Solving Stress-Deformation Problems with Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 733

14.2.1.2 Separation of Compressibility Measurements
into Elastic Modeling Parameters
The compression and swelling indices C c and C s provide
a number that gives an indication of the volume change
properties of the soil. It is often necessary for the compres-
sion index to be converted into a different form for use
in numerical modeling software. Even when the compres-
sive index (e.g., C c ) is converted to a compressibility value
(e.g., m 1 ) corresponding to a particular stress state, there is
still the limitation that a single value is computed while, in
reality, two soil properties are required: Young's modulus
E and Poisson's ratio μ . Stated another way, the laboratory
experiment generally measures one soil property linking vol-
ume change to the stress state while two soil properties are
required for numerical modeling purposes.
A value is commonly assumed for Poisson's ratio and
then the compression index can be converted to an equiv-
alent Young's modulus value. Poisson's ratio varies over a
fairly narrow range from 0.0 to 0.5. A Poisson's ratio of 0.0
corresponds to the case where there is no lateral movement
as the soil is loaded in uniaxial loading. A Poisson's ratio
of 0.5 corresponds to the situation where volume change in
the vertical direction is shared by the volume changes in
the other two orthogonal directions (i.e., no overall volume
change of the soil specimen). Typical values for Poisson's
ratio are shown in Table 14.1.
The magnitude of Poisson's ratio μ is most commonly
estimated based on past experience and published results
even though it is possible to measure Poisson's ratio in a
uniaxial-type triaxial test. It is possible to convert the com-
pression index of a soil into an equivalent Young's modulus
value once a value is selected for Poisson's ratio.
Values of Young's modulus E change linearly with
compression index. The mathematical relationship between
Young's modulus and compression index depends on the
laboratory testing procedure. Young's modulus is defined
using a uniaxial test procedure and therefore measurements
made using one-dimensional compression tests or some
other test procedure will need to be calculated. Let us
assume that results from a one-dimensional oedometer test

are to be converted to equivalent Young's modulus values.
The compression index of the soil can be written as follows
in terms of a coefficient of volume change, m 1 :

0 . 435 C c

m 1 =

(14.6)

(σ − u a ) ave ( 1 + e 0 )

The coefficient of volume change for one-dimensional
oedometer loading can be written in terms of Poisson's ratio
and Young's modulus as follows:

( 1 + μ)( 1 − 2 μ)

m 1 = (14.7)

E( 1 − μ)

Therefore, Young's modulus corresponding to the oedo-
meter loading path can be written as follows:

( 1 + μ)( 1 − 2 μ)(σ − u a ) ave ( 1 + e 0 )

E = (14.8)

0 . 435 C c ( 1 − μ)

Once a Poisson's ratio value is assumed for a particular
soil, Eq. 14.8 provides a relationship between Young's mod-
ulus and the compression index of the soil. Young's modulus
can be calculated for a series of selected net normal stress
states.

14.2.2 Role of SWCC When Establishing
Volume-Mass Constitutive Surfaces
The SWCC relates water content to soil suction but does
not play a direct role in characterizing the volume change
soil properties required for numerical modeling. Rather, the
SWCC becomes most useful when it is combined with the
shrinkage curve of the soil. In this way it is possible to
obtain the soil suction versus volume change soil properties
of the soil. The computed compressibility with respect to soil
suction must then be converted into an appropriate elasticity
parameter for numerical modeling purposes.
The shrinkage curve provides the relationship between
water content and void ratio. By cross-plotting the SWCC
and the shrinkage curve, it is possible to obtain the change
in void ratio versus soil suction. The shrinkage curves can
either be measured or estimated for a particular soil. The
drying shrinkage curve needs to have the same initial con-
ditions as were used for the SWCC test.
Overall volume changes for a particular geotechnical engi-
neering problem can be computed using a numerical solu-
tion such as a finite element analysis. Once overall volume
change has been computed, other volume-mass properties
can be estimated with the assistance of the SWCC. In es-
sence, this is an uncoupled, incremental solution for volume
change.

Table 14.1 Typical Values of Poisson's Ratio

Soil Type Description Poisson's Ratio, μ

Clay Soft 0.35-0.40

Medium 0.30-0.35

Stiff 0.20-0.30

Sand Loose 0.15-0.25

14.2.3 Role of Shrinkage Curve in Establishing
Constitutive Surfaces
The relationship between overall volume change (i.e.,
defined using void ratio e or specific volume v ) and

Medium 0.25-0.30

Dense 0.25-0.35

Source: From Budhu (2007).