Fig. 8.7 Variation of the coefficient Nc with depth (after Skempton, 1951).

The coefficient Nq allows for the surcharge effects due to the soil above the foundation level and N7 allows for the size of the footing, B. The effect of N7 is of little consequence with clays, where the angle of shearing resistance is usually assumed to be the undrained value, </>u, and assumed equal to 0°, but it can become significant with wide foundations supported on cohesionless soil.

Terzaghi's solution for a circular footing is:

qu = 1.3cNc + 7zNq + O.37BN7 (where B = diameter) (7)

For a square footing:

and for a rectangular footing:

Skempton (1951) showed that for a cohesive soil (<j> = 0°) the value of the coefficient Nc increases with the value of the foundation depth, z. His suggested values for Nc, applicable to circular, square and strip footings, are given in Fig. 8.7. In the case of a rectangular footing on a cohesive soil a value for Nc can either be estimated from Fig. 8.7 or obtained from the formula:

with a limiting value for Nc of Nc = 7.5(1 +0.2B/L) which corresponds to a z/B ratio greater than 2.5 (Skempton, 1951).

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