Engineering Rock Mechanics

Rock support 275

displacements are proportional to the radius of the opening and inversely
proportional to Young's modulus. Moreover, any deviation from CHILE
behaviour towards DIANE characteristics results in increased displacement
values.
The rock stabilization strategy can be based on the need to restrict the
displacements as governed by the engineering objective. The ground
response cume is a graph of the support pressure required to maintain
equilibrium of the boundary at a given displacement value versus the
displacement value. The ground response curves shown in Fig. 16.6
illustrate this relation for the cases of linearly elastic, 'stable' non-elastic and
'unstable' non-elastic behaviour.
Where the elastic ground response curve intersects the boundary
displacement axis in Fig. 16.6(a), the u,-value is found from the expression
above: this point represents total elastic deformation of the boundary of
the excavation and no support pressure is required, providing that the
magnitude of this displacement is acceptable. For most rock engineering
situations, such an elastic displacement will be less than 0.1% of the radius
and will be acceptable.
Considering the 'stable' non-elastic curve of Fig. 16.6(a), the intersection
of the curve with the boundary displacement axis occurs at a higher
displacement value, say up to 10% of the radius. Whether such a displace-
ment is acceptable or not depends on the engineering objective: for
example, in a high-speed rail tunnel it may be unacceptable, whereas in a
temporary mine opening it may be tolerable.
Finally, the curve in Fig. 16.6(a) corresponding to 'unstable' non-elasticity
definitely indicates the need for support, because the curve does not inter-
sect the boundary displacement axis, i.e. the opening will collapse without
support. Because of the general nature of the ground response curve
concept and the ability to study a variety of associated factors, it has become
a widely used semi-empirical tool in the design of support for excavations.
As an example of the utility of the ground response curve method,
consider the curves in Fig. 16.6(b), which are similar to those in Fig. 16.6(a)
but occur when the same rock mass is excavated by different methods.

Unstable

non-elastic

Stable

Boundary displacement

(a)

Curve I: 'perfect' excavation

Curve 2: machine excavation

Curve 3: good quality blasting

Curve

Curve 4

Curve 3

Boundary displacement

(b)

Figure 16.6 Ground response curves in (a) different types of rock and (b) in the

same rock type but excavated by different methods.