Stability of Slopes - Elements of Soil Mechanics - page 389

Example 13.1: Safe angle of slope

A granular soil has a saturated unit weight of 18.0 kN/m 3 and an effective angle of shear-
ing resistance of 30°. A slope is to be made of this material. If the factor of safety is to
be 1.25, determine the safe angle of the slope (i) when the slope is dry or submerged
and (ii) if seepage occurs at and parallel to the surface of the slope.

Solution:

(i) When dry or submerged:

tan
tan

′ 0 5774

1 25

.

φ
β

F = ⇒ tan β = = 0 462 .

.

⇒ = ° β 25

(ii) When flow occurs at and parallel to the surface:

′ ′

γ tan

tan

φ ( 18 9 81 0 5774

1 25 18

− . ) ×

×

.

F = ⇒ tan β = = 0 210 .

γ β .

sat

⇒ = ° β 12

Seepage more than halves the safe angle of the slope in this particular example.

13.1.3 Planar translational slip

Quite often the surface of an existing slope is underlain by a plane of weakness lying parallel to it. This
potential failure surface (often caused by downstream creep under alternating winter-summer conditions)
generally lies at a depth below the surface that is small when compared with the length of the slope.
Owing to the comparative length of the slope and the depth to the failure surface we can generally
assume that the end effects are negligible and that the factor of safety of the slope against slip can be
determined from the analysis of a wedge or slice of the material, as for the granular slope.
Consider Fig. 13.4. Angle of slope = β , depth to failure surface = z, width of slice = b, and weight of
slice, W = γ zb/unit width.

Fig. 13.4 Planar translational slip.