Engineering Rock Mechanics

468 Questions^7 6.7 -^7 6.7 0: rock reinforcement and rock support

support

Rock pressure

displacement

Rock

displacement

With reference to these curves, explain:

(a) why the in situ stress condition before excavation cannot be re-estab-

lished by the support pressure applied after excavation;

(b) why it is inappropriate for an engineer to insist that the rock should

be supported in such a way that no displacement whatsoever occurs.

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 rock
has occurred; and
(b) the lining is installed following a radial convergence of 1 mm.

Q16.10 The sketch shows a pillar of rectangular
cross section, which is very long in the y-direction
(i.e. out of the plane of the paper) and is made of a
linearly elastic isotropic rock. A support pressure is
applied to the horizontal sides of the pillar through
the action of springs that pass horizontally through
the pillar.
(a) Develop an expression linking the vertical
stress, a,, to the support pressure, p, in terms of the
elastic constants of the pillar material and the spring stiffness. Use this
expression to show that, for zero horizontal strain of the pillar, the ratio
of vertical stress to support pressure is (1 - u)/u.
(b) If the strength of the pillar can be described by the Hoek-Brown
criterion with a, = 37 MPa, s = 1 and m = 15, and the elastic modulus
and Poisson’s ratio of the rock are 75 GPa and 0.27, respectively, what
spring stiffness is required if the pillar is to withstand a vertical stress of
55 MPa?

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