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w
w
ψ
w
ψ
d
ψ
ψ
Drying suction,
ψ
d
Wetting suction,
ψ
w
(a)
(b)
Figure 13.33
(a) Collapsible and (b) noncollapsible pores used to explain SWCC hysteresis
(modified from Poulovassilis, 1962).
The volume of the air-filled pore is the same as that of a pore
with a suction equal to the air-entry value, while the water
content in the specific pore under consideration is assumed
to be equal to zero. An illustration of the overall volume and
water volume changes of a pore along the drying process
from an initial slurry condition is shown in Fig. 13.35. The
volume of a pore,
v
p
(ψ,
0
)
, at a suction equal to
ψ
along
the drying curve can be calculated as follows:
Drying-wetting of
collapsible pores
w
w
u
Drying-wetting of
noncollapsible pores
(interconnected pores)
Insignificant hysteresis
w
r
v
p
(
1
,
0
)
−
V
s
C
c
log
(ψ)
for
ψ
≤
ψ
aev
v
p
(ψ,
0
)
=
10
6
ψ
Logarithmic soil suction
v
p
(
1
,
0
)
−
V
s
C
c
log
(ψ
aev
)
for
ψ > ψ
aev
(13.90)
Figure 13.34
Behavior of two types of pores associated with
boundary drying and wetting SWCCs (from Pham, 2002).
where:
ψ
aev
=
air-entry value of the pore,
13.6.3 Volume Change of Pore under Various Stress
Paths
Volume-mass constitutive relationships for unsaturated soils
are stress path dependent (Alonso, 1993; Pham, 2005). The
stress-strain relationship for the soil structure surrounding a
pore can be considered for four basic stress paths (i.e., load-
ing, unloading, drying, and wetting). The net mean stress
also affects the air-entry value and the water-entry value of
the soil. Consideration is given to a pore volume from a
representative soil element.
C
c
=
virgin compression index of the pore,
V
s
=
volume of the solid phase of the representa-
tive soil element, and
v
p
(ψ,
0
)
=
volume of the pore at a suction of
ψ
and zero
net mean stress.
A similar equation can be written to represent the volume
of water in a pore,
v
w
(ψ,
0
)
, along the drying process:
v
p
(
1
,
0
)
−
V
s
C
c
log
(ψ)
for
ψ
≤
ψ
aev
v
w
(ψ,
0
)
=
0
for
ψ > ψ
aev
(13.91)
13.6.3.1 Drying-Wetting Processes under Zero Net
Mean Stress
Let us consider the drying process for an initially saturated
soil element. The starting soil suction is less than the air-
entry value of the soil. The pores are filled with water and
the stresses acting on the soil structure surrounding the pore
are equal to the soil suction
ψ
. When soil suction is higher
than the air-entry value, some pores become filled with air
and soil suction is assumed to not further affect the soil
structure surrounding the emptied pore. The yield stress of
the pore becomes equal to the air-entry value of the pore.
where:
C
c
=
virgin compression index of the pore and
v
w
(ψ,
0
)
=
volume of water at a soil suction of
ψ
and
zero net mean stress.
The volume of the pore does not change until soil suction
is equal to the water-entry value during the wetting process
of an air-filled pore (Fig. 13.35). A pore is filled with water
when soil suction is less than the water-entry value and the
soil will expand as soil suction decreases. The volume of the
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