Geotechnical Engineering

DHARM

156 GEOTECHNICAL ENGINEERING

∴ k 2 = 0 2025

0 1296

.

.

× 0.36 = 5.625 × 10–1 mm/s.

Example 5.15. Permeability tests on a soil sample gave the following data:

Test No. Void ratio Temperature °C Permeability in 10–3

mm/s

1 0.63 20 0.36

2 1.08 36 1.80

Estimate the coefficient of permeability at 27°C for a void ratio of 0.90.

Viscosity at 20 C = 1.009 10 N.sec/mm

Viscosity at 36 C = 0 10 N.sec/mm

Viscosity at 27 C = 0 10 N.sec/mm

Unit weight = 9.81 10 N/mm

2

2

2

63

°×

°×

°×

U

V

|

W

|

×

−

−

−

−

9

9

9

706

855

.

.

γ

According to Poisuelle’s equation adapted to flow through soil,

k = D

e

e

s^2 C

3

1

..

()

.

γ

μ+

From test 1,

0 36 10 9 81 10

1 009 10

063

163

3

2

6

9

.^3
.

.

.

.(. )

(. )

× = ×

×

−−

DC −

s

= 1491.46

∴ Ds^2. C = 2.414 × 10–7

From test 2,

1 80 10 9 81 10

0 706 10

108

208

3

2

6

9

.^3
.

.

.

.(. )

.

× = ×

×

−−

DC −

s

= 8415.35

∴ Ds^2. C = 2.139 × 10–7

Average value of Ds^2. C = 2.2765 × 10–7

∴ At 27°C and a void ratio of 0.90,

k = 2.2765 × 10–7 ×

981 10

0 855 10

090

19

6

9

.^3
.

.(. )

.

×

×

−

− = 1.002 × 10–3 mm/s.

Example 5.16. To what height would water rise in a glass capillary tube of 0.01 mm diam-
eter? What is the water pressure just under the meniscus in the capillary tube?

Capillary rise, hc =

4 T

d

s

γwc

, where Ts is surface tension of water and γw is its unit weight

and dc is the diameter of the capillary tube.

∴ hc =

47310

981 10 001

6

6

××

××

−

..− mm, assuming Ts = 73 × 10

–6 N/mm and

= 30/0.01 mm γw = 9.81 × 10–6 N/mm^3.

= 3000 mm or 3 m.

Water pressure just under the meniscus in the tube

= 3000 × 9.81 × 10–6 N/mm^2