Engineering Rock Mechanics

Design against stress-controlled instab;/;?/ 387

response curve and the available support line, such that practical support
pressures are generated at tolerable radial displacements. With reference
to Fig. 20.28:

(a) support type 3 (the shotcrete ring) may be both too stiff and installed

too early, as it generates unnecessarily high support pressures;

(b) support type 4 (early installed rock bolts) is ideal for the roof;

(c) support type 1 (well installed steel sets) is similarly successful;

(d) support type 2 (poorly installed steel sets) is insufficent because the sets

yield at a support pressure less than that required to support the

roof;

(e) support type 5 (late installed rock bolts) is unsatisfactory because of

the danger of the bolts being unable to maintain equilibrium of the

excavation periphery at sufficiently low radial displacments, i.e. the

support line may not intersect the ground response curve.

Note that in the preceding discussion, we have been discussing the
effectiveness of the support with respect to roof stability, rather than
the need to restrict sidewall and floor displacements. It is clear from
Fig. 20.28 how one would use this technique to determine other such
support criteria.

Pillar-country rock interaction. A natural extension to the analysis above
is to consider other excavation shapes and natural support methods. Using
the rock itself as the support element, rather than introducing artificial, and
hence more expensive, materials is an elegant engineering solution to rock
engineering projects. This is not always possible, but the concept of the
ground response curve and available support lines can be successfully
extended to the case of supporting the roof and floor during the excava-
tion of a wide rectangular opening (as, for example, occurs during mining
operations in a horizontal tabular ore body).
Consider the support of a slot-like excavation with a large width-to-
height ratio, as illustrated in Fig. 20.29. We proceed according to the
following steps:

(a) first, the displacement that would result should the entire excavation

be opened are determined;

(b) second, the displacement induced by the application of a unit normal

stress over the anticipated support area is determined;

(c) third, the two results are used to produce the ground response curve,

assuming that the rock proximal to the excavation remains linearly

elastic;

(d) fourth, the stress-strain behaviour of a natural pillar is considered, this

being the supporting element;

(e) finally, the analysis described earlier is used to study the stability of the

total structure, as shown in Fig. 20.30.

The ground response curve for the country rock is a straight line fror-1 a

support pressure of 19.3 MPa at zero displacement, to a support pressure