Geotechnical Engineering

DHARM

326 GEOTECHNICAL ENGINEERING

Let AB be a trial slip surface (a circular arc of radius r) as shown in Fig. 9.8.

q

O

r

A

B

e

G

W C= .cl

l=rq

Fig. 9.8 Total stress analysis for a purely cohesive soil
Let W be the weight of the soil within the slip surface and G the position of its centre of
gravity. The shearing strength of the soil is c, since φ = 0°.

Taking moments about 0, the centre of rotation:

W.e. = c.l.r = c.r.θ.r = cr^2 .θ, for equilibrium (incipient failure).

Factor of safety, F =

Restraining moment

Sliding moment

=

cr

We

..

.

(^2) θ
...(Eq. 9.17)
Here W.e is dependent on the cohesion mobilised which will be less than the maximum
cohesion of soil.
The exact position of G is not required and it is only necessary to ascertain the position
of the line of action of W. This may be got by dividing the sector into a set of vertical slices and
taking moments of area of these slices about any convenient vertical axis.
Effect of Tension Cracks
When slip is imminent in a cohesive soil there will always develop a tension crack at the
top surface of the slope along which no shear resistance can develop, as indicated in Fig. 9.9.
q¢
O
r
A
l=rq¢
hc
B
B¢
Fig. 9.9 Effect of tension crack in a purely cohesive soil