1. Recovery of copper sulphides mineral grains at coarse rock fragments
size
Nenad Djordjevic ⇑
JKMRC/SMI, The University of Queensland, Brisbane, Australia, 40 Isles Road, Indooroopilly, Qld 4068, Australia
a r t i c l e i n f o
Article history:
Received 26 March 2014
Accepted 5 June 2014
Available online 25 June 2014
Keywords:
Copper
Chalcopyrite
Liberation
Coarse rock
Crushing
Blasting
a b s t r a c t
Assuming the random distribution of sulphide mineral grains and random rock breakage, a relatively
small percentage of sulphide grains will be exposed on the rock surface. Early liberation of sulphide
grains needs to be considered in terms of the mechanical properties of such grains relative to the prop-
erties of the host rock matrix.
Clustering of sulphide mineral grains, will make early liberation possible. Depending on the nature of
mineral associations, crushing of such rocks will result in different outcomes. Where clustering is manly
of very soft copper minerals, with the host rock being moderately strong feldspars or quartzite’s, the cop-
per rich parts of rock are likely to fragment first, resulting in relatively small size being rich in copper
minerals. However, in the case of moderately strong chalcopyrite, the difference in elastic properties
between chalcopyrite and feldspar or quartz, will not be significant enough to cause a propensity for early
liberation.
Where clustering of copper minerals occurs with grains of pyrite (or magnetite), the stronger part of
the rock fragment will be one rich in valuable minerals. During crushing of such rock, the sulphides rich
zones will fragment in a different way than gangue. Stress concentration within pyrite (or magnetite) will
result in failure of the relatively soft surrounding matrix, thus promoting liberation of chalcopyrite or
chalcocite grains. Therefore, textural information about the associations of sulphide minerals (copper
sulphides vs. pyrite/magnetite/garnet) will be of critical significance in the evaluation of the propensity
for coarse liberation of copper sulphide minerals. An absence of close spatial associations will signifi-
cantly reduce the possibility of early liberation of copper sulphides.
During blasting ore is exposed to sufficiently intense, high-strain rate loading to be able to induce
micro-fracturing originating from individual sulphides mineral grains as well as their clusters. Due to
the high rate of loading, a substantial amount of energy can be dissipated with embryonic rock fragment,
before macro-failure of rock, which will relieve rock of blast induced stress. Created micro-cracks will
play a significant role in subsequent comminution, where rock fragments with enhanced density of
micro-cracks will be crushed more easily. Extensive micro-cracking is also likely to play a significant role
during heap or dump leaching, stimulating infiltration/diffusion of leaching fluids into the interiors of
rock fragments.
Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction
The most important objective of the rock size reduction process
is to release all targeted valuable mineral from the host rock at as
coarse rock fragment size as possible. Achieving this would bring
about huge savings in the overall cost of mineral production. Con-
sidering that the density of metal rich grains, such as sulphides of
copper, are generally much higher than the density of gangue, in
many mines, metal rich sulphides grains represent only 1–2% of
the volume of the mined and processed ore. Therefore, for typical
porphyry copper ore, close to 99% of the treated ore volume is a
costly by-product of the production of copper concentrate.
At present, liberation of such minerals is achieved primarily
through crushing and grinding of ore to a fragment size compara-
ble to minerals grain size (80% passing size 100–300 lm). Rejection
of part of the waste material at a coarser fragment size will greatly
improve the efficiency of mineral recovery (Bearman, 2013). When
final mineral recovery is achieved through processes such as leach-
ing, the more modest objective would be to achieve a high expo-
sure of valuable minerals at as coarse as a rock fragment size as
possible. In the context of this paper, the term liberation is used
http://dx.doi.org/10.1016/j.mineng.2014.06.003
0892-6875/Ó 2014 Elsevier Ltd. All rights reserved.
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E-mail address: n.djordjevic@uq.edu.au
Minerals Engineering 64 (2014) 131–138
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2. in a broader sense, to include not just full liberation of minerals,
but also their substantial exposure on the surface of rock
fragments.
