5.6 Bishops 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 nth slice have been drawn as shown in Figure 7. Here



 

If we introduce the factor of safety with respect to cohesion as FOSc and that with respect to friction as   defined as

Where, c is the cohesion strength,  is the angle of friction, while cd 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