Geotechnical Engineering

DHARM

STABILITY OF EARTH SLOPES 319

strata are present the strata boundaries are assumed to be parallel to the surface. Failure

tends to occur only along a plane parallel to the surface. The stability analysis for such slopes

is relatively simple and it is dealt with for the cases of purely cohesionless soil, purely cohesive

soil and cohesive-frictional soil; the cases in which seepage forces under steady seepage and

rapid drawdown occur are also considered for a purely cohesionless soil.

9.2.1 Infinite Slope in Cohesionless Soil
Let us consider an infinite slope in cohesionless soil, inclined at an angle β to the horizontal, as
shown in Fig. 9.1.

b

T W N

Cohesionless

soil

b

T

W

N

(a) Infinite slope (b) Triangle of forces

Fig. 9.1 Infinite slope in a cohesionless soil

If the weight of an element of the oil mass at the surface is W, the components of W

parallel to and perpendicular to the surface of the slope are T = W sin β and N = W cos β

respectively. The maximum force restraining the sliding action of T is the shear resistance

that could be mobilised by the normal component N. For a cohesionless soil, this is given by N

tan φ or W cos β tan φ, where φ is the angle of internal friction.

The factor of safety F against sliding or failure is given by:

F =

Restraining force

Sliding force

==W

W

cos tan

sin

tan

tan

βφ

β

φ

β

...(Eq. 9.1)

For limiting equilibrium (F = 1),

tan β = tan φ

or β = φ.

Thus, the maximum inclination of an infinite slope in a cohesionless soil for stability is
equal to the angle of internal friction of the soil. It is interesting to note that the stability is
affected neither by the unit weight of the soil nor by the water content, provided seepage
forces do not enter into the picture.

Purely granular soils are infrequent as most soils possess some cohesion, but a study of
the former affords useful introductory ideas to the treatment of cohesive-frictional soils which
are of most frequent occurrence in nature.

Even if a vertical element extending to a finite depth is considered, similar situations
exist and the factor of safety against slippage on a plane parallel to the surface at that depth is
crucial. In terms of the shearing stresses and the shearing strength as defined by the Mohr-
Coulomb envelope, the limit angle of inclination for stability of the slope may be indicated as in
Fig. 9.2.