Environmental Engineering Reference
In-Depth Information
stress
p
y
and then dried under a constant net mean stress
p
is as follows:
There are two types of pores after a wetting process:
(i) water-filled pores and (ii) air-filled pores. A pore that
is filled with air after the wetting process is called the
con-
tinuously air-filled pore.
For a water-filled pore, the volume
of the pore at a suction
ψ
and a net mean stress
p
can be
calculated as follows:
ψ
aev
ψ
aev
(p, p
y
)
(C
c
−
C
s
)
log
(p
y
)
+
C
s
log
(ψ
aev
+
p)
−
C
c
log
(ψ
aev
)
3
e
sat
−
C
c
log
(ψ
aev
)
v
p
(ψ,p,p
y
)
=
v
p
(
1
,
0
)
−
V
s
C
c
log
(p
y
)
=
1
−
η
+
V
s
C
s
log
(p
+
ψ/p
y
)
(13.106)
(13.104)
where:
The yield stress of a pore filled with water after the wetting
process can be calculated as follows:
p
y
=
yield stress of the soil and
ψ
aev
(p, p
y
)
=
air-entry value of a pore when the yield
stress is equal to
p
y
and drying takes place
under a net mean stress
p
.
p
0
for (
ψ
+
p)
≤
p
0
p
y
=
p
y
(ψ
wev
)
=
p
+
ψ
wev
for (
ψ
+
p) > p
0
(13.107)
where:
13.6.3.3 Wetting Process under Constant Net
Mean Stress
The water-entry value of a pore having a yield stress
p
y
that is wetted under a constant net mean stress
p
[i.e.,
ψ
wev
(p, p
y
)
] is higher than when the pore is dried and wet-
ted under zero net mean stress (i.e., reference water-entry
value,
ψ
wev
). The relationship between the two water-entry
values can be calculated in a similar manner to that used for
the drying process:
ψ
wev
=
reference water-entry value of the pore and
p
0
=
yield stress prior to the wetting process.
The volume-mass constitutive model for unsaturated
soils must reflect yield in the soil structure surrounding
continuously air-filled pores. This concept is consistent with
elastoplastic theories for soils subjected to isotropic loading
conditions. There are three alternative assumptions that might
be made regarding the stress-strain relationship surrounding
a continuously air-filled pore. These can be stated as follows.
Alternative 1.
The simplest solution is to assume that
continuously air-filled pores are incompressible (Fig. 13.37).
Under this assumption the yield stress of a continuously air-
filled pore does not change with a change in soil suction or
net mean stress, and the yield stress
p
y
ψ
wev
ψ
wev
(p, p
y
)
(C
c
−
C
s
)
log
(p
y
)
+
C
s
log
(ψ
wev
+
p)
−
C
c
log
(ψ
aev
)
3[
e
sat
−
C
c
log
(ψ
aev
)
]
=
1
−
η
can be written as
(13.105)
where:
p
y
=
p
y
(ψ
aev
)
=
p
0
(13.108)
ψ
aev
=
air-entry value of the pore at zero net
mean stress
where:
(i.e.,
reference
air-entry
value),
p
y
=
yield stress of the continuously air-filled pore (i.e.,
having a reference air-entry value of
ψ
aev
)afterthe
wetting process and
ψ
wev
=
water-entry value of the pore having zero
yield stress and being wetted under zero
net mean stress (i.e., reference water entry
value), and
p
0
=
yield stress of a pore prior to the wetting process.
ψ
wev
(p, p
y
)
=
water-entry value of the pore when it has
experienced a yield stress of
p
y
and is
wetted under a constant net mean stress of
p
, where
p
y
is equal to the yield stress of
the pore with a pore-shape parameter,
η
.
Alternative 2.
Another solution is to assume that the
compression curve of a continuously air-filled pore at con-
stant soil suction (on a logarithmic net mean stress scale)
can be expressed as a combination of two straight lines cor-
responding to the virgin compression line and the unloading-
reloading line (Fig. 13.37). The unloading-reloading index
of an air-filled pore would be taken as zero (i.e., assump-
tion 7). Therefore, the
volume change of an air-filled pore
would only depend on the yield stress of the pore.
The yield
stress of a continuously air-filled pore is a function of the
virgin compression index of the pore (i.e., when it is filled
with air).
Alonso (1993) observed that stress paths related to the
wetting process were stress path independent. It appears rea-
sonable to assume that the volume of a pore after wetting to
a selected soil suction
ψ
and then subjected to a net mean
stress
p
is equivalent to that of the pore that is first loaded
to a net mean stress
p
and then wetted to a soil suction
ψ
.
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