Considering that the cost of rock size reduction is the principal
operational cost of mining/mineral processing, a reduction of the
communication cost could have a very significant impact on the
overall economics of mineral recovery from a particular deposit.
In some cases, this impact may result in some marginal or sub-
economic ore bodies, currently considered as resources, becoming
reclassified into reserves, with subsequent ramifications to the
value of deposits and mining companies.
2. Modelling of liberation of randomly distributed grains
Where sulphide grains are randomly distributed within the vol-
ume of the rock, it is of interest to examine what percentage of sul-
phide grains will be exposed on the surface of rock fragments. By
doing so a base case can be established, i.e., what can be expected
if there is no early liberation of sulphide minerals.
Sulphides are present in the form of numerous grains, their total
number is a function of grade and size. Even in a very marginal ore,
the number of grains is likely to be in the hundreds, (for the rock
fragment size in the range of 30–50 mm). Hsih and Wen (1994)
and Hsih et al. (1995) developed a geometrical model to calculate
the fraction of mineral grains that are exposed on particle surfaces
during comminution of a two-phase ore.
In the case of random breakage, with large number of grains
present within the rock, the fraction of sulphide grains that will
end-up exposed on the rock surface is determine by the ratio of
rock size vs. grain size. Assuming constant grain size, the frac-
tion of available sulphide grains that are partially exposed on
the rock surface will increase with a decrease in rock size, as
expected.
Similarly, for constant size of rock, the fraction of available sul-
phide grains that will be exposed on the rock surface will increase
with an increase of the grain size. So coarse grain mineralization
will be more liberated than fine grain (i.e., greater percentage of
available grains will have some exposure on the rock surface).
For example, assuming that grains size is in the range 0.1–
0.3 mm, for the rock size of 30 mm, application of the model shows
that only about 2–7% of sulphides grains will be exposed on the
rock surface. Therefore, assuming random breakage and random
distribution of sulphide grains, a relatively small fraction of such
grains can be relatively easily recovered from the rock. In such
case, only further reduction of rock fragments size will ensure ful-
ler liberation/surface exposure of valuable sulphide minerals.
In the case of copper ore, the typical grain size of copper miner-
als is often in the range of 0.1–0.3 mm. Difficulties in liberation are
further highlighted by the modest grade of many major copper
deposits ($0.5%Cu). Considering that for chalcopyrite the copper
content is 35%, and copper grade is 0.5%, for uniform distribution
of copper minerals, each grain of chalcopyrite will be surrounded
by 200 grains of gangue minerals. It will be difficult to expect that
the process of rock size reduction will be so efficient as to prefer-
entially liberate such small mineral grains, homogeneously distrib-
uted within volume of rock fragment.
How to define coarse particle liberation; i.e., from which frag-
ment size and above does liberation of valuable minerals becomes
coarse particle liberation? It is possible to assume that the required
final size of fragments coming from comminution is dictated by the
requirements of the next step in the process of mineral recovery. In
the case of sulphide minerals, this is often flotation. In such case,
ore is ground to, at least 300 lm, depending on the size of sulphide
grains. Thus, if valuable minerals can be liberated, fully or partially,
while grinding ore to a size coarser than $300 lm, then that
specific coarser size would represent liberation at coarse fragment
size.
Although the final fragment size of gangue particles could be
coarser than 300 lm, the size of fragments containing valuable sul-
phide grains should remain the same, i.e., under 300 lm (i.e., at the
top size that will maximise their subsequent recovery). For
instance, if ore comminution to top size of 1 mm, would liberate
(fully or partially), all valuable sulphide minerals grains by having
them in the fragment size range up to $0.3 mm; then that would
constitute liberation at coarse fragment size. Obviously, it would
be highly advantageous if such liberation of sulphide minerals
can be achieved at a much coarser fragment size of gangue, for
instance 5 or 10 mm, or even coarser.
