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 RA and RB 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 RA and RB 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 RA and RB, (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 RA and RB can be found by solving the equations as follows:
where FOSW is the factor of safety of the wedge supported by friction only, and FOSP is the factor of safety of a plane failure in which the sliding plane with friction angle φ, dips at the same angle as the line of intersection angle Ө. Wedge factor (K) depends upon the included angle of the wedge ξ and the angle of tilt β of the wedge.