Engineering Rock Mechanics

382 Design and analysis of underground excavations

When these values are compared to those in Fig. 20.24 determined from
a boundary element analysis, the approximation is found to have provided
a good early indication of the appropriate stress concentrations. In fact,
from both this and the examples above, simple closed form solutions do
provide a valuable insight into the stress distributions around complex
excavation shapes.

20.2.3 Effect of rock bolting on the stress field

Rock bolts serve two purposes: they act to ensure that the rock around an

opening behaves as a continuum; and they modify the stress field induced

around the opening. Earlier in the book, we discussed the use of rock bolts

to enhance the mechanical integrity of the rock mass. Here, we indicate the

direct influence of installing a rock bolt on the stress field around a circular

opening.

In Figure 20.25 the circumferential stress component on the boundary

of the opening is shown, induced solely by a tensioned rock bolt anchored

at points A and B. The geometry of the installation is shown in the upper

left-hand diagram of Fig. 20.25, and the distribution of the induced

tangential stress component is shown in the upper right-hand diagram. The

maximum induced stress is at the bolt head, where a tensile stress with a

magnitude of 0.99P/u is developed, and at an angular distance of 90" the

induced stress has effectively diminished to zero. When a circular opening

is subjected to an internal pressure of magnitude p, the corresponding

induced tangential stress is -p. Thus, the effect of installing a rock bolt is

similar, given that the applied load of P has been normalized by dividing

by a, the radius of the opening.

In the lower part of Fig. 20.25, the tangential and radial stress distri-

butions in the rock mass along the rock bolt length are shown. There is a

Stresses shown are

from BEM analysis

0.82~~

k = 0.5

1 .35pz

Tensile I .6 Ipz

Region of

Figure 20.24 Application of closed form solutions to the analysis of a complex

boundary shape.