## Analytical methods for the determination of the ultimate bearing pressure of a foundation

The ultimate bearing capacity of a foundation is given the symbol qu and there are various analytical methods by which it can be evaluated. As will be seen, some of these approaches are not all that suitable but they still form a very useful introduction to the study of the bearing capacity of a foundation.

### 8.3.1 Earth pressure theory

Consider an element of soil under a foundation (Fig. 8.1). The vertical downward pressure of the footing, qu, is a major principal stress causing a corresponding Rankine active pressure, p. For particles beyond the edge of the foundation this lateral stress can be considered as a major principal stress (i.e. passive resistance) with its corresponding vertical minor principal stress 7Z (the weight of the soil).

"I 7X1

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