Simplified Bishop Method for Slope Stability
The simplified Bishop method uses the method of slices to discretize the soil mass and determine the FS (Factor of Safety).
This method satisfies vertical force equilibrium for each slice and overall moment equilibrium about the center of the circular trial surface. Since horizontal forces are not considered at each slice, the simplified Bishop method also assumes zero interslice shear forces. Using the notation shown in Figure B.1, the overall moment equilibrium of forces acting on each slice is provided by:
Note that the effective normal and pore pressure forces, acting on the base slice, do not affect the moment equilibrium expression since they pass through the center of the circle. Thus, Bishop’s method should not be applied to compute an FS for non circular surfaces.
If the same FS is assumed for all the slices, the Mohr – Coulomb criterion becomes:
One important limitation for the Bishop method to be correctly applied is that all failure surfaces must be circular.
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