**
5.6 Bishop’s
Simplified Method of Slices **

Bishop (1955) proposed a more refined solution to the ordinary method of slices.
This method is probability is most widely used method for circular failure. When
incorporated into a computer program, it yields satisfactory results in most
cases. In this method, the effects of forces on the sides of each slice are
considered. The forces that act on the n^{th}
slice have been drawn as shown in Figure 7. Here

If we introduce the factor of safety with respect to cohesion as FOS_{c }
and that with respect to friction as defined
as

Where, c is the cohesion strength,
is
the angle of friction, while c_{d }and _{
}_{ }are
the cohesion and friction developed along the potential failure surface.

Summing the forces in the vertical direction gives

Or

For equilibrium of the wedge ABC (Figure 7), taking moment about O gives

Where

Thus

Where

For simplicity, if we assumed then factor of safety become