Geotechnical Engineering

DHARM

554 GEOTECHNICAL ENGINEERING

and y, with respect to the outer edge, B, of the footing may be obtained from Wilson’s chart,
shown in Fig. 14.5.

1.5

1.0

0.5

x/b and y/b

0 0.5 1.0 1.5 1.75

y/b

x/b

D/bf
Fig. 14.5 Wilson’s chart for location of centre of critical
circular arc for use with Fellenius’ method
Wilson found that the net ultimate bearing capacity by this method has an almost ex-
actly linear variation with the depth to breadth ratio upto a value of 1.5 for this ratio. Wilson’s
results lead to the following equation for the net ultimate bearing capacity of long footings
below the surface of highly cohesive soils:

qnet ult = 5.5c (1 + 0.38Df /b) ...(Eq. 14.40)
It can be demonstrated that the critical circle for a surface footing is as shown in Fig.
14.6 and that the ultimate bearing capacity is given by:

qult = 5.5c ...(Eq. 14.41)
The method is particular useful when properties of soil vary in the failure zone ; in this
case Wilson’s critical circle may be tried first and other circles nearby may be analysed later to
arrive at a reasonably quick solution.

qult

b

23 12° ¢

O

Centre of critical circle

Fig. 14.6 Location of critical circle for surface footing in Fellenius’ method

14.5.4Prandtl’s Method

Prandtl analysed the plastic failure in metals when punched by hard metal punchers (Prandtl,
1920). This analysis has been adapted to soil when loaded to shear failure by a relatively rigid
foundation (Prandtl, 1921). The bearing capacity of a long strip footing on the ground surface
may be determined by this theory, illustrated in Fig. 14.7.

The assumptions in Prandtl’s theory are:

(i) The soil is homogeneous, isotropic and weightless.