Engineering Rock Mechanics

Rock support 277

be exceeded. This strength may be reached before equilibrium with the
ground response curve is attained. Such an effect can be achieved by the
use of compressible inserts placed between the knuckle joints of pre-cast
concrete segments, or clamped joints in steel arch supports. In a more
precise way, the yielding of the support can be determined by the control
of the fluid pressure in hydraulic rams, a technique used effectively in
longwall mining practice.
There are other engineering conclusions to be drawn from a ground
response curve diagram. No support is necessary to achieve equilibrium
in the elastic and stable non-elastic cases: if support is used in these cases,
the displacement at equilibrium is simply reduced. In the case of the unsta-
ble, non-elastic curve, support must be used. For the case illustrated in Fig.
16.7, the stiff support (e.g. pre-cast concrete segments) will be successful,
but the soft support (e.g. steel arches at 1 m centres) will not bring the
system to equilibrium. Another point that is demonstrated by this diagram
is that the engineer should never attempt to achieve zero displacement by
introducing as stiff a support as possible-this is never possible, and will
also induce unnecessarily high support pressures. The support should be
in harmony with the ground conditions, with the result that an optimal
equilibrium position is achieved.
Through a knowledge of the mechanics of support as illustrated by the
ground response curve and associated available support lines in Fig. 16.7,
a purely observational approach to providing support can be utilized. It has
been seen that it is unnecessary to install stiff support elements at an early
stage: it is better to allow the rock to displace to some extent and then
ensure equilibrium is achieved before any deleterious displacement of the
rock occurs. In practice, it may not be possible to establish the exact form
of the ground response curve, but we can measure the displacement that
occurs, usually in terms of the convergence across an excavation. The
ground response curve and and convergence curves are linked because
they are different manifestations of a single phenomenon.
The three curves in Fig. 16.8 serve as an aid to understanding this linkage.
Commencing with a ground response curve and an available support line,
the information is redrawn as a single curve of the pressure ‘difference’

Ground

(^0) Q Q
,’ Available
,’ support line
Boundary displacement
System response curve
(evolves with excavation
advance. and hence time)
Boundary displacement
(evolves with excavation
advance, and hence time)
I Convergence curve
a,
C
P

c
u
Figure 16.8 Link between ground response curves and observed convergence.