Ultimate Bearing Capacity for Local Shear Failure: Equations for the Lower Bound Values for the Various Types of Footings.

When a soil fails by local shear, the actual shear parameters c and Ø are to be reduced as per Terzaghi
(1943). The lower limiting values of c and Ø are

The equations for the lower bound values for the various types of footings are as given below.
Strip Foundation

Square Foundation

Circular Foundation

Rectangular Foundation

where Nc , Nq and Nγ are the reduced bearing capacity factors for local shear failure. These factors may be obtained either from Table 12.1 or Fig. 12.7 by making use of the friction angle Ø.