Geotechnical Engineering

DHARM

STABILITY OF EARTH SLOPES 329

1.56

1.54

1.52

1.50

1.65 1.60

1.70 1.57

1.57

Fig. 9.12 Location of centre of critical circle by contours of factor of safety
The centre of each trial circle is plotted and the value of the corresponding factor of
safety marked near it. After analysing a number of such trial circles, contours of the factor of
safety may be drawn. These will be nearly elliptical. The centre of these ellipses indicates the
most probable centre for the critical circle. It may be noted that the value of the safety factor is
more sensitive to horizontal movement of the centre of the circle than to vertical movement.

If the slope is made out of homogeneous cohesive soil it is possible to determine directly
the centre of the critical circle by a procedure given by Fellenius (1936) which is indicated in
Fig. 9.13.

d

a

b

Fig. 9.13 Centre of critical circle–Fellenius’ procedure
The centre of the critical circle is the intersection of two lines set off from the base and
top of the slope at angles α and δ respectively. The values given by Fellenius for α and δ for
different values of slope angle β are set out in Table 9.1.