At best such early liberation may result in the product of SAG
milling or HPGR crushing, being composed of coarse, almost barren
gangue fragments, and finely crushed sulphide rich fragments. This
creates an opportunity for avoiding highly energy intensive ball
milling or reducing such a need to a minimum. Strongly bimodal
fragment size distribution coming from SAG mill or HPGR, can be
separated into a dominant coarse gangue part and highly enriched
fines (size less than $0.3 mm). In the context of a modest grade of
typical copper ores, it is worth noting that the amount of high
grade fines does not need to be large to contain almost all valuable
minerals present in ore (<5% of total ore mass).
Consideration of the propensity for earlier substantial liberation
of sulphide minerals (while the rock fragments are still coarse),
should start from an analysis of the mechanical properties of valu-
able minerals in the context of properties of host gangue minerals.
3. Elastic properties of minerals
The values of modulus of elasticity of minerals and solid rock
are of critical significance in the evaluation of the propensity for
early liberation, Fig. 1. Related parameters such as strength (in
compression and tension) can be approximated based on knowl-
edge of elastic constants. Vickers hardness is frequently available
and can be used as proxy to elastic constants of minerals.
The most interesting aspect of the above figure is the difference
between the elastic modulus of chalcopyrite and the group of typ-
ical gangue minerals such as feldspars, quartz and calcite. The dif-
ference is not very large. In contrast, the elastic constants of pyrite
and magnetite are much higher than those of the most common
gangue minerals. Other main copper sulphides such as chalcocite
and bornite, due to their much higher copper content and lack of
iron, have an even lower modulus of elasticity than chalcopyrite.
In the course of this work, strength properties as well as elastic
properties are determined through instrumented, computer con-
trolled, micro-indentation testing. In contrast to traditional hard-
ness testing, instrumented indentation testing allows the
Fig. 1. Modulus of elasticity of some common minerals (after Mavko et al., 2009).
132 N. Djordjevic / Minerals Engineering 64 (2014) 131–138

3. application of a specified force or displacement history. Force and
displacement are measured continuously over a complete loading
cycle. In the case of homogenous minerals, testing produce an
indent of highly reproducible size and shape, Fig. 2. From the
unloading part of the load–deformation curve, elastic modulus of
the indented surface can be calculated.
Elastic properties of the same mineral vary depending on the
specific history of mineralization, and presence of impurities within
minerals. However, within the same mineralization the mechanical
properties of a particular mineral tend to vary in a relatively narrow
range. This is illustrated in the case of chalcopyrite, Fig. 3.
Beside elastic parameters, fracture mechanics parameters can
also be of critical significance in evaluating the potential for min-
eral liberation. Particularly from the point of view of whether frac-
turing will occur along the grains boundaries or through the grains,
even in the case of the same types of grains. Results presented by
Tromans and Meech (2002) show that, on average, grain boundary
fracture toughness are lower than trans-granular fracture tough-
ness. By fitting numerical values presented by these authors, we
concluded that grain boundary fracture toughness is lower on
average by about 9% than trans-granular fracture toughness, of
the same minerals, Fig. 4.
At a rate of pressure application (strain rate), typical for commi-
nution equipment, due to their small size, individual mineral grains
will not act as initial flaws from which fractures will be initiated. In
such cases, sulphide grains will not be able to extract themselves,
by initiating fracturing of rock fragment from within. This is con-
firmed by Garcia et al. (2009), who demonstrated through X-ray
micro-tomography, that some breakage along grain boundaries
between chalcocite grain and gangue occurs only during a slow
loading process. At higher loading rates, applicable for rock commi-
nation equipment, breakage occurs primarily by random fracture.
Therefore they concluded that preferential chalcocite grain bound-
ary breakage of examined copper ore will not be achieved with tra-
ditional cone crushers under normal operating conditions.
Therefore, it appears that copper sulphides will be conducive for
early liberation during conventional comminution, only if they are
clustered, forming much larger effective ‘‘grains’’. Such clusters or
‘‘mega grains’’ will then be able to act as local weak zones, which
will influence the initiation of cracks and/or their preferential
propagation. Clustering could be with the same type grains, i.e.
chalcopyrite; or could be with grains of some minerals which have
distinctive properties, that may facilitate early liberation.
