Geotechnical Engineering

DHARM

330 GEOTECHNICAL ENGINEERING

Table 9.1 Fellenius’ values for α and δ for the different values of β

S.No. Slope Angle of slope β Angle α at base Angle δ at top

1 1 : 5 11°.32 25° 37°

2 1 : 3 18°.43 25° 35°

3 1 : 2 26°.57 25° 35°

4 1 : 1.50 33°.79 26° 35°

5 1 : 1 45° 28° 37°

6 1 : 0.58 60° 29° 40°

This procedure is not applicable in its original form to cohesive-frictional soils; however,

Jumikis (1962) modified it to be applicable to c – φ soil, provided they are homogeneous. The

modified procedure is shown in Fig. 9.14.

H

P

H

4.5 H

Curve of

factor of safety

Fmin

O 1

Possible

positions

of O Centre of

critical circle

Fig. 9.14 Fellenius’ procedure, modified by Jumikis for
a c – φ soil for the centre of the critical circle
The centre of the Fellenius’ circle, O 1 , is fixed as given earlier. Then a point P is fixed
such that it is 2H below the top of the slope and 4.5H horizontally from the toe of the slope, H
being the critical height of the slope. The centre of the critical circle O, lies on the line PO 1
produced beyond O 1. The distance O 1 O increases with the angle of internal friction. After a few
trials with centres lying on PO 1 produced, the critical circle is located as the one which gives
the minimum factor of safety.
These procedures becomes less reliable for non-homogeneous conditions such as irregu-
lar slope or the existence of pore water pressures.
Typical Failure Surfaces
A study of the various types of slip that can occur is helpful in determining a reasonable
position of the centre of a trial slip circle.
The following information relating to homogeneous soils is relevant.