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This is the formula for the ultimate bearing capacity, qu. It will be seen that it is not satisfactory for shallow footings because when z = 0 then, according to the formula, qu also = 0.

Bell's development of the Rankine solution for c-(f) soils gives the following equation:

8.3.2 Slip circle methods

With slip circle methods the foundation is assumed to fail by rotation about some slip surface, usually taken as the arc of a circle. Almost all foundation failures exhibit rotational effects and Fellenius (1927) showed that the centre of rotation is slightly above the base of the foundation and to one side of it. He found that in a cohesive soil the ultimate bearing capacity for a surface footing is qu = 5.52c

To illustrate the method we will consider a foundation failing by rotation about one edge and founded at a depth z below the surface of the soil

For (j> = 0°, qu = 7Z + 4c or qu = 4c for a surface footing.

Disturbing moment about O:

Fig. 8.2 Foundation failure rotation about one edge.

Resisting moments about O

Cohesion along cylindrical sliding surface = C7rLB

Cohesion along CD = czL

Weight of soil above foundation level = 7zLB 7zLB2

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