4. Role of blasting
In the broader context, blasting can be considered as part of com-
minution. During blasting in-situ ore is exposed to sufficiently
intense, high-strain rate loading to be able to induce micro-
fracturing originating from individual sulphides mineral grains. In
such a way, blasting may pre-condition ore, resulting in more effi-
cient early liberation of valuable minerals in subsequent stages of
the rock size reduction process.
Particularly tensile tail of the stress wave will be able to provide
stress loading conditions required for creation of micro-cracks
within solid rock, Fig. 5. Due to the short duration of such loading
(<0.1 ms), the length of crated cracks will be limited, and may not
result in full crack coalescence (Nemat-Nasser and Horii, 1999).
Micro cracks will be formed either simultaneous or before, creation
of fragments forming macro-fractures. The created micro-cracks
within rock fragments will play significant role in subsequent com-
minution, where fragments with enhanced density of micro-crack
Fig. 2. Size of indent for constant force, indicates that Galena is softer, less elastic,
mineral than Sphalerite.
Fig. 3. Young’s modulus of elasticity of chalcopyrite measured at 11 samples from
same ore.
Fig. 4. Relationship between grain boundary fracture toughness and transgranular
fracture toughness for a range of minerals (modified after Tromans and Meech,
2002).
Fig. 5. Modelled strain-rate time history for ANFO blast in amphibolite, shows
tensile straining (positive values) after initial high intensity compressive loading
(negative initial peak).
N. Djordjevic / Minerals Engineering 64 (2014) 131–138 133

4. will be crushed more easily (Nielsen and Malvik, 1999). Clearly,
rock with stronger degree of heterogeneity, such as one caused
by presence of sulphide minerals grains, will be more prone to cre-
ation of such micro-cracks.
For instance in the case of blasting as method of rock fragmen-
tation, it is more likely that post-blast, smaller rock fragments will
originate from the richer parts of the ore matrix, relative to the
coarser fragments. Blast induced breakage, particularly intensive
breakage, exhibits a preference for those parts of the ore that are
relatively rich in valuable, softer, minerals (Djordjevic, 2002).
Blasting of ore and waste with same the specific amount of
explosive (powder factor), results in significantly different frag-
ment size distributions, Fig. 6. Ore due its heterogeneity is charac-
terised with much finer fragmentation, compared to relatively
homogenous waste rock. This is further manifested in grade distri-
bution, which for particular ore, is strongly biased toward the
smaller fragments, Fig. 7.
This is also in agreement with results presented by Ma et al.
(2011). Through numerical modelling of the strain rate effect on
the failure pattern of heterogeneous material, the authors demon-
strated that in the case of higher strain rate loading (50 and
200 1/s), there is an increased tendency for the development of a
larger number of smaller cracks within the rock sample.
The location of such micro-cracks is linked to the presence of
rock elements with reduced strength. Total deformation energy
introduced intro the sample, until complete loss of residual
strength, in the case of high strain rate loading is much higher than
in the case of low strain rate loading (0.1–1 1/s). This is compen-
sated for by the creation of a greater number of fractures within
the rock in the case of higher strain rate loading.
Due to its unique nature, blast induced strain energy will fill the
void which exists in conventional rock crushing and grinding. Dur-
ing crushing and grinding, rock fragmentation occurs due to the
application of force along the periphery of the rock fragments.
Due to such geometry, spatial energy distribution tends to be a
strong function of the shape of rock and position of the loading
points. The highest intensity being at contact points on the rock
surface and gradual decrease toward the interior. In many cases,
the deformation pattern within rock is critically influenced by
the loading geometry and shape of rock, rather than internal
structure.
Blasting will result in a different pattern of deformation/fractur-
ing, particularly at close distances from the blastholes (with $1 m
from the blasthole). Due to high strain rate of loading, the blast
induced stress wave is able to introduce damage from within rock
fragments. Considering that damage will be frequently initiated
from the grains of sulphide minerals, this could than stimulate
preferential fragmentation of higher grade fragments within the
mineral processing circuit. Using HSBM code (Furtney et al.,
2009) we modelled the occurrence of rock damage as a function
of explosive and rock properties.
