Engineering Rock Mechanics

294 Surface excavation instability mechanisms

Line of intersection

I

face

Wedge

/ Direction of sliding

Forces on wedge

View perpendicular

to line of intersection

W sin (Ji

View along

line of intersection

W cos (Ji

Figure 17.7 Geometry of static analysis of friction-only wedge instability.

17.1.3 Wedge sliding

The previously presented method of analysing the basic mechanism of
plane sliding can be adapted to the case of wedge sliding. Wedge sliding
is illustrated in Figs 17.2(c) and 17.3(c), and the extension from plane sliding
is to consider sliding on the two sliding planes simultaneously. In Fig. 17.7,
the geometry of the wedge instability and the primary forces acting on the
system are shown. The problem has been simplified to one in which there
is no cohesion on either sliding plane, and both of the planes possess the
same angle of friction. A solution to the comprehensive problem, in which
both planes possess differing cohesion and angles of friction, as well as
the existence of a water-filled tension crack, is presented by Hoek and
Bray (1977).
Assuming that the direction of sliding is parallel to the line of intersection
of the two sliding planes, forces parallel to this line and perpendicular to
the two sliding planes can be resolved in order to determine the factor of
safety. This analysis leads to

F= (RA + REJtan$J

W sin yi

W cos yi sin p

sin 6

and RA + R, =