Stability of Slopes - Elements of Soil Mechanics - page 392

Fig. 13.8 Total stress analysis.

13.2.1 Total stress analysis

This analysis, also referred to as an undrained analysis, is intended to give the stability of an embankment
or cutting immediately after its construction. At this stage it is assumed that the soil in the slope has had
no time to drain (i.e. the soil is considered to be in an undrained state) and the strength parameter used
in the analysis is the undrained cohesion which is found from either the unconfined compression test or
an undrained triaxial test without pore pressure measurements.
Consider in Fig. 13.8 the sector of soil cut off by arc AB of radius r. Let W equal the weight of the sector
and G the position of its centre of gravity. The shear strength of the soil is c u . The mass of the soil tends
to rotate clockwise, but is resisted by the shear strength acting along the failure surface.
Taking moments about O, the centre of rotation:

We = c lR = c R R θ = c R for equilibrium 2

u u u

Restoringmoment
Disturbingmoment

c R
We

2 θ

u

F = =

Note: the term R θ is the length of the slip circle through the soil (length of an arc of a circle) where θ is
measured in radians.
The position of G is not needed, and it is only necessary to ascertain where the line of action of W is.
This can be obtained by dividing the sector into a set of vertical slices and taking moments of area of
these slices about a convenient vertical axis.

13.2.2 Effect of tension cracks

With a slip in a cohesive soil there will be a tension crack at the top of the slope (Fig. 13.9) , along which
no shear resistance can develop. In the undrained state the depth of the crack, h c , is given by the follow-
ing formula (see Chapter 7 ):

= 2
γ

c u

h

c

The effect of the tension crack is to shorten the arc AB to AB ′ . If the crack is to be allowed for, the
angle θ ′ must be used instead of θ in the formula for F, and the full weight W of the sector is still used in
order to compensate for any water pressures that may be exerted if the crack fills with rainwater.