**
4.2 Wedge Failure Analysis **

Failure of a slope in the form of wedge can occur when rock masses slide along two intersecting discontinuities, both of which dip out of the cut slope at an oblique angle to the cut face thus forming a wedge-shaped block. These rock wedges are exposed by excavations that daylight the line of intersection forming the axis of sliding. The size of a wedge failure can range from a few cubic meters to very large slides. Rock masses with well-defined orthogonal joint sets or cleavages in addition to inclined bedding or foliation are generally favorable condition for wedge failure. The geometry of the wedge for analyzing the basic mechanics of sliding is explained in figure 8.

Figure 8: Geometric conditions of wedge failure: (a) pictorial view of wedge failure; (b) stereoplot showing the orientation of the line of intersection

**
4.2.1
Analysis of wedge failure considering only frictional resistance**

The factor of safety of the wedge defined in figure 9, is analysed assuming that
sliding is resisted only by friction and there is no contribution of cohesion.
The friction angle for the both the sliding plane is *φ*. Under this
condition the factor of safety is given by:

where *R*_{A} and *R*_{B} are the normal reactions
provided by planes A and B as illustrated in figure 9, and the component of the
weight acting down the line of intersection is *WsinӨ*. The forces *R*_{A}
and *R*_{B} are found by resolving them into components normal and
parallel to the direction along the line of intersection:

Figure 9: resolution of forces to calculate factor of safety of wedge: (a) view
of wedge looking at face showing definition of angles β and α, and reactions on
sliding Plane R_{A} and R_{B}, (b) stereonet showing measurement
of angles β and α, (c) cross-section of wedge showing resolution of wedge weight
W.

Angles *ξ *and *β *are measured on the great circle containing the
pole to the line of intersection and the poles of the two slide planes. In order
to meet the conditions for equilibrium, the normal components of the reactions
should be equal. Therefore, the sum of the parallel components should equal the
component of the weight acting down the line of intersection. The values of *R*_{A}
and *R*_{B} can be found by solving the equations as follows:

where FOS