Engineering Rock Mechanics

Questions and answers: rock reinforcement and rock support 269

(a) The component of the bolt force acting parallel to the slope
can be considered as either a positive restraining component or as
a negative actuating component. Derive an expression for the factor
of safety in both these cases.
(b) For the situation when W = 1000 kN, /3 = 15O, $ = 42O and
4 = 36O, what bolt tension is required to give a factor of safety of
unity for each of the cases?
(c) Examine the behaviour of the two expressions for factor of
safety as the bolt tension varies from 25 kN less than, to 25 kN more
than, the force computed for each case above. Which of these two
expressions should we use for design purposes, when we require a
factor of safety in excess of 1?
(d) Rock bolts function by developing a tensile force within them,
and are sometimes tensioned at the time of installation in order to
generate this force. In the case of untensioned bolts, how is this force
generated? Should we regard untensioned bolts as providing a
positive restraining component or a negative actuating component?
(e) Imagine that we require a factor of safety of three for the rock
block shown above. Should we use tensioned or untensioned bolts?

A16.3 (a) As the strength of the interface between the block and the
slope is purely frictional, we can define the factor of safety
forces resisting sliding -- N tan 4
F= -
forces causing sliding S
where N and S are the shear and normal forces acting across the
interface.
The free body diagram of the block,
with the various forces acting on it
resolved parallel and normal to the in-
terface, is as shown to the right. From
this we obtain
N= Wcos$+Tsinb

wcos w

Tcosp

Wsin ly

and

S= WsinI,brTcos/3.

If we consider that the component

T cos is a negative actuating force, these relations then lead to

(W cos $ + T sinp) tan4

W sin I++ - T cos6

Fa =.