Geotechnical Engineering

DHARM

STABILITY OF EARTH SLOPES 337

q

R

f

r

r sinf

r

W C=c.mm

l

q

R

f

r

r sinf

r

Fig. 9.19 Concept of friction circle Fig. 9.20 Forces on the sliding wedge
The total reaction R, strictly speaking, will not be exactly tangential to the friction
circle, but will pass at a slightly greater radial distance than r sin φ from the centre of the
circular arc. Thus, it can be considered as being tangential to modified friction circle of radius
kr sin φ where k is a constant greater than unity, the value of which is supposed to depend
upon the central angle θ and the nature of the distribution of the intergranular pressure along
the sliding surface. The concept will be clear if the reactions from small finite lengths of the arc
are considered as shown in Fig. 9.21, the total value of R being obtained as the vector sum of
such small values.

f

dRm R

f

lc(chord length)

l(arc length)f

dRn

kr sinf

Modified

friction circle

Fig. 9.21 Resultant frictional force-tangential to modified friction circle