Geotechnical Engineering

DHARM

SHEARING STRENGTH OF SOILS 279

H

T

Torque head

Vanes of

high tensile

steel

Four-blade

shear vane

D

Sheared

cylindrical

surface

Plan

Pictorial view

Fig. 8.19 Laboratory shear vane

if both the top and bottom of the vane partake in shearing the soil.

Here, T = torque

D = diameter of the vane

H = height of the vane

If only one end of the vane partakes in shearing the soil, then

s =

T

πDH^2 (/ 212 +D/ )

...(Eq. 8.46)

Equation 8.45 may be derived as follows :
The shearing resistance is mobilised at failure along a cylindrical surface of diameter D,
the diameter of the vane, as also at the two circular faces at top and bottom.

The shearing force at the cylindrical surface = π/D.H.s., where s is the shearing strength
of the soil. The moment of this force about the axis of the vane contributes to the torque and is
given by

πDH.s. D/2 or πs H. D^2 /2

For the circular faces at top or bottom, considering the shearing strength of a ring of

thickness dr at a radius r, the elementary torque is

(2π r dr). s. r

and the total for one face is

0

D/ 2

z^2 πsr

(^2) dr (^) =^2
3812
ππsD^3 s

. =. D^3

Laboratory vane:

H = 20 mm

D = 12 mm

t = 0.5 to 1 mm

Field vane:

H = 10 to 20 cm

D = 5 to 10 cm

t = 2.5 cm