Environmental Engineering Reference
In-Depth Information
0.5
GW-GM with sand
SM with gravel
SC with gravel
Sandy ML
CL with sand
Fredlund and Xing (1994)
0.4
0.3
0.2
0.1
0
0.1
1
10
100
1000
10,000
100,000 1,000,000
Soil suction, kPa
Figure 7.44
SWCCs for colluvial soils (after Li et al., 2009).
The total flow volume of water passing through section
B
in Eq. 7.73 can then be written as
where:
h
A
h
A
k
w
=
instantaneous coefficient of permeability at a spe-
cific section along the soil column and
θ
h
h, t
1
Adh
θ
h, t
1
Adh
Q
B
=
−
−
i
=
hydraulic gradient at that section.
h
B
h
B
h
B
h
A
θ
h, t
1
Adh
θ
h, t
1
Adh
=
−
The hydraulic gradient can be calculated as
h
B
−
h
h
A
−
h
(7.77)
=
−
dh
+
dψ/γ
w
dh
dψ
γ
w
dh
−
The first part of Eq. 7.77 can be calculated as
h
B
i
=
1
(7.82)
θ
h, t
1
Adh
0
.
5
θ
h
B
,t
1
+
θ
h
B
−
h, t
1
≈
The hydraulic gradient at time
t
2
at section
B
can be
obtained by substituting Eq. 7.76 into Eq. 7.82,
h
B
−
h
0
.
5
θ
h
B
,t
1
+
θ
h
B
,t
2
Ah
×
Ah
≈
(7.78)
ψ
h
B
,t
2
+
ψ
h
B
+
h, t
2
=
−
If the initial water content is low (and therefore the coeffi-
cient of permeability is extremely small), the water content
change in the initially air-dried soil zone can be ignored
during the limited wetting period. Consequently, the water
contents in this zone remain at the initial water content
θ
i
during the entire wetting process. The second part of
Eq. 7.77 can be calculated as follows:
h
A
i
−
1
γ
w
h
ψ
h
B
,t
1
−
ψ
h
B
,t
2
γ
w
h
=
−
1
(7.83)
The average coefficient of permeability
k
w
from
t
1
to
t
2
at section
B
can be calculated by substituting Eqs. 7.80 and
7.83 into Eq. 7.81:
θ(h,t
1
)A dh
≈
0
.
5[
θ(h
A
,t
1
)
h
A
−
h
Q
B
iC
t
2
−
t
1
k
w
=
+
θ(h
A
−
h, t
1
)
]
Ah
≈
θ
i
Ah
(7.79)
θ
h
B
,t
1
+
θ
h
B
,t
2
−
2
θ
i
γ
w
h
2
By substituting Eqs. 7.78 and 7.79 into Eq. 7.77,
Q
B
can
be calculated
=
2
ψ
h
B
,t
1
−
ψ
h
B
,t
2
−
γ
w
h
t
2
−
t
1
(7.84)
0
.
5
θ
h
B
,t
1
+
θ
h
B
,t
2
−
2
θ
i
Ah
Q
B
≈
(7.80)
The wetting-front advancing velocity (see Fig. 7.45b) is
defined as
The flow quantity can be written using Darcy's law,
h
t
v
=
(7.85)
Q
=
k
w
iAdt
(7.81)
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