W

.'. F = / .-E[c'l + W(cos a - ru sec a) tan 4>']

EW sin a

This formula gives a solution generally known as the conventional method which allows rapid determination of F when sufficient slip circles are available to permit the determination of the most critical. For analysing the stability of an existing tip it should prove perfectly adequate.

In the case of an earth embankment F is usually considered to be satisfactory if it is not less than 1.25, and for economic reasons it should not be designed for a greater F value than 1.5.

Bishop's rigorous method

The formula for the conventional method of analysis can give errors of up to 15 per cent in the value of F obtained, although the error is on the safe side since it gives a lower value than is the case. In the construction of new embankments and earth dams, however, this error can lead to unnecessarily high costs and becomes particularly pronounced with a deep slip circle where the variations of a over the slip length are large.

Returning to the equation: R

Let the normal effective force, (P - ul) = P'. Resolving forces vertically:

J C . \ tan <p' . 11 u cos a + — sin a J +F I cos a H--p— sin a

W — 1 ( u cos a + — sin a tan 0 sin a cos a H--—-

0 0