4.1.2 Plane failure analysis along a discontinuity

This type of failure can occur if a single discontinuity is present or a series of discontinuities form a single plane to initiate failure in a slope (figure 2). This failure can be considered as an unstable block of weight (W) resting on a plane surface which is inclined at an angle θ to the horizontal. The height of slope is H and α is the slope angle. The block will try to move along the joint plane AC due to gravity. The factor of safety (FOS) is defined under limit equilibrium method as ratio of shear strength to shear stress.

 

        

                  Figure 2: Geometry of a slope for plane failure

 

Thus,

Factor of safety =

Factor of safety =

Length of discontinuities;   

Area of failure surface; AC x 1 m2 (unit thickness of slope is assumed)

Weight of the unstable block;

Normal Stress;

Shear Stress;

= Shear Stress, MPa

c = Cohesive strength of failure surface, MPa

ф= Friction angle of failure surface, Degree

γ = Density of rock, KN/m3

γw = Density of water, KN/m3

 

Therefore,

Factor of safety =  =