Engineering Rock Mechanics

Design against structural/y-contro//~ instability 367

e zone I

Figure 20.7 Simple model of rock bolts in stratified roofs.

the excavation side walls in the right-hand diagram correspond to the trend
of the excavation in the left-hand diagram. The dotted lines in both parts
of Fig. 20.8 represent the base edges and upper edges of the block, as these
are formed by the intersections of the discontinuity planes. This
demonstrates the geometric congruence of the lower-hemispherical pro-
jection and the plan view.
In a similar way to the calculation of the rock bolting requirements in a
stratified roof (Fig. 20.7), a bolting configuration can now be established for
any discontinuity geometry, assuming that the objective is to support the
deadweight of individual blocks as calculated in Fig. 20.8. The circum-
stances may not be as simple as accounting for individual blocks because
of the possibility of smaller blocks being formed behind the largest block
identified and, hence, it is necessary to determine the bolt lengths by estab-
lishing the optimal anchorage positions.
If the block is not falling but sliding then there is an element of constraint,
and the calculations can be modified to account for this frictional resistance,

N I Trend of

eation

Af = ill12 sin €Il2 = L1 1 sin €Iz3 = i1311 sin e,, and h = 1

Block volume, V = ihAf block weight, W = yV support pressure, p =w =$ yh

223 112 tan PI2 =^1123 tan p23 = 1,31 tan P,,

Af

thus Af = 10.07m2, h = 1.48m, V = 4.97m3, W = 114.3kN and p = 11.35kPa for the example here.

Figure 20.8 Lower-hemispherical projection of three discontinuity planes, and the

associated maximal tetrahedral block in the roof of an excavation with given width

and orientation.