Geotechnical Engineering

DHARM

SOIL EXPLORATION 745

where, τ = shear strength (N/mm^2 )

T = torque in mm-N,

D = overall diameter of the vane in mm, and

H = height of the vane in mm.

The assumptions involved are:

(i) shearing strengths in the horizontal and vertical directions are the same;

(ii) at the peak value, shear strength is equally mobilised at the end surface as well as

at the centre;

(iii) the shear surface is cylindrical and has a diameter equal to the diameter of the

vane; and

(iv) the shear stress distribution on the vane is as shown in Fig. 18.14.

tt

tt

D/2 D/2

Fig. 18.14 Assumed stress distribution on blades of vane

For equilibrium, the applied torque, T = moment of resistance of the blades of the vane.

∴ T = surface area × surface stress × lever arm

+ end areas × average stress × lever arm.

= πτ

πτ

DH

DD

×× + × ×D

L

N

M

O

Q

2 2 42 P

2

3

2

= τ

ππDH^23 D

26

+

L

N

M

O

Q

P

This leads to Eq. 18.7 for τ.

If H = 2D, Eq. 18.7 reduces to

τ =^6

7

3

33

T

D

T

π D

≈

11.

...(Eq. 18.8)

A shoe is used for protecting the vane if it is to penetrate direct from the ground surface.
A 100-mm vane is recommended for very soft soils. For moderately firm saturated soils,
a 75-mm vane is recommended. The 50-mm vane is used infrequently but is intended for firm
saturated soils.