p._ available where F= 1 at failure.

In order to obtain a solution to the problem, slope stability analyses examine the equilibrium of the mass of soil which is being considered. A number of different solutions, therefore, can be derived, depending on the approach taken in the analysis. Methods used to derive the basic equations are:

(1) Force equilibrium of a single slice.

(2) Moment equilibrium of a single slice.

(3) Force equilibrium of the total mass of soil above the slip surface.

(4) Moment equilibrium of the total mass of soil above the slip surface.

For example, Bishop's method combines (1) and (4), Janbu uses

(1) and (3), and Morgenstern and Price use a combination of (1),

(2) and (3). A solution cannot be obtained for the complete stability of the slipped mass without making simplifying assumptions, and therefore it is common to make assumptions concerning the interslice forces E and X (Figure 9.26), for example, in deriving a factor of safety for a circular failure surface. From the definitions of factor of safety:

For moment equilibrium about the centre of the circle:

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