Terzaghi was the first to develop a theory for the evaluation of the ultimate bearing capacity of shallow foundations. His theory assumes that a foundation is shallow if the depth of the foundation is less than or equal to its width. However, it was later suggested that foundations with depth up to 3 or 4 times the width of the foundation might be considered as shallow.
He based his theory on the assumption that the failure surface in soil at ultimate load takes the form shown in Figure 1, thus forming a triangular zone and two bulges delineated by two log spiral curves and extending to the ground surface.
The angles a between the footing base and the sides of the triangle in the triangular zone are assumed to be equal to the soil friction angle, f.
Using the equilibrium analysis, Terzaghi expressed the ultimate bearing capacity in the form:
where Nc, Nq, and Ng are the bearing capacity factors and are only function of the soil friction angle, f.
This equation, however, is subjected to the following restrictions:
As for the case where the foundation is square, the initial Terzaghi equation was modified into:
And for circular foundation:
For foundations that exhibit local shear failure, the basic equation was modified into the following:
where the values of N'c, N'q, and N'g are obtained by replacing f in the equations of Nc, Nq, and Ng by: f’=tan-1 (2/3tanf).
Again, for the case where the foundation is square, Terzaghi modified this equation into:
And for circular foundation:
