Environmental Engineering Reference
In-Depth Information
C
c
(
x
)
13.6.4.2 Equation for Compression Indices of Pores
and Reference Drying Pore-Size Distribution
A soil is completely dry at a soil suction of approximately
10
6
kPa (Fredlund and Rahardjo, 1993a). Let us denote the
soil suction at which a soil is completely dry as
ψ
max
and
designate
ξ
max
as log(
ψ
max
) on a logarithmic suction scale. Let
us consider a representative element of soil dried from slurry
where the volume of solids is equal to
V
s
. The total volume
of the pores,
V
p
, in the soil element under dry conditions (i.e.,
at a soil suction of
ψ
max
) can be calculated as follows:
=
summation of the virgin compression index of pores
having the same reference drying suction of
x
(i.e.,
air-entry value), and
V
s
=
volume of solid phase.
The following equation for the virgin compression index
of a group of pores can be derived by combining Eqs. 13.98,
13.110, 13.111, 13.112, and 13.113:
d
−
G
s
w
(
10
ξ
)C
c
/(e
sat
−
C
c
ξ)
dξ
C
c
(ξ)
=
(13.114)
ξ
max
where:
V
p
=
V
a
=
f
d
(x) dx
(13.110)
e
sat
=
void ratio of the soil at the reference stress state of
1 kPa and
0
where:
w
(ψ)
=
water content along the initial drying SWCC.
f
d
(x)
=
reference DPD,
The reference DPD can also be obtained by forcing all pores
in the soil to dry to respective drying soil suctions (Pham,
2005). An equation for the reference DPD can be written as
V
p
=
total volume of pores, and
V
a
=
total volume of air in the soil element at a suction
of
ψ
max
.
⎡
⎣
⎤
⎦
ξ
ξ
max
w
(
10
x
)C
c
e
sat
−
C
c
x
dx
f
d
(x) dx
=
V
dry
−
G
s
V
s
The volume of the soil element at a suction
ψ
can be
calculated as the summation of the volume of solids, water,
and air in the soil:
w
(ψ)
−
0
ξ
(13.115)
V(ψ)
=
V
s
+
V
a
(ψ)
+
V
w
(ψ)
(13.111)
13.6.4.3 Volume Change of Collapsible
and Noncollapsible Pores
There does not need to be a distinction between collapsible
pores and interconnected pores. Noncollapsible pores are
interconnected pores that do not exhibit significant hystere-
sis between the wetting and drying processes. Water appears
to exist only in the noncollapsible pores when soil suction
exceeds residual conditions. The total volume of the non-
collapsible pores at residual suction is assumed to be equal
to the volume of water at residual suction.
The water content in a soil at a particular soil suction
can be divided into two components: (i) water in collapsi-
ble pores and (ii) water in noncollapsible pores. At suctions
higher than residual suction the water content in the soil
reflects the water in collapsible pores (Fig. 13.38). At soil
suctions less than residual suction the water content is equal
to that of the collapsible pores (or the water content at
residual suction). Let us denote a function that presents
gravimetric water content in the collapsible pores as
w
c
(ψ)
.
The function
w
c
(ψ)
can be calculated as follows:
where:
V,V
s
,V
a
,V
w
=
overall volume of the representative soil
element, volume of solid phase, volume
of air phase, and volume of water phase
at a soil suction
ψ
, respectively.
The volume of the solid phase,
V
s
, is a constant at any soil
suction or net mean stress. The volume of the air phase at a
suction
ψ
is equal to the summation of the volume of pores that
have an air-entry value smaller than the designated suction:
ξ
V
a
(ψ)
=
f
d
(x) dx
(13.112)
0
The volume of the water phase,
V
w
, at any suction value
ψ
is equal to the summation of the volume of pores that have an
air-entry value greater than a suction
ψ
. An equation for the
volume of water in the soil at a suction
ψ
can be written as
w
(ψ)
−
w
r
for
ψ
≤
ψ
r
w
c
(ψ)
=
(13.116)
ξ
max
0
for
ψ > ψ
r
f
d
(x)
+
C
c
(x)V
s
(x
−
ξ)
dx
V
w
(ψ)
=
(13.113)
where:
ξ
w
c
(ψ)
=
where:
gravimetric water content along the initial dry-
ing curve for an initially slurry soil and
ξ
=
log(
ψ
),
ψ
r
=
residual suction for the soil.
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