Page 122 - Rock Mechanics For Underground Mining

ROCK STRENGTH AND DEFORMABILITY

was carried out on a limestone with a constant value of 3 = 69 MPa, but with various
levels of pore pressure in the range u = 0 − 69 MPa applied. There is a transition
from ductile to brittle behaviour as u is increased from 0 to 69 MPa. In this case,

mechanical response is controlled by the effective confining pressure, = 3 − u,
3
calculatedusingTerzaghi’sclassicaleffectivestresslaw.Forlesspermeablerocksthan
this limestone, it may appear that the classical effective stress law does not hold. Brace
and Martin (1968) conducted triaxial compression tests on a variety of crystalline
−3
−1
silicate rocks of low porosity (0.001–0.03) at axial strain rates of 10 –10 −8 s .
They found that the classical effective stress law held only when the strain rate was
less than some critical value which depended on the permeability of the rock, the
viscosity of the pore fluid and the specimen geometry. At strain rates higher than the
critical, static equilibrium could not be achieved throughout the specimen.

4.4.4 Polyaxial compression ( 1 > 2 > 3 )
These tests may be carried out on cubes or rectangular prisms of rock with different
normal stresses being applied to each pair of opposite faces. The difficulties caused by
end effects are even more marked than in the comparable case of biaxial compression
(section 4.4.2). By the addition of an internal fluid pressure, the hollow cylinder
biaxial compression test may be converted into a polyaxial test. Hoskins (1969) gives
a detailed account of such tests. However, the test also suffers from the difficulties
noted for the hollow cylinder biaxial compression test.
The results of polyaxial compression tests on prismatic specimens are often con-
flicting, but generally indicate some influence of the intermediate principal stress, 2 ,
on stress–strain behaviour. Generally, the peak strength increases with increasing 2
for constant 3 , but the effect is not as great as that caused by increasing 3 by a
similar amount (Paterson, 1978). However, doubts must remain about the uniformity
of the applied stresses in these tests and the results should be interpreted with great
care.

4.4.5 Influence of stress path
In the tests described in the preceding sections, it is usual for two of the principal
stresses ( 2 and 3 ) to be applied and held constant and for the other principal stress
( 1 ) to be increased towards the peak strength. This stress path is not necessarily that
which an element of rock influenced by an excavation will follow when the excavation
is made.
As an example, consider a long excavation of circular cross section made in an
elasticrockmassinwhichtheinsituprincipalstresseswere p vertically, p horizontally
parallel to the axis of the excavation, and 0.5p horizontally perpendicular to the axis.
Results to be presented in Chapter 7 show that on completion of the excavation,
the principal stresses at mid-height on the boundary of the excavation change from
1 = p, 2 = p, 3 = 0.5p,to 1 = 2.5p, 2 = (1 + )p where is Poisson’s ratio
of the rock, and 3 = 0. As a result of excavation, two principal stresses are increased
and the other decreased. It is necessary to determine, therefore, whether the behaviour
described earlier is stress-path dependent or whether it is simply a function of the
final state of stress.
A test of considerable relevance in this regard is the triaxial extension test which is
carried out in a triaxial cell with the confining pressure, r , greater than the axial stress,
a . The test may be commenced at a = r with a being progressively reduced so that
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