Stress-Deformation Analysis for Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 701

When soil suction
equals 10 6 kPa

v p ( ψ aev , 0, 0) C cd V s

v p (10 6 , 0, 0)

v p ( ψ , p , 0)

C c V s

When soil suction
equals ψ kPa

v p (0, p , 0)

Saturation

C c V s

p a = ψ aev
Logarithmic net mean stress (kPa)

p y

0.1 p

Figure 13.37 Compression curves for pore at three different soil suctions (0, ψ , and 10 6 kPa)
(from Pham, 2002).

The virgin compression index of a continuously air-filled
pore should lie between the virgin compression indices of a
pore when the soil is completely dry and a pore when soil
suction is equal to zero. Figure 13.37 illustrates compression
curves for a pore at three different soil suctions: (i) satura-
tion (i.e., zero soil suction); (ii) when soil suction is equal
to a specified value ψ , where the pore is filled with air; and
(iii) at 10 6 kPa (i.e., soil is completely dry). Further details
concerning the equations associated with each of the men-
tioned alternatives can be found in Pham (2005) and Pham
and Fredlund (2011a).
Alternative 3. A third solution could assume that there
are some small particles and cementing materials that act to
bond the larger particles together at completely dry condi-
tions. Along the wetting process, water gradually fills the
pores and reduces the bonding strength that holds soil parti-
cles in position (Lawton et al., 1991a, 1991b; Pereira, 1996).
It can be assumed that all bonds are removed when all inter-
connected pores (i.e., noncollapsible pores) are filled with
water. The continuously air-filled pores reach maximum col-
lapse conditions and the equivalent yield stress on the soil
structure surrounding a continually air-filled pore is equal
to the magnitude of the net mean stress. The equivalent
yield stress of the soil structure surrounding continuously
air-filled pores could be assumed to be a function of the
amount of water in the interconnected pores and the net
mean stress.

water and becomes a water-filled pore when soil suction is
less than the water-entry value. Loading-unloading of the
soil structure surrounding a water-filled pore is similar to
the loading-unloading of a saturated soil. If soil suction is
higher than the water-entry value, the pore is still filled with
air after the loading process and is called a continuously
air-filled pore.

13.6.4 Mathematical Formulation for Drying Process
of Initially Slurry Soil
Equations for the compression indices associated with each
group of pores along with the pore-size distribution are
presented for the reference pore-size distribution function.
Details of the mathematical derivation of each equation can
be found in Pham (2005).

13.6.4.1 Curve-Fitting Model for SWCC
The drying SWCC starting from an initial slurry condition
(i.e., gravimetric water content versus soil suction) can be best
fit using the following SWCC equation (Pham and Fredlund,
2008):

w sat −

w r a

C c
G s

w (ψ) = log (ψ) −

ψ b + a

w r 1

ln ( 1 + ψ/ψ r )

+ − (13.109)

ln ( 1 + 10 6 /ψ r )

where:

13.6.3.4 Loading-Unloading Processes at Constant
Soil Suction
Two types of pores (i.e., air-filled pores and water-filled
pores) are considered during loading-unloading processes of
an unsaturated soil. The pore may collapse and the water-
entry value of the pore is decreased when the soil structure
surrounding an air-filled pore is loaded. The pore absorbs

C c = virgin compression index of the soil,

G s = specific gravity of the soil particles,

w r = residual gravimetric water content,

w sat = water content of the slurry soil at an effective stress

of 1 kPa, and

=

a, b curve-fitting parameters.