on a number
of soil types would indicate that the angle of friction tends
toward zero at high soil suctions (Nishimura and Fredlund,

Figure 5.123 Continuum mechanics equivalence of area and vol-
ume representations of water in a soil.