Page 239 - Rock Mechanics For Underground Mining

PROBLEMS

of installed support in massive rock subject to peripheral failure is to maintain ra-
dial continuity of contact between rock fragments. It also serves to generate a radial
confining stress at the excavation boundary. The mode of action of the support is
to generate and maintain a high triaxial state of stress in the fractured domain, by
mobilising friction between the surfaces of the rock fragments. The significance of
frictional action in the fractured rock can be readily appreciated from equation 7.16.
This indicates that the radius of the fractured zone is proportional to some power of
the friction parameter.
A significant issue neglected in this analysis is the dilatancy of undisturbed, frac-
tured rock. The inclusion of a dilatancy term would result in a significant increase
in the effective angle of friction of the fractured material, and a consequent marked
increase in effectiveness of the installed support.

Problems

1 A long opening of circular cross section is located 1000 m below ground surface. In
the plane perpendicular to the tunnel axis, the field principal stresses are vertical and
horizontal. The vertical stress p is equal to the depth stress, and the horizontal stress
−3
is defined by 0.28p. The unit weight of the rock mass is 27 kN m , the compressive
◦
strength is defined by a Coulomb criterion with c = 20 MPa, = 25 , and the tensile
strength by T 0 = 0.
(a) Predict the response of the excavation peripheral rock to the given conditions.
(b) Propose an alternative design for the excavation.

2 The figure on the left represents a cross section through a long opening. The
magnitudes of the plane components of the field stresses are p xx = 13.75 MPa, p yy =
19.25 MPa, p xy = 4.76 MPa, expressed relative to the reference axes shown.
(a) Calculate the maximum and minimum boundary stresses in the excavation
perimeter, defining the locations of the relevant points.
(b) If the strength of the rock mass is defined by a maximum shear strength criterion,
and the shear strength is 20 MPa, estimate the extent of boundary failure, in terms
of the angular range over the perimeter.
(c) Comment on the significance of this result for any mining operations in the
opening.

3 The figure overleaf shows the locations of two vertical, parallel shafts, each 4 m
in diameter. The pre-mining stress field is defined by p xx = p yy = p zz = 20 MPa.
Estimate approximate values for the boundary stresses around each opening, and
calculate the principal stresses at point A, and their orientations.
4 In the development of a haulage level in a mine, a horizontal opening horseshoe
cross section, 4 m wide and 4 m high, is to be mined parallel to an existing haulageway
of the same cross section and on the same horizon. The field principal stresses are
p(vertical) and 0.5p (horizontal). Ignoring any boundary loosening due to blasting
effects, propose a minimum distance between the centrelines of the haulageways

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