Civil Engineering Reference
In-Depth Information
Unless k
x
is equal to k
z
the equation is not a true Laplacian and cannot therefore be solved by a flow
net.
To obtain a graphical solution the equation must be written in the form:
k
k
∂
∂
h
z
2
+
∂
∂
2
h
z
x
0
=
2
2
z
or
h
x
2
h
z
2
∂
∂
+
∂
∂
=
0
2
2
t
where
1
k
k
1
x
z
= ⋅
x
2
x
2
t
or
k
k
z
x
2
=
x
2
t
x
i.e.
k
k
z
x
=
x
t
x
This equation is Laplacian and involves the two co-ordinate variables x
t
and z. It can be solved by a flow
net provided that the net is drawn to a vertical scale of z and a horizontal scale of
k
k
z
x
=
z
t
x
2.15.2 Calculation of seepage quantities in an anisotropic soil
This is exactly as before:
q kh
N
N
f
=
d
and the only problem is what value to use for k.
Using the transformed scale a square flow net is drawn and Nf
f
and N
d
obtained. If we consider a 'square'
in the transformed flow net it will appear as shown in Fig.
2.25a
. The same figure, drawn to natural scales
Let k
′
be the effective permeability for the anisotropic condition. Then k
′
is the operative permeability
in Fig.
2.25a
.
Hence, in Fig.
2.25a
:
∆
h
a
=
′
=
′
Flow ak
k
∆
h