For instance modelling of blast of ANFO (density 800 kg/m3
)
within strong amphibolite block, show that 15.8% of produced
fragments are damaged, i.e. with reduced strength than intact rock
of nominally same size. Where same rock was blasted with EMUL-
SION explosive (density 1150 kg/m3
), 21.2% of fragments are dam-
aged; i.e., will be reduced strength, compared to strength of intact
rock matrix, Fig. 8.
Due to higher specific energy (as a result of higher density), the
total number of fragments will also be higher in the case of emul-
sion, compared to ANFO blast. Under relatively constrained condi-
tions of modelled blast, in the case of ANFO 16% of fragments will
be reduced strength, while in the case of emulsion 21% of created
rock fragments will be with reduced strength. What is more inter-
esting is that for emulsion blast, not only that more fragments are
crated but the fraction of fragments that have significant internal
damage is increased by 34% compared to ANFO blast. It is reason-
able to expect that performance of the crushing and grinding will
be significantly improved in the case of blasting with high
energy/high density explosive (Michaux and Djordjevic, 2005).
Volume of rock that will be affected by blast induced damage
strongly depends on the nature of blast design (number and prox-
imity of free/unconstrained rock surfaces, mass of explosive per
unit of rock volume, etc.). But in any case, envelope of rock damage
extends beyond envelope of rock fragmentation, Fig. 9. In such
way, nominally part of solid rock which will remain in place, after
Fig. 6. Fragment size distribution produced by blasting of two types of rock from
the same deposit.
Fig. 7. Copper grade after blasting under same conditions. Homogenous sample is
characterised with uniformly low grade (blue). (For interpretation of the references
to color in this figure legend, the reader is referred to the web version of this
article.)
Fig. 8. Occurrence of damage within blasted rock fragments is function of explosive
type.
134 N. Djordjevic / Minerals Engineering 64 (2014) 131–138

5. the blast, will be precondition for next phase of mining (Djordjevic,
2013a,b).
5. Effect of the mineral clustering
Assuming that valuable minerals grains are of significantly
lower elastic properties/strength than dominant gangue minerals,
and that valuable minerals form a cluster of some kind, elements
of the rock volume which contain such clusters are likely to be
more efficiently fragmented than the adjoining rock volume, which
is relatively poor in valuable minerals, therefore more homoge-
nous. Due to the large difference in mechanical properties of valu-
able minerals and gangue, the ore matrix could exhibit preferential
breakage. Part of the ore matrix, with a larger concentration of the
softer inclusions (valuable minerals), is on average mechanically
weaker than a similar matrix with fewer soft minerals. Rock
strength is proportional to its modulus of elasticity €, with high
modulus rock being of higher compressive strength (UCS). The
ratio between two parameters (E/UCS) varies, depending on
the rock type. For rocks, like granite and similar, the ratio is in
the range 300–500 (Deere and Miller, 1966).
In the comminution process, rock size reduction, is achieved by
straining, to extent controlled by set, reduction ratio (crushers/
HPGR). In other cases, fragmentation is controlled by intensity of
force and contact time (duration of force application). In both of
these scenarios, the application of external force to rock continues
blindly, ignoring the state of mineral liberation or exposure. This
may result in part of the rock with a high concentration of
relatively soft grains, of chalcopyrite for instance, being frag-
mented earlier than the rest of the rock fragment.
In order for micro-cracks to occur, it is necessary for stress con-
centration to occur. The most common cause of stress concentra-
tion is geometrical defects, such as micro-pores. At the boundary
of such pores, the application of external stress may result in stress
concentration sufficient for the initiation of micro-cracks. Another
frequent source of stress concentration is the heterogeneities in the
deformation of individual mineral grains. Due to different elastic
properties, and to some extent the shape, of the ore and gangue
minerals, under load, differential deformation will result in the
development of micro-cracks along the mineral boundaries, (Blair
and Cook, 1998).
