Engineering Rock Mechanics

292 Foundation and slope instability mechanisms

and the pressure for F = 1 is given by

yH (sin2+ - (1 + cos 214) tan$) - 4c

(sin2$ + (1 - cos 2$) tan$)

9=

411.3 For the case of wedge instability in rock slopes, the factor of
safety can be related to that of an equivalent plane instability (i.e.
plane sliding in the same direction as that of the wedge) by
Fw = kw x Fp

where the wedge factor, kw, is computed from kw = sin jllsin :,$, and
the angles jl and ,$ are defined as shown below.

\

of intersection

For the particular case of wedge instability in a slope of ori-
entation 124/63 (dip direction/dip angle) with a horizontal top,
intersected by two sets of fractures with orientations 182/52 and
046/69 and friction angle 29O, determine Fw.

A17.3 There are two main parts to the solution: to determine the factor
of safety of the equivalent plane instability, and to determine the angles
/3 and 6.
Although the factor of safety for friction-only plane instability is
a well-known result, it is easily confirmed by sketching a free body
diagram of a block on a plane and noting the associated equilibrium
conditions, as shown below.
Resolving forces parallel and normal to,the plane gives
S = W sin+ and N = W cos$

For the equilibrium condition of S = N tan $, we define the factor of
safety as

N tan$

S

Wcos+tan$ tan$

Fp = ___

from which we find

Fp = - -
W sin+ tan +.
This means that the equation for the factor of safety of the wedge
instability can be written as

sin #? tan $

sin i6 tan +

Fw=kwxFp=-x-