Page 114 - Rock Mechanics For Underground Mining

ROCK STRENGTH AND DEFORMABILITY
Figure 4.12 Two classes of stress– (b) local and macroscopic shear fracture (faulting).
strain behavior observed in uniaxial
compression tests (after Wawersik and
Fairhurst, 1970).
(Figure 4.12). For class I behaviour, fracture propagation is stable in the sense that
work must be done on the specimen for each incremental decrease in load-carrying
ability. For class II behaviour, the fracture process is unstable or self-sustaining; to
control fracture, energy must be extracted from the material.
The experiments of Wawersik and Fairhurst and of subsequent investigators, indi-
cate that, in uniaxial compression, two different modes of fracture may occur:
(a) local ‘tensile’ fracture predominantly parallel to the applied stress;
The relative predominance of these two types of fracture depends on the strength,
anisotropy, brittleness and grain size of the crystalline aggregates. However, sub-
axial fracturing generally precedes faulting, being initiated at 50–95% of the peak
strength.
In very heterogeneous rocks, sub-axial fracturing is often the only fracture mech-
anism associated with the peaks of the a –ε a curves for both class I and class II
behaviour. In such rocks, shear fractures develop at the boundaries and then in the
interiors of specimens, well beyond the peak. This observation is at variance with
the traditional view that through-going shear fracture occurs at the peak. Generally,
these shear fractures, observed in ‘uncontrolled’ tests, are associated with sudden
unloading in a soft testing machine.
In homogeneous, fine-grained rocks such as the Solenhofen Limestone (Figure
4.11), the peak compressive strength may be governed by localised faulting. Be-
cause of the internal structural and mechanical homogeneity of these rocks, there
is an absence of the local stress concentrations that may produce pre-peak crack-
ing throughout coarser-grained crystalline aggregates. In these homogeneous, fine-
grained rocks, fracture initiation and propagation can occur almost simultaneously. If
violent post-peak failure of the specimen is to be prevented, the strain energy stored
in the unfractured parts of the specimen, and in the testing machine, must be removed
rapidly by reversing the sense of platen movement. This produces the artefact of a
class II curve.
It is important to recognise that the post-peak portion of the curve does not reflect
a true material property. The appearance of localised faulting in laboratory tests on
rock and around underground excavations may be explained at a fundamental level
by bifurcation or strain localisation analysis. In this approach, it is postulated that the
material properties may allow the homogeneous deformation of an initially uniform
material to lead to a bifurcation point, at which non-uniform deformation can be
incipient in a planar band under conditions of continuing equilibrium and continuing
homogeneous deformation outside the zone of localisation (Rudnicki and Rice, 1975).
Using a rigorous analysis of this type with the required material properties determined
from measured stress–strain and volumetric strain curves, Vardoulakis et al. (1988)
correctly predicted the axial stress at which a particular limestone failed by faulting
in a uniaxial compression test, the orientation of the faults and the Coulomb shear
strength parameters (section 4.5.2) of the rock.
4.3.8 Influence of loading and unloading cycles
Figure 4.13 shows the axial force–axial displacement curve obtained by Wawersik
and Fairhurst (1970) for a 51 mm diameter by 102 mm long specimen of Tennessee
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