This behaviour was modelled using the FLAC finite difference
code (ITASCA, 2000). A relatively soft mineral was embedded into
the hard matrix. Samples were gradually loaded in compression
along the vertical axis. The process of failure was gradual, with
the first failure occurring within the soft mineral. Due to heteroge-
neous deformation along the boundary of the soft minerals and
hard matrix, tensile stress concentration occurs in the matrix, next
to the failed soft mineral.
A further increase in external load causes extension of the
cracks, resulting in macroscopic failure of the modelled rock sam-
ple. In the case of multiple soft minerals, extension of the cracks
is preferential: cracks first connect the soft inclusions, followed
by the creation of the large shear cracks, Fig. 10. Formation of the
macro shear fractures is also influenced by the shape of the rock
sample. From the presented results it is clear that the average
Fig. 9. Extent of rock fracturing (left) and rock damage (right) around blasthole for the case of ANFO blast-5 ms after explosive initiation; rock cube size is 10 Â 10 Â 10 m,
with top face being free boundary.
Fig. 10. Increase heterogeneity of rock, due to presence of relatively soft grains, results in improved fragmentation, under slow loading conditions (red – active shear failure;
purple – active tensile failure, green – elastic, but failed in past). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of
this article.)
N. Djordjevic / Minerals Engineering 64 (2014) 131–138 135

6. fragment size in the case of multiple inclusions will be smaller than
the fragment size when only a few grains are present in the sample.
This modelling has been performed under static loading condi-
tions, with a significantly slower rate of load application, than that
expected in comminution machines. As observed, through X-ray
tomography (Garcia et al., 2009), during very slow loading rate of
rock samples, there is a clear tendency for cracks to propagate pref-
erentially, along the interface of soft and hard minerals. The rate of
loading during comminution is much faster. Under such condi-
tions, the developed fracture will have be with much higher
energy, and their propagation will be mostly governed by the
shape of the rock sample and the loading configuration, rather than
the small scale heterogeneity of internal composition.
This issues is further investigated, using image based modelling
of rock failure process. The significance of the difference in elastic
properties between sulphide grains and host matrix is illustrated
in the case of chalcopyrite and pyrite ended in k-feldspar rich
matrix. Elastic moduli of chalcopyrite and feldspars are compara-
ble, while elastic modulus of pyrite is much higher.
A simplified elasto-plastic model has been crated based on the
image of the rock surface. The model is composed from the sul-
phide grains embedded into feldspar matrix. In one case, proper-
ties of chalcopyrite are assigned to the sulphides phase, while in
the second case properties of pyrite were used. Although pyrite
and chalcopyrite may have tendency to be with different spatial
distribution in-situ, intention of modelling is to show effect of
different mechanical properties, under otherwise identical
conditions.
The sample was loaded along vertical direction, with the base
being fixed. After deforming the sample in vertical direction, to a
prescribed level, the pattern of failure was observed. Modelling s
has been performed with, object oriented, OOF finite element code
(Langer et al., 2001). In both cases failure of the rock, is localised
within the matrix. However, in the case of chalcopyrite rich matrix,
only minor failure of the matrix was noticed, at selected level of
strain, while in sample with pyrite, extensive failures of the matrix
occurred. The extent of matrix failure, associated with pyrite, is
such that in real life it would result in the disintegration of the
sample, Figs. 11 and 12.
These modelling results, refers to a relatively small area of the
rock, within which clustering of sulphide minerals occurred
(fragment size $1–5 mm). Based on modelling results, feldspar
matrix which includes pyrite will be fragmented earlier and more
completely than rock matrix which contains chalcopyrite.
Within comminution equipment, due to uncontrolled loading
conditions, in the scale of individual rock fragments, load is applied
to the rock, until rock fail. Therefore the dynamics of the failure
process, in the scale of individual rock fragment, is of relevance
for the recovery of valuable minerals. Due to the much higher elas-
tic modulus of pyrite vs. chalcopyrite, pyrite will act as a more effi-
cient stress raiser, inducing micro cracks in relatively low strength
feldspar. The effect of magnetite will be similar. Due to the similar
elastic modules, of chalcopyrite and feldspar, chalcopyrite in isola-
tion is not able to induce failure of the rock matrix, from within.
