Geotechnical Engineering

DHARM

192 GEOTECHNICAL ENGINEERING

6.8.5 Analogy Methods

Lapalce’s equation for fluid flow also holds for electrical and heat flows. The use of electrical
models for solving complex fluid flow problems in more common. In an electrical model, volt-
age corresponds to total head, current to velocity and conductivity to permeability. Ohm’s Law
is analogous to Darcy’s Law. Measuring voltage, one can locate the equipotentials. The flow
pattern can be sketched later.

The versatility of electrical analogy in taking into account boundary conditions too dif-
ficult to deal with by other methods, makes the method suitable for solving complex flow situ-
ations. Electrical models are considered convenient for instructional purposes, especially in
connection with the determination of the top flow line and flow nets for earth dams.

6.9 Quicksand

Let us consider the upward flow of water through a soil sample as shown in Fig. 6.26.

Over

flow

Water supply

Stand

pipe

L

h(head loss)

Sand

Area A

Screen

Fig. 6.26 Upward flow of water through soil
Total upward water force on the soil mass at the bottom surface
= (h + L)γw. A
Total downward force at the bottom surface = Weight of the soil in the saturated condi-
tion

= γsat. L. A.

=

()

()

Ge

e

• 1 +. γw. L. A.
  Assuming that there is no friction at the sides, it is evident that the soil will be washed
  out if a sufficiently large value of h is applied. Such a boiling condition will become imminent
  if the upward water force just equals the weight of the material acting downward; that is,

(h + L) γw. A =

()

()

Ge

e

+

1 +

. γw L. A. ...(Eq. 6.30)

whence i = h/L = (G – 1)/(1 + e) ...(Eq. 6.31)

This means that an upward hydraulic gradient of magnitude (G – 1)/(1 + e) will be just
sufficient to start the phenomenon of ‘‘boiling’’ in sand. This gradient is commonly referred to
as the ‘‘Critical hydraulic gradient’’, ic. Its value is approximately equal to unity. A saturated