Stability of Slopes - Elements of Soil Mechanics - page 386

Chapter 13

Stability of Slopes

13.1 Planar failures

Soils such as gravel and sand are collectively referred to as granular soils and normally exhibit only a
frictional component of strength. A potential slip surface in a slope of granular material will be planar and
the analysis of the slope is relatively simple. However, most soils exhibit both cohesive and frictional
strength and purely granular soils are fairly infrequent. Nevertheless a study of granular soils affords a
useful introduction to the later treatment of soil slopes that exhibit both cohesive and frictional strength.
Figure 13.1 illustrates an embankment of granular material with an angle of shearing resistance, φ ′ , and
with its surface sloping at angle β to the horizontal.
Consider an element of the embankment of weight W:

Force parallel to slope = W sin β
Force perpendicular to slope = W cos β

For stability,

Restraining forces
Factor of safety F

Sliding forces =

( )

i.e.

′

W cos β tan φ

W sin β =

F

tan
tan

φ
β

′

⇒ = F

For limiting equilibrium (F = 1), tan β = tan φ ′ , i.e. β = φ ′ .
From this it is seen that (a) the weight of a material does not affect the stability of the slope, (b) the
safe angle for the slope is the same whether the soil is dry or submerged, and (c) the embankment can
be of any height.
Failure of a submerged sand slope can occur however, if the water level of the retained water falls
rapidly while the water level in the slope lags behind, as seepage forces are set up in this situation.

13.1.1 Seepage forces in a granular slope subjected to rapid drawdown

In Fig. 13.2a the level of the river has dropped suddenly due to tidal effects. The permeability of the soil
in the slope is such that the water in it cannot follow the water level changes as rapidly as the river, with