Failure of the rock in this case will be caused by the fractures orig-
inated at the rock surface.
Based on the observed patterns, we can conclude that chalcopy-
rite grains alone may not be able to promote failure of the rock.
However if they are in close proximity to pyrite, collateral damage
caused by the presence of pyrite, may result in liberation of chalco-
pyrite. Based on the elastic properties, a similar effect will be also
caused by magnetite (Djordjevic, 2013a,b).
6. Modelling elastic properties of mineral clusters
Using the concept of effective medium theory (Garboczi and
Barryman, 2001; Mavko et al., 2009), it is possible to estimate what
is the effective ‘‘average’’, modulus of elasticity of the unit of rock
volume, populated to a certain extent with sulphide grains. Based
on the elastic constants, strength and the minimum required com-
minution energy can then be estimated.
Assuming that the host matrix is quartz, and not knowing the
shape of chalcopyrite grains, based on the published value for elas-
tic properties of chalcopyrite and quartz, it is possible to determine
the effective properties of ore made mostly of quartz or feldspar
with embedded chalcopyrite grains. In this case the best that can
be done is to calculate the upper and lower bounds of elastic prop-
erties as a function of the relative concentrations. The best bounds
for linear elastic, isotropic material, without specifying any shape
parameters of individual components are Hashin–Shtrikman
bounds (Hashin and Shtrikman, 1962). A more general form is
sometimes called Hashin–Shtrikman–Walpole bounds (Walpole,
1969).
Fig. 11. Progression of rock fracturing after set level of vertical strain is reached
(pyrite case).
Fig. 12. Progression of rock fracturing after set level of vertical strain is reached
(chalcopyrite case).
136 N. Djordjevic / Minerals Engineering 64 (2014) 131–138

7. Where sulphide minerals have higher values of elastic con-
stants, this will result that region with clustered sulphide grains,
having higher effective value of modulus of elasticity. Conse-
quently crushing of such rock, will result in the gangue part of
the rock being fragmented first and more efficiently, than the
enriched part of the rock.
Under such conditions, at moderate loading rate, the first stage
of comminution may result in the enriched part being liberated
from the gangue, and ending in the coarse size fraction. Final liber-
ation of copper sulphides may occur in the second stage, when
high grade progeny become subjected to pressure. Using the pub-
lished values of elastic constants for some material, and measured
for chalcopyrite (Table 1), we calculated the effective elastic con-
stants for two types of host matrix, one predominantly in the form
of feldspars and second one mostly composed of quartz.
In the case of pyrite embedded in feldspar, based on the speci-
fied parameters, increases in pyrite concentration will increase val-
ues of elastic constants, Fig. 13. Therefore this will create spatial
heterogeneity in terms of elastic properties of rock. Assuming that
chalcopyrite is closely associated with pyrite, part of the rock with
more copper will appear as ‘‘stronger’’. As a result in the initial
stage of rock crushing, that the sulphide rich part may become
detached from the rest of rock, earlier.
Where the host rock is predominantly quartz, a change in spa-
tial concentrations of chalcopyrite will have negligible influence on
the effective elastic modulus within the rock, Fig. 14. This is result
of relatively similar values of Young’s modulus of chalcopyrite and
quartz, as per Table 1.
Therefore, only the presence of hard minerals such as pyrite (or
magnetite, garnet) will influence the early liberation of chalcopy-
rite, when embedded in rock rich in quartz. Where sulphide grains
are significantly softer than quartz, their presence will noticeably
reduce the elastic modulus of composite rock, as well as macro-
scoping strength. This is illustrated in Fig. 15, for the case of sulp-
hides which elastic properties are one third of those values for
chalcopyrite.
