Geotechnical Engineering

DHARM

SOIL MOISTURE–PERMEABILITY AND CAPILLARITY 155

We know,

k =

qrr

zz

log ( / )e

()

21

2

2

1

π−^2

=

2 303 2 70 15 100

60 31 3 29

10

22

.log(/)

(. )

××

×−π

cm/s

= 1.18 × 10–1 mm/s.

Example 5.13. Determine the order of magnitude of the composite shape factor in the Poiseulle’s
equation adapted for flow of water through uniform sands that have spherical grains and a
void ratio of 0.9, basing this determination on Hazen’s approximate expression for permeabil-
ity.

Poiseulle’s equation adapted for the flow of water through soil is:

k = D e

e

s^2 C

3

1

..

()

γ.

μ+

with the usual notation, C being the composite shape factor.

By Allen Hazen’s relationship,

k = 100 D 102

D 10 is the same as the diameter of grains, Ds, for uniform sands.

∴ k = 100 Ds^2. Here Ds is in cm while k is in cm/s.

Substituting –

100 Ds^2 = D

e

e

s^2 C

3

1

..

()

.

γ

μ+

C =^100

1

.. 3

μ ()

γ

+e

e

; here μ is in N-Sec/cm^2 and γ is in N/cm^3.

C =

100 10 10 1 9

981 10 09

76

33

×××

××

−.

.(.)

since μ = 10–3 N-sec/cm^2 (at 20°C) and γ = 9.81 kN/m^3

= 0.002657.

Example 5.14. A cohesionless soil has a permeability of 0.036 cm per second at a void ratio of
0.36. Make predictions of the permeability of this soil when at a void ratio of 0.45 according to
the two functions of void ratio that are proposed.

k 1 : k 2 =

e

e

e

e

1

3

1

2

3