Geotechnical Engineering

DHARM

SOIL MOISTURE–PERMEABILITY AND CAPILLARITY 157

= 3 × 9.81 kN/m^2

= 29.43 kN/m^2.

Example 5.17. The D 10 size of a soil is 0.01 mm. Assuming (1/5) D 10 as the pore size, estimate
the height of capillary rise assuming surface tension of water as 75 dynes/cm.
(S.V.U.—B.Tech., (Part-time)—April, 1982)
The effective size D 10 of the soil = 0.01 mm
Pore size, dc = (1/5)D 10 = (1/5) × 0.01 mm = 0.002 mm.
Surface tension of water = 75 dynes/cm = 75 × 10–-6 N/mm.
Height of Capillary rise in the soil:

hc =

4 T

d

s

γwc

=

47510

9 81 10 0 002

6

6

××

××

−

..− mm, since γw = 9.81 × 10

–6 N/mm 3

=^475

9 81 0 002 1000

×

..××

m

= 15.3 m.

Example 5.18. What is the height of capillary rise in a soil with an effective size of 0.06 mm

and void ratio of 0.63?

Effective size = 0.06 mm

Solid volume ∝ (0.06)^3

∴ Void volume per unit of solid volume ∝ 0.63(0.06)^3

Average void size, dc = (0.63)1/3 × 0.06 mm = 0.857 × 0.06 = 0.0514 mm

Capillary rise, hc =

4 T

d

s

γwc

=

47310

9 81 10 0 0514

6

6

××

××

−

..− mm

≈ 0.58 m.

Example 5.19. The effective sizes of two soils are 0.05 mm and 0.10 mm, the void ratio being

the same for both. If the capillary rise in the first soil is 72 cm, what would be the capillary rise

in the second soil?

Effective size of first soil = 0.05 mm

∴ Solid volume ∝ (0.05)^3

∴ Void volume ∝ e(0.05)^3

Average pore size, dc = e1/3 × 0.05 mm

Capillary rise of hc =

4 T

d

s

γwc

∴ hc ∝ 1/dc

Since the void ratio is the same for the soils, average pore size for the second soil

= e1/3 × 0.10 mm.