Civil Engineering Reference
In-Depth Information
This total flow must equal the sum of the flow through each layer, therefore:
Ak i A k i A k i A k i
=
+
+
+ +
A k i
3 3
…
x
1 1
2 2
n n
Considering unit width of soil:
Hk i
=
i Hk
(
+
H k
+
H k
+ +
H k
)
3 3
…
x
1 1
2 2
n n
hence
Hk
+
H k
+
H k
3 3
+ +
H k
1 1
2 2
n n
k
=
x
H
Considering flow perpendicular to the bedding planes:
Total flow q Ak i Ak i
= =
=
=
Ak i
=
Ak i
=
Ak i
z
11
2 2
3 3
n n
Considering unit area:
q k i
= =
k i
=
k i
=
k i
=
k i
z
11
2 2
3 3
n n
Now
(
h
+ + + +
h
h
3
h
)
1
2
n
k i
=
k
z
z
H
where h
1
, h
2
, h
3
, etc., are the respective head losses across each layer.
Now
k h
H
k h
H
k h
H
k h
H
1 1
1
2 2
2
3 3
3
n n
n
=
q
;
=
q
;
=
q
;
=
q
qH
k
qH
k
qH
k
qH
k
1
2
3
n
⇒
h
=
;
h
=
;
h
=
;
h
=
1
2
3
n
1
2
3
n
qH
k
qH
k
qH
k
qH
k
=
1
2
3
n
k
+
+
+ +
z
⇒
1
2
3
n
q
H
hence
H
k
=
z
H
k
H
k
H
k
H
k
1
2
3
n
+
+
+ +
1
2
3
n
Example 2.11:
Quantity of low
A three-layered soil system consisting of fine sand, coarse silt, and fine silt in horizontal
layers is shown in Fig.
2.29.
