Geotechnical Engineering

DHARM

STABILITY OF EARTH SLOPES 349

(b) Rigorous approach:

The calculations for the rigorous approach are set out in the tabular form (Table 9.3).

F with the first approximation =

294 45

209 08

= 1.41

Columns (2) and (3) are recalculated with an F value of 1.4.

F with the second approximation =

290 55

209 08

= 1.39,

which is very near the assumed value of F, i.e. 1.4

Thus, the factor of safety may be taken as 1.4 by the rigorous approach.

Summary of Main Points

1. Earth slopes may be classified as infinite slopes and finite slopes; practically speaking, a slope
   with a large height is treated as an infinite one.


2. The critical angle of slope of an infinite earth slope in cohesionless soil is equal to the angle of
   internal friction.


3. For an infinite slope in cohesive soil, the critical depth, zc, is related to the angle of slope, β; the
   stability number, Sn, defined as (c/γ.zc) equals sin β cos β.
   For an infinite slope in a cohesive frictional soil, the stability number, Sn, equals cos^2 β (tan β –
   tan φ). In both these cases, the factor of safety is zc/z, where z is the actual height.


4. For steady seepage and rapid drawdown conditions, both total stress analysis and effective stress
   analysis may be performed. Bishop’s approach is considered more rational for the latter.


5. The factor of safety, F, as per the total stress analysis for a purely cohesive soil is given by

F =

cr

We

(^2) θ
.
, with respect to a trial slip circle of radius r with a central angle θ. The least of such
values is the factor of safety for the slope. The effect of a tension crack is to reduce the value of F.

6. The factor of safety, as per the Swedish method of slices for a cohesive-frictional soil, is given by

F =

cr N

T

θφ+Σ

Σ

tan

.

7. Fellenius’ procedure is useful for the location of the most critical circle. The type of failure sur-
   face is partly dependent upon φ-value. If there exists a hard stratum at or near the base of the
   slope, the slip circle is taken to be tangential to it.


8. The friction circle method is based upon the premise that the resultant reaction along a slip
   surface is tangential to a circle of radius r sin φ, where r is the radius of the slip circle.
   The factors of safety with respect to cohesion and with respect to friction are Fc = c/cm and

Fφ =

tan

tan

,

φ

φ

′

m

respectively, where cm and φm are mobilised values.

9. Taylor’s stability number N is defined as cm/γH; the procedure is based on the friction circle
   method and is an analytical approach. The results are embodied in Taylor’s design charts which
   may be used for determining the factor of safety of a slope or for designing the height for a
   desired safety factor.