Geotechnical Engineering

DHARM

BEARING CAPACITY 553

If φ = 0, we have qult = 4c + γDf , the same as Eq. 14.30, for pure clay.

In other words, for pure clay, the size of foundation does not affect bearing capacity.

14.5.3Fellenius’ Method

The Fellenius method of circular failure surfaces (Fellenius, 1939) may be used to determine
the ultimate bearing capacity of highly cohesive soils. The failure is assumed to take place by
slip and the consequent heaving of a mass of soil is on one side only as shown in Fig. 14.4.
Model tests and observation of failure surfaces confirm this; the possible reasons being lack of
homogeneity of soil and a slight unintended eccentricity of loading.

Df

b

Qult

B DA

O

E

Assumed centre

of rotation

Assumed circular

failure surface

R

W

lr

Ty

l 0

C

qult F

Fig. 14.4 Fellenius’ method of determining bearing capacity
A trial cylindrical failure surface is chosen with centre O, the co-ordinates of which are
x and y with respect to B, the outer edge of the base of the footing. The weight W of the soil
mass within the slip surface for unit length of the footing and its line of action are determined.

The total cohesive force C, resisting the slip surface is determined (C = c. BF

—→
). Qult(= qult. b.
l, since unit length of the footing is considered). It will tend to cause slip, and W and C will tend
to resist slip.

At imminent failure, their moments about the centre of rotation must balance:

Qult. l 0 = W. lr + C. R ...(Eq. 14.37)

or Qult = W.

l

l

C

R

l

r

00

+. ...(Eq. 14.38)

∴ qult =

Wl

bl

CR

bl

Wl CR

bl

.rr. ()

00 0

+=

+

...(Eq. 14.39)

This procedure is repeated for several possible slip surfaces and the minimum value of
qult so obtained is the bearing capacity of the footing.

The method is considered most suitable and satisfactory for cohesive soils, although it
can be extended to allow for friction. Wilson (1941) extended it by preparing a chart for locat-
ing the centre of the most critical circle, applicable only for cohesive soils and for footings
founded below the ground surface. The co-ordinates of the centre of the most critical circle, x