Bearing Capacity and Shallow Foundations - Elements of Soil Mechanics - page 259

Fig. 9.4 Location of centre of critical circle for use with Fellenius' method.

For a surface footing the formula for q u is:

q = 6 28 . c u u

This value is high because the centre of rotation is actually above the base, but in practice a series of
rotational centres are chosen and each circle is analysed (as for a slope stability problem) until the lowest
q u value has been obtained. The method can be extended to allow for frictional effects but is considered
most satisfactory when used for cohesive soils; it was extended by Wilson ( 1941 ), who prepared a chart
(Fig. 9.4) which gives the centre of the most critical circle for cohesive soils (his technique is not applicable
to other categories of soil or to surface footings).
The slip circle method is useful when the soil properties beneath the foundation vary, since an approxi-
mate position of the critical circle can be obtained from Fig. 9.4 and then other circles near to it can be
analysed. When the soil conditions are uniform Wilson's critical circle gives

q = 5 52 . c

u u

for a surface footing.

9.3.3 Plastic failure theory
Forms of bearing capacity failure

Terzaghi ( 1943 ) stated that the bearing capacity failure of a foundation is caused by either a general soil
shear failure or a local soil shear failure. Vesic ( 1963) listed punching shear failure as a further form of
bearing capacity failure.

(1) General shear failure
The form of this failure is illustrated in Fig. 9.5, which shows a strip footing. The failure pattern is clearly
defined and it can be seen that definite failure surfaces develop within the soil. A wedge of compressed
soil (I) goes down with the footing, creating slip surfaces and areas of plastic flow (II). These areas are
initially prevented from moving outwards by the passive resistance of the soil wedges (III). Once this
passive resistance is overcome, movement takes place and bulging of the soil surface around the
foundation occurs. With general shear failure collapse is sudden and is accompanied by a tilting of
the foundation.