Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Engineering, 1988. / Mining induced fracturing and associated deformations can commonly be observed around
deep gold mining excavations. As the rockmass behaviour and the stability of the
excavations are directly influenced by these processes, a proper understanding of this
influence would certainly improve current mining practices with respect to blasting, rock
breaking, support design and mining lay-outs.
The main subject of this thesis is the physics of failure and post failure behaviour of rock
and similar materials. Failure is denned here as a state at which the material has been
subjected to fracture and/or damage processes. The applicability of commonly used
constitutive models in representing such failure and post failure processes has been
investigated mainly by means of numerical simulations. Mechanisms which control
fundamental fracture and damage processes have been analysed by comparing the results
from relevant laboratory experiments with numerical models.
Linear elastic fracture mechanics has been applied to explain and simulate the formation of
large scale extension fractures which form in response to excessive tensile stresses. Using
the flaw concept it is demonstrated that these fractures not only initiate and propagate from
the surface of an opening in compressed rock, but that so called secondary fracturing can
be initiated from within the solid rock as well. The effect of geological discontinuities such
as bedding planes, faults and joints on the formation of (extension) fractures has also been
investigated and it has been shown how the presence of such discontinuities can cause the
formation o f additional fractures.
Micro mechanical models have been, used to investigate the interaction and coalescence
processes of micro fractures. It was found that the formation of large scale extension
fracturing can be explained from such processes, but so called shear fractures could not
directly be reproduced, although such a possibility has been claimed by previous
researchers. The formation of shear fractures is of particular- interest as violent failure of
rock, which is subjected to compressive stresses only, is often associated with such
fractures. In an all compressive stress environment, only shear deformations would allow
for the relief of excess stress and thus energy.
The formation of shear fractures is associated with complex mechanisms and shear
fractures can therefore not directly be represented by tingle cracks. In contrast to the
propagation of tensile fractures, which can readily be explained by traditional fracture
mechanics in terms of stress concentrations around the crack tip, the propagation of shear
fractures requires a different explanation. In this thesis an attempt has nevertheless been
made to reproduce shear fractures by direct application of fracture mechanics. This his
been done by representing a shear fracture as a single crack and by assuming fracture
growth criteria which are either based on critical excess shear stresses, or on a maximum
energy release. Both criteria are completely empirical and require a value for the critical
shear resistance in the same way as a critical tensile resistance is required to represent the
formation of tensile fracture; , The determination of a critical tensile resistance ( Kk ) is
relatively straight forward, as the formation of tensile fractures from a pre-existing flaw
can be reproduced and observed in standard laboratory tests. The determination of a critical
shear resistance is, however, not a common practice, as the formation of a shear fracture
from a pre-existing flaw is very infrequently observed.
The application of shear fracture growth criteria nevertheless resulted in plausible fracture
patterns, which suggests that such criteria are realistic. It is argued here however that the
formation of shear fractures cannot be associated with primary fracture growth, but rather
with the localisation of failure and damage in an area which is subjected to plastic
deformation. The application of fracture mechanics is therefore not correct from a
fundamental point of view as these processes are not represented. For this reason plasticity
theory has also been applied in order to simulate failure in general, and shear failure
localisation in particular. It was in principle possible to reproduce the shear fractures with
the use of this theory, but numerical restraints affected the results to such an extent that
most of the simulations were not realistic. Plasticity theory can also be extended to include
brittle behaviour by the use of so called strain softening models. The physical processes
which lead to brittle failure are however not directly represented by such models and they
may therefore not result in realistic failure patterns. It was in fact found that strain
softening models could only produce realistic results if localisation of failure could be
prevented. The effect of numerical restraints becomes even more obvious with a strain
softening model in the case of failure localisation.
While the plasticity models appear inappropriate in representing brittle failure, they
demonstrated that plastic deformations can be associated with stress changes which may
lead to subsequent brittle fracturing. Although only indirect attempts have been made to
reproduce this effect, as appropriate numerical tools are not available, it is clear that many
observations of extension fracturing could be explained by plastic deformations preceding
the brittle fracturing processes. Many rocks are classified as brittle, but plastic deformation
processes often occur during the damage processes as well. The sliding crack for instance,
which is thought to represent many micro mechanical deformation processes in rock,
directly induces plastic deformations when activated. A pure brittle rock, which may be
defined as a rock in which absolutely no plastic deformation processes take place, may
therefore only be of academic interest as it is inconceivable that such a rock materiel exists.
