Page 159 - Rock Mechanics For Underground Mining

PROBLEMS

7 The following results were obtained in a series of direct shear tests carried out on
100 mm square specimens of granite containing clean, rough, dry joints.

Normal stress Peak shear Residual shear Displacement at
strength strength peak shear strength
Normal Shear
n (MPa) p (MPa) r (MPa) v(mm) u(mm)
0.25 0.25 0.15 0.54 2.00
0.50 0.50 0.30 0.67 2.50
1.00 1.00 0.60 0.65 3.20
2.00 1.55 1.15 0.45 3.60
3.00 2.15 1.70 0.30 4.00
4.00 2.60 – 0.15 4.20

(a) Determine the basic friction angle and the initial roughness angle for the joint
surfaces.
(b) Establish a peak shear strength criterion for the joints, suitable for use in the
range of normal stresses, 0–4 MPa.
(c) Assuming linear shear stress-shear displacement relations to peak shear strength,
investigate the influence of normal stress on the shear stiffness of the joints.

8 A triaxial compression test is to be carried out on a specimen of the granite referred
◦
to in Problem 7 with the joint plane inclined at 35 to the specimen axis. A confining
pressure of 3 = 1.5 MPa and an axial stress of 1 = 3.3 MPa are to be applied. Then
a joint water pressure will be introduced and gradually increased with 1 and 3 held
constant. At what joint water pressure is slip on the joint expected to occur? Repeat
the calculation for a similar test in which 1 = 4.7 MPa and 3 = 1.5MPa.
9 In the plane of the cross section of an excavation, a rock mass contains four sets of
discontinuities mutually inclined at 45 . The shear strengths of all discontinuities are
◦
given by a linear Coulomb criterion with c = 100 kPa and = 30 .

◦

Develop an isotropic strength criterion for the rock mass that approximates the
strength obtained by applying Jaeger’s single plane of weakness theory in several
parts.
10 A certain slate can be treated as a transversely isotropic elastic material. Block
samples of the slate are available from which cores may be prepared with the cleavage
at chosen angles to the specimen axes.
Nominate a set of tests that could be used to determine the five independent elastic
constants in equation 2.42 required to characterise the stress–strain behaviour of the
slate in uniaxial compression. What measurements should be taken in each of these
tests?

141