Stress-Deformation Analysis for Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 707

G s = specific gravity of the soil particles,

Horizontal

e dry

w sat = gravimetric water content at reference

stress state,

C c ,C s = compression indices of the soil at satu-

rated condition (i.e., zero soil suction),

C cd

=

p net mean stress,

p 0 = uniform yield stress, and

w r = residual water content of the soil.

Concave

13.6.6.3 Equation for Degree-of-Saturation
Constitutive Surface
The equation for the degree of saturation surface can be
derived from the equations for gravimetric water content
surface (Eq. 13.129) and the void ratio surface (Eq. 13.130)
as follows:

ψ aev ψ r

1

Log (mean effective stress)

Figure 13.43 Compression curve of air-dried specimen from ini-
tially slurry soil sample along with method for estimation of virgin
compression index of a dry specimen, C cd

w (ψ,p,p 0 )G s
e(ψ, p, p 0 )

(from Pham, 2005).

S(ψ,p,p 0 ) = (13.131)

a straight line at net mean stresses equal to residual soil
suction (Fig. 13.43). The dry virgin compression index C cd
of an air-dried soil is estimated in the same manner as for
saturated soils. It is suggested that for most soils C cd can be
assumed to be zero (Pham, 2005).

13.6.7 Determination of Model Parameters
The proposed volume-mass constitutive model has complex
equations but requires relatively simple and conventional
laboratory test data as the required input soil parameters.
The data required to define the volume-mass constitutive
equations are as follows:

13.6.8 Model Predictions on Three Artificial Soils
The proposed volume-mass constitutive model is fit to soil
properties for three artificial soils and three sets of soil data
from the research literature. The prediction results are pre-
sented for (i) several simple stress paths (i.e., 2D graphs)
and (ii) several complete volume-mass constitutive surfaces
(i.e., 3D graphs).

1. The initial drying SWCC for the initially slurry soil.
2. The pore shape parameter η to represent the effect of
net mean stress and stress history on the change in
the air-entry value of pores. This parameter can be set
to 1 (Pham, 2005) unless SWCCs are available where
laboratory measurements have been made at different
preconsolidation pressures.
3. Parameters for the hysteretic nature of the SWCC of
the soil, namely, the distance between the two inflec-
tion points of the two bounding hysteretic curves, D SL ,
and the ratio between the slopes of the bounding drying
and the bounding wetting curves, R SL . These values
can be estimated as suggested by Pham (2005).
4. The virgin compression index of the air-dried soil from
an initially slurry specimen (i.e., completely dry spec-
imen; Fig. 13.43).
5. The soil parameter m required to determine the com-
pressibility of the soil structure surrounding contin-
uously air-filled pores. It is suggested that the soil
parameter be assumed to be 1 in cases where there
is no measured data.
The yield stress acting on the soil structure surrounding
pores of a soil that is air dried from slurry conditions is
equal to the air-entry values of pores. It can be assumed
that noncollapsible pores are incompressible. The maximum
yield stress acting on the soil structure surrounding col-
lapsible pores at suctions equal to and beyond the residual
soil suction is the residual soil suction of the soil. There-
fore, the compression curve of an air-dried soil becomes

13.6.8.1 Material Simulated
Descriptions of the three artificial soils are presented in
Table 13.2. The initial drying SWCCs of the three soils
starting from slurry conditions are shown in Fig. 13.44. The
assumption is made that the “dry pores are incompressible.”
The m soil parameter is not required and, as well, the virgin
compression index of the soil under completely dry condi-
tion, C cd , is not required.

13.6.8.2 Prediction Results for Several Simple
Stress Paths
The shrinkage curve for each soil can be predicted using the
proposed constitutive model for the void ratio and the water
content along the drying process from slurry conditions to a
suction of 10 6 kPa. The predicted shrinkage curves for the
three artificial soils are shown in Fig. 13.45.
The shrinkage curve for the sand soil is almost horizontal
since sand undergoes little volume change during a dry-
ing process. The shrinkage curves for silt and clay are as
anticipated. The shrinkage curves follow a 45 ◦ line at high
water contents. The shrinkage curves tend to be horizontal