Only in such an academic case would (linear) elastic fracture mechanics be directly
applicable. As plastic deformation processes do play a role in real rock materials it is
important to investigate their influence on subsequent brittle failure processes. The elastic
stress distribution, which is often used to explain the onset of brittle fracturing, may be
misleading as plastic deformations can substantially affect the stress distribution . -recediny
fracture initiation.
In an attempt to combine both plastic and brittle failure, use has been made of tessellation
models, which in effect define potential fracture paths in a random mesh. The advantage of
these models is that various failure criteria, with or without strain softening potential, can
be used without the numerical restraints which are normally associated with the
conventional continuum models. The results of these models are also not free from
numerical artefacts, but they appear to be more realistic in general. One o f the m;ij, r
conclusions based on these results is that shear failure does not occur in a localised
fashion, but is associated with the uniform distribution and extension of damage. Shear
failure, which can be related directly to plastic failure, can however induce brittle, tensile,
failure due to stress redistribution.
While the theories of fracture mechanics and plasticity are well established, their
application to rock mechanical problems often leads to unrealistic results. Commonly
observed firacture patterns in rock, loaded in compression, are most often not properly
reproduced by numerical models for a combination of reasons. Either a model concentrates
on the discrete fracturing processes, in which case the plastic deformation processes are
ignored, or plasticity is represented, but brittle failure is pooxiy catered for. While
theoretically a combination of these models might lead to better representations and
simulations, numerical problems do affect all models to a certain extent and a practical
solution is not immediately available. The results of numerical models can therefore only
be analysed with caution and the underlying assumptions and numerical problems
associated with a particular technique need to be appreciated before such results can be
interpreted with any sense. Many of the problems are identified here and this may assist
researchers in the interpretation of results from numerical simulations.
Laboratory experiments, which have been chosen for analyses, involve specimens which
have been subjected to compressive stresses and which contain openings from which
failure and fracturing is initiated. Such specimens are less subjective to boundary
influences and are far more representative of conditions around mining excavations than
typical uni- and tri-axial tests. The uniform stress conditions in these latter tests allow
boundary effects to dominate the stress concentrations, and thus failure initiation, in the
specimens. The large stress gradients, which can be expected to occur around underground
excavations, are not reproduced in such specimens. As a consequence failure is not
u atained within a particular area, but spreads throughout the complete specimen in the
uni- and tri-axial tests. Specimens containing openings are therefore far more likely to
reproduce the fracture patterns which can be observed around deep level mining
excavations.
Numerical simulations of brittle, tensile fracturing around mining excavations resulted in
consistent fracture patterns. Fracture patterns could however be strongly influenced by the
presence of geological (pre-existing) discontinuities such as bedding planes. Although
tensile stresses are often assumed to be absent around deej: <y vel excavations because
typical hanging- and foot-walls are subjected to compressive horizontal strain and thus
stress, the numerical models identified alternative locations o f Ix 'sile stress and also
mechanisms which could induce secondary tensile stresses, A failure criterion has
therefore been identified as the most likely cause of large scale fracturing while shear
fracturing may only occur in the absence of such tensile stresses .and only as a consequence
of failure localisation in damaged rock rather than fracture propagation (in solid rock).
Geological discontinuities can easily induce tensile stresses vVher mobilised and may even
replace the mining induced fractures by offering a more efficient meat s for energy release.
The latter possibility is a true three dimensional issue which has not be en addressed any
further in this study, but may be very relevant to jointed rock.
Although dynamic failure has not directly been addressed, one of the micliamsms lor
brittle, and thus stress relieving, failure under compressive strass conditi ons has been
investigated in detail, namely shear fracturing. Shear fractures are effect vely the only
discontinuities which allow for stress relief under such conditi ons', in the ibaence of preexisting,
geological discontinuities, and are therefore quite rele vant to dynamic rock
failure, such as rock bursts, in deep level mining conditions. Potential mechanisms for
shear fracture formation and the numerical simulation of these features have been
investigated and this may especially assist further research into rock bursts.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/13969 |
| Date | 26 February 2014 |
| Creators | Kuijpers, J.S. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf, application/pdf |
Page generated in 0.0024 seconds