7. Conclusions
Assuming the random distribution of sulphide minerals and
random rock breakage, a relatively small percentage of sulphide
grains will be exposed on the rock surface. The percentage of valu-
able sulphide minerals that will have some exposure on the surface
of the rock is a function of size of grains vs. size of the rock frag-
ment. Early liberation of sulphide grains needs to be considered
in terms of the mechanical properties of such grains relative to
the properties of the host matrix.
Depending on the nature of mineral associations, crushing of
rocks will result in different outcomes. Where clustering is of
mostly very soft copper minerals, with the host rock being moder-
ately strong feldspars or quartzite’s, the copper rich parts of rock
are likely to fragment first, resulting in relatively small size frag-
ments being rich in copper minerals. The remaining, copper
depleted gangue will be of much coarser size. In the case of mod-
erately strong chalcopyrite, the difference in elastic properties
between chalcopyrite and feldspar or quartz rich rock, will not
be significant enough to cause a propensity for early liberation,
while crushing macro rock fragments at loading rates relevant
for ore comminution.
Where clustering of copper minerals occurs with grains of pyr-
ite (or magnetite), the stronger part of the rock will be one rich in
valuable minerals. During crushing of such rock, the sulphides rich
zones will fragment in a different way than gangue. Depending on
the loading configuration, such zones may end up in an initially
coarser size fraction.
Subsequent, crushing of these relatively strong progeny frag-
ments will result in preferential liberation of the copper minerals.
This will occur due to the close proximity of the pyrite grains,
Table 1
Elastic constants of minerals.
Mineral Bulk modulus
(GPa)
Shear modulus
(GPa)
Young’s modulus
(GPa)
‘‘Average’’
feldspar
37.5 15 40.5
Quartz 37 44 93.2
Pyrite 147.4 132.5 309.5
Chalcopyrite 77 32 78.5
Fig. 13. Effective elastic properties of feldspars as function of fraction of sulphides.
Fig. 14. Effective elastic properties of quartz as function of fraction of sulphides.
Fig. 15. Effective elastic modulus of quartz as function of fraction of with
embedded soft sulphide grains.
N. Djordjevic / Minerals Engineering 64 (2014) 131–138 137

8. which will act as stress amplifier. Stress concentration within
pyrite (or magnetite; garnets) will result in failure of the rela-
tively soft surrounding matrix, thus promoting liberation of chal-
copyrite or chalcocite grains.
Therefore, textural information about the associations of sul-
phide minerals (copper sulphides vs. pyrite/magnetite/garnet) will
be of critical significance in the evaluation of the propensity for
coarse liberation of copper sulphide minerals. An absence of close
spatial associations will significantly reduce the possibility of early
liberation of copper sulphides. This would not be the case where
copper sulphides are predominantly on the surface of rock frag-
ments, or very close. In such cases simple abrasive action within
mills, will quickly transfer copper sulphides into fines, leaving
coarse fragment essentially barren.
During blasting in-situ ore is exposed to sufficiently intense,
high-strain rate loading to be able to induce micro-fracturing
originating from individual sulphides mineral grains as well as
their clusters. Due to the high rate of loading, a substantial
amount of energy can be dissipated with rock fragment, before
macro-failure of rock, which will relieve rock of blast induced
stress. The extent of blast induced rock preconditioning will be
directly proportional to the amount of energy delivered into the
rock during blasting. Spatial energy density within the blast can
be to certain extent modulated, through precise control of explo-
sive initiation times. However, due to the short duration of high
intensity dynamic loading, the length of crated micro cracks are
likely to be limited.
Created micro-cracks will play a significant role in subsequent
comminution, where rock fragments with enhanced density of
micro-cracks will be crushed more easily. Extensive micro-crack-
ing is also likely to play a significant role during heap or dump
leaching, stimulating infiltration/diffusion of leaching fluids into
the interiors of rock fragments.
Acknowledgments
The author would like to thank Julius Kruttschnitt Mineral
Research Centre and Sustainable Minerals Institute, University of
Queensland for financial support and permission to publish this
paper. I would like to acknowledge assistance of Dr. Luke Keeney
(CRCORE) who performed micro-indentation testing. Thanks are
also due to Mrs. K. Holtham for editing help.
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