Soil-Water Characteristic Curves for Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 224

There are some pressure plate apparatuses available that
attempt to measure overall volume change as well as water
volume change. The equipment is more elaborate and more
costly to operate but may provide measurements of the degree
of saturationversus soil suction. Anormal stress canbe applied
to the soil specimen while vertical deformation is measured.
Volume changes can be measured provided the soil specimen
does not separate from the sides of the K 0 ring during increases
in soil suction. The alternative is to measure the shrinkage
curve for the soil in conjunction with the SWCC test. The
degree of saturation versus soil suction relationship can then
be computed and used in the interpretation of the test results.

5.6 PHAM AND FREDLUND (2011) EQUATION
FOR ENTIRE SWCC

Early empirical equations proposed for the best fit of water
content-soil suction data (i.e., prior to about the year
2000) failed to adequately define the portion of the SWCC
below the air-entry value. The shortcoming in the empirical
SWCCs was pronounced when the soil exhibited significant
volume change as soil suction was increased (e.g., initially
slurry soils). An asymptotic equation was not appropriate
for the low-soil-suction range because water storage tended
toward zero and created numerical instability problems
during the modeling of water flow problems.
Pham and Fredlund (2011) proposed two SWCC equations
that assist in modeling the low-suction range as well as the
entire soil suction range for a soil (Fredlund and Pham, 2006).
The two proposed equations for the SWCC are referred to as
(i) themeaningful parameter SWCC equation, and (ii) the sim-
plified SWCC equation. The meaningful parameter SWCC
equation has curve-fitting parameters that have physical sig-
nificance and meaning. The simplified SWCC equation is
particularly useful when performing analytical solutions for
unsaturated soil engineering applications.
The SWCC (i.e., in terms of gravimetric water content)
typically is S shaped (i.e., for unimodel behavior). Soil suc-
tion changes have a similar influence on the soil to changes
in net mean total stress when suctions are less than the
air-entry value. The first portion of the gravimetric SWCC
should therefore have a slope consistent with the volume
change properties of the soil. The magnitude of the initial
slope depends on the stress history of the soil (Fig. 5.53).
Let us consider the drying or wetting of a soil under zero
net mean total stress. When soil suction is less than the
air-entry value, the volume change due to a soil suction
change is equal to the application of an isotropic net mean
total stress. The slope of the initial portion of the SWCC at
soil suctions less than the air-entry value can be calculated
as in Eq. 5.63. The differentiation applies for the virgin
compression branch (or the recompression branch) as long
as the applied suctions are less than the air-entry value:

5.5.6 Linkage between SWCC and Unsaturated Soil
Properties
The SWCC can be used to undertake a subsequent set of
estimations related to unsaturated soil property functions
(USPFs). Examples of subsequent estimations of functions
are the hydraulic conductivity function, the water storage
function, the shear strength function, and the volume-mass
change functions. The accuracy of the computed USPFs
are dependent upon the accuracy with which the SWCC is
characterized.
There is an interrelationship between the SWCC and the
estimated USPFs (Fredlund et al., 1995b; 1997b). A consis-
tent linkage to the SWCC must be respected and maintained
throughout all estimations for modeling purposes. In other
words, it is not possible to use the SWCC to estimate a USPF
and then subsequently change any aspect of the USPF in order
to alleviate convergence problems associated with solving a
highly nonlinear partial differential equation. The numerical
modeler must be aware that a change in a USPF means that
there is a change in the soil being analyzed. Consequently,
any change in one of the USPFs produces an inconsistency
with respect to other USPFs used in the analysis.
USPFs can produce highly nonlinear water storage and per-
meability functions, particularly for sand soils. The highly
nonlinear functions may subsequently create convergence dif-
ficulties when solving partial differential equations such as the
unsaturated soil seepage equation. Convergence difficulties
may tempt themodeler to adjust one or more of the unsaturated
soil parameters in order to obtain a converged solution. This
is “ill-advised practice” and should not be advocated. Rather,
it is important to use partial differential equation solvers that
can ensure convergence under highly nonlinear conditions.
Misfeldt et al., (2006) reported on the “preliminary design”
of a cover system where it was shown that a change in one of
the soil parameters associated with the hydraulic conductiv-
ity function significantly affected the outcome of the cover
design. Changing any one soil parameter changes the soil that
is being analyzed. It should also be noted that while estima-
tion techniques can be used to obtain SWCCs for preliminary
design purposes, it is important that individual unsaturated
soil property parameters not be arbitrarily changed when per-
forming a numerical modeling simulation.

⎧
⎨

C c
G s

for ψ > p c

dw
dψ

d(e/G s )
dψ

= = (5.63)

⎩

C s
G s

for ψ ≤ p c

where:

w = gravimetric water content,

e = void ratio,

G s = specific gravity,

C s = unloading-reloading index,

C c = virgin compression index,

p c = preconsolidation pressure, and

ψ = soil suction.