Engineering Rock Mechanics

470 Questions 17.7- 7 7.7 0: foundation and slope instability mechanisms

417.2 Consider extending the method of equilibrium analysis for plane
failures (see Q16.3) to the case of retaining walls. The failing block, ABC
in the sketch below, is restrained in three cases by the application of load
to the vertical face, AB:
(a) by a horizontal force of magnitude T acting through the centroid of

(b) by a horizontally acting uniform pressure distribution p from the top

(c) by a pressure distribution varying linearly from zero at the top of the

In each case, derive an expression for the factor of safety and, for the

the block;

of the face to the point where the failure plane daylights; and

face to q at the point where the failure plane daylights.

special case of F = 1.0, give an expression for T, p or q as appropriate.

*11. Case a)

417.3 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 B/ sin kt, and the
angles B and 6 are defined as shown below.

vie

of

For the particular case of wedge instability in a slope of orientation
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 29", determine Fw.

4 17.4 Determine an upper bound for the collapse pressure, p, for the
foundation shown below consisting of three rock wedges formed by the
fracture sets in the rock mass.