Engineering Rock Mechanics

Questions and answers: rock reinforcement and rock support 277

support pressure, it is in theory possible to apply support pressure

such that there is zero radial rock displacement at a given position,

as indicated by the black circle on the support pressure axis in the

sketch below. This could well involve considerable practical problems

and would be expensive.

support

pressure& Zero rock displacement

Rock displacement

However, attempting to insist on zero rock displacement at the ex-

cavation periphery is unnecessary. In the case of curve A, the rock

unloads to a stable position at zero support pressure, so no support is

necessary. If support is installed after some displacement has occurred,

as represented by the dashed line in the sketch, the rock displacement

will be stopped at point SA, where the support line meets the ground

response curve, with less support pressure than that required for zero

displacement.

In the case of curve B, assuming that the rock is not unloading to

a stable position, the installation of support is necessary. If the same

support represented by the dashed line in the sketch is used, the rock

displacement will be stopped at point %, where the support line meets

the ground response curve, again with less support pressure than that

required for zero displacement.

416.9 A tunnel of radius 1.85 m is excavated in rock subjected

to an initial hydrostatic stress field of 20 MPa and provided with a

concrete lining of internal radius 1.70 m. Assuming elastic behaviour

of the rock and lining, calculate the radial pressure and the radial

displacement at the rock-lining interface if:

(a) the lining is installed at the face before any displacement of the

(b) the lining is installed following a radial convergence of 1 mm.

rock has occurred; and

A16.9 (a) We solve this problem by plotting the ground characteristic
(i.e. ground response curve) and the support characteristic (i.e. available
support line) on the same axes, and identifymg where they intersect. This
is the operating or equilibrium point. Firstly, we are told that both the
rock and the lining remain elastic. This means that both characteristics
are straight lines.
To find the ground characteristic we need to identify the two end
points of the line: one is the in situ condition of zero displacement