Geotechnical Engineering

DHARM

130 GEOTECHNICAL ENGINEERING

5.5.6 Indirect Methods of Determination of Permeability

These constitute the methods which relate the permeability with grain-size and with specific

surface of the soil. The influence of grain-size or permeability is also referred to in Sec. 5.6 and

sub-sec. 5.6.2.

It is logical that the smaller the grain-size, smaller are the voids, which constitute the

flow channels, and hence the lower is the permeability. A relationship between permeability

and particle-size is much more reasonable in silts and sands than in clays, since the particles

are nearly equidimensional in the case of silts and sands. From his experimental work on

sands, Allen Hazen (1892, 1911) proposed the following equation :

k = 100 D 102 ...(Eq. 5.28)

where

k = permeability coefficient in cm/sec, and

D 10 = Hazen’s effective size in cm.

This relation assumes that the distribution of particle sizes is spread enough to prevent

the smallest particles from moving under the seepage force of the flowing water. Flow in soils

which do not have hydrodynamic stability can result in washing away of the fines and a corre-

sponding increase in permeability. Particle-size requirements to prevent such migration of

fines are discussed in Chapter 6.

The following equation is known as Kozeny-Carman equation, proposed by Kozeny (1927)

and improved by Carman :

k =

1

0 2 1

3

kS

e

. e

..

()

γ

μ+

...(Eq. 5.29)

where,

e = void ratio,
γ = unit weight of fluid,
μ = viscosity of fluid,
S = specific surface area, and
k 0 = factor depending on pore shape and ratio of length of actual flow path to the thick-
ness of soil bed.
Loudon (1952) developed the following empirical relationship :
log 10 (kS^2 ) = a + bn ...(Eq. 5.30)
Here a and b are constants, their values being 1.365 and 5.15 respectively at 10°C, and
n is the porosity.

5.6 FACTORS AFFECTING PERMEABILITY

Since permeability is the property governing the ease with which a fluid flows through the

soil, it depends on the characteristics of the fluid, or permeant, as well as those of the soil.

An equation reflecting the influence of the characteristics of the permeant fluid and the

soil on permeability was developed by Taylor (1948) based on Poiseuille’s law for laminar flow