Engineering Rock Mechanics

366

of the arch is such that excessive inter-block compressive stress is
generated, then instability will arise because the strength of the rock blocks
forming the arch elements is reached, the block integrity is prejudiced and
the arch collapses. Finally, buckling instability can occur if the ratio of the
induced compressive stress to the slenderness of the arch becomes too
large-for example, if a thin, highly competent, and thus highly stressed
stratum forms the rock structure.

Design and ana& of underground excavations

Rock bolting. Elastic materials do not fail (because the definition of elas-

ticity is that all strain energy is recoverable). If voussoir arch mechanics is

assisting in the stability of the roof but the roof is vulnerable to pertur-

bations of stresses and strains, rock bolts can be installed in the roof strata,

thus connecting the suite of potential voussoir arches and maintaining

essentially elastic behaviour. This is illustrated in Fig. 20.7. Not only do the

rock bolts reinforce the strata, but any block movement could lead to more

stable conditions, due to the bolt forces being increased.

A first estimate with a simple model of the induced rock bolt tension is

obtained by assuming that each bolt supports the representative prism of

rock surrounding it as shown in Fig. 20.7. If the bolts are arranged on a

square grid with a spacing of s metres and the depth of the rock prism is

D metres, then the tension, T, required is simply the rock prism weight, i.e.

T = yDs2 kN, where yis the unit weight of the rock (kN/m3). For example,

to support strata with a unit weight of^23 kN/m3 for a depth of^3 m using

a rock bolt spacing of^1 m, a rock bolt tension of^69 kN (i.e. close to^7 tonnes)

is indicated.

The calculation tacitly assumes that the bolts are ungrouted and

anchored solely at the end embedded in the rock. With bolts that are

grouted along their length, the support mechanics are more complicated,

but in terms of stabilizing the voussoir arches they are more effective.

20.7.3 Support of falling und sliding blocks

The idea of providing the necessary force to retain blocks in the roof can

be extended to the falling and sliding blocks which were discussed in

Chapter 19. The calculation is achieved by determination of the block

weight for the case of a falling block, with a modification to account for the

angle of sliding and the effect of frictional resistance in the case of a sliding

block. The calculation can be made more rigorous by accounting for the

effect of the stresses present in the rock adjacent to the boundary of the

excavation.

Simplefalling and sliding analysis. The left-hand diagram of Fig. 20.8 shows

a lower-hemispherical projection of three discontinuity planes which,

together with the excavation surface, form a tetrahedral block in the roof

of an excavation. In addition, diametral lines indicating the trend of a long

excavation and the strikes of the three discontinuity planes are included.

In the right-hand diagram of Fig. 20.8, there is a plan view of the associated

largest block that can be formed by these four surfaces, in the roof of an

excavation with a specific width. Note that the dashed lines representing