Environmental Engineering Reference
In-Depth Information
suction
ψ
. The volume of the pore under dry conditions
(i.e., dry under zero net mean stress) can be calculated from
Eq. 13.90 as follows:
At soil suction
ψ
>
ψ
aev
:
no change in volume
V
s
C
p
v
p
(ψ
aev
,
0
)
=
v
p
(
1
,
0
)
−
C
c
V
s
log
(ψ
aev
)
(13.94)
V
s
C
p
where:
ψ
wev
ψ
aev
1
10
6
ψ
aev
=
air-entry value of a pore when drying takes
place under zero net mean stress and
log(
ψ
)
Logarithmic soil suction
(a)
v
p
(
1
,
0
)
=
volume of the pore corresponding to the ref-
erence stress state (i.e., 1 kPa soil suction and
zero net mean stress).
V
s
C
p
The air-entry value of a pore dried under a net mean
stress is higher than that of a pore dried under zero net
mean stress (Fig. 13.36). Net mean stress and soil suction
have the same effect when a pore is filled with water. The
volume of a pore at a suction value equal to the air-entry
value,
ψ
aev
(p)
, and a net mean stress of
p
can be presented
as follows:
V
s
C
p
ψ
wev
ψ
aev
1
10
6
log(
ψ
)
Logarithmic soil suction
(b)
v
p
(ψ
aev
(p), p)
=
v
p
(
1
,
0
)
−
C
c
V
s
log
(ψ
aev
(p)
+
p)
(13.95)
Figure 13.35
(a) Volume change and (b) water content change
of pore during initial drying process (from Pham, 2002).
pore at any suction
ψ
along a wetting process (i.e., from an
initially air-filled condition) can be calculated as follows:
v
p
(ψ,
0
)
⎧
⎨
v
p
(ψ
aev
,
0
)
+
V
s
C
s
log
ψ
ψ
aev
for
ψ
≤
ψ
wev
V
s
C
p
=
⎩
v
p
(ψ
aev
,
0
)
for
ψ > ψ
wev
(13.92)
where:
ψ
aev
ψ
aev
(
p
)
10
6
log(
ψ
)
Logarithmic soil suction
(a)
C
s
=
unloading-reloading index of the pore and
ψ
wev
=
water-entry value of the pore.
An equation for the volume of water in a pore along a
wetting process (i.e., initially air-filled condition) can be
written as follows:
V
s
C
p
v
w
(ψ,
0
)
⎧
⎨
v
p
(ψ
aev
,
0
)
+
V
s
C
c
log
ψ
ψ
aev
for
ψ
≤
ψ
wev
=
ψ
aev
ψ
aev
(
p
)
10
6
log(
ψ
)
⎩
for
ψ
>
ψ
wev
(13.93)
0
Logarithmic soil suction
(b)
Figure 13.36
Effects of net mean stress on air-entry value, vol-
ume change, and water content change of pore during drying
process: (a) volume change comparison of pore drying under zero
load and drying under a constant net mean stress
p
; (b) water con-
tent change comparison of pore drying under zero load and drying
under constant net mean stress
p
(from Pham, 2002).
13.6.3.2 Drying Process under Constant Net
Mean Stress
The air-entry value of a pore,
ψ
aev
, is also a function of net
mean stress
p
and can be expressed as
ψ
aev
(p)
. The volume
of a pore is a function of the net mean stress
p
and soil
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