coarse liberation

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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 article info Article history: Received 26 March 2014 Accepted 5 June 2014 Available online 25 June 2014 Keywords: Copper Chalcopyrite Liberation Coarse rock Crushing Blasting abstract 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. Tel.: +61 7 3365 5888; fax: +61 7 3365 5999. E-mail address: [email protected] Minerals Engineering 64 (2014) 131–138 Contents lists available at ScienceDirect Minerals Engineering journal homepage: www.elsevier.com/locate/mineng

Transcript of coarse liberation

Page 1: coarse liberation

Minerals Engineering 64 (2014) 131–138

Contents lists available at ScienceDirect

Minerals Engineering

journal homepage: www.elsevier .com/locate /mineng

Recovery of copper sulphides mineral grains at coarse rock fragmentssize

http://dx.doi.org/10.1016/j.mineng.2014.06.0030892-6875/� 2014 Elsevier Ltd. All rights reserved.

⇑ Tel.: +61 7 3365 5888; fax: +61 7 3365 5999.E-mail address: [email protected]

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 2014Accepted 5 June 2014Available online 25 June 2014

Keywords:CopperChalcopyriteLiberationCoarse rockCrushingBlasting

a b s t r a c t

Assuming the random distribution of sulphide mineral grains and random rock breakage, a relativelysmall percentage of sulphide grains will be exposed on the rock surface. Early liberation of sulphidegrains 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 ofmineral associations, crushing of such rocks will result in different outcomes. Where clustering is manlyof 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 copperminerals. However, in the case of moderately strong chalcopyrite, the difference in elastic propertiesbetween chalcopyrite and feldspar or quartz, will not be significant enough to cause a propensity for earlyliberation.

Where clustering of copper minerals occurs with grains of pyrite (or magnetite), the stronger part ofthe rock fragment will be one rich in valuable minerals. During crushing of such rock, the sulphides richzones will fragment in a different way than gangue. Stress concentration within pyrite (or magnetite) willresult in failure of the relatively soft surrounding matrix, thus promoting liberation of chalcopyrite orchalcocite grains. Therefore, textural information about the associations of sulphide minerals (coppersulphides vs. pyrite/magnetite/garnet) will be of critical significance in the evaluation of the propensityfor 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 inducemicro-fracturing originating from individual sulphides mineral grains as well as their clusters. Due tothe 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 willplay a significant role in subsequent comminution, where rock fragments with enhanced density ofmicro-cracks will be crushed more easily. Extensive micro-cracking is also likely to play a significant roleduring heap or dump leaching, stimulating infiltration/diffusion of leaching fluids into the interiors ofrock fragments.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The most important objective of the rock size reduction processis to release all targeted valuable mineral from the host rock at ascoarse rock fragment size as possible. Achieving this would bringabout huge savings in the overall cost of mineral production. Con-sidering that the density of metal rich grains, such as sulphides ofcopper, are generally much higher than the density of gangue, inmany mines, metal rich sulphides grains represent only 1–2% of

the volume of the mined and processed ore. Therefore, for typicalporphyry copper ore, close to 99% of the treated ore volume is acostly by-product of the production of copper concentrate.

At present, liberation of such minerals is achieved primarilythrough crushing and grinding of ore to a fragment size compara-ble to minerals grain size (80% passing size 100–300 lm). Rejectionof part of the waste material at a coarser fragment size will greatlyimprove the efficiency of mineral recovery (Bearman, 2013). Whenfinal 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 aspossible. In the context of this paper, the term liberation is used

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in a broader sense, to include not just full liberation of minerals,but also their substantial exposure on the surface of rockfragments.

Considering that the cost of rock size reduction is the principaloperational cost of mining/mineral processing, a reduction of thecommunication cost could have a very significant impact on theoverall 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, becomingreclassified into reserves, with subsequent ramifications to thevalue of deposits and mining companies.

Fig. 1. Modulus of elasticity of some common minerals (after Mavko et al., 2009).

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. Bydoing so a base case can be established, i.e., what can be expectedif there is no early liberation of sulphide minerals.

Sulphides are present in the form of numerous grains, their totalnumber 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 rockfragment size in the range of 30–50 mm). Hsih and Wen (1994)and Hsih et al. (1995) developed a geometrical model to calculatethe fraction of mineral grains that are exposed on particle surfacesduring comminution of a two-phase ore.

In the case of random breakage, with large number of grainspresent within the rock, the fraction of sulphide grains that willend-up exposed on the rock surface is determine by the ratio ofrock size vs. grain size. Assuming constant grain size, the frac-tion of available sulphide grains that are partially exposed onthe rock surface will increase with a decrease in rock size, asexpected.

Similarly, for constant size of rock, the fraction of available sul-phide grains that will be exposed on the rock surface will increasewith an increase of the grain size. So coarse grain mineralizationwill be more liberated than fine grain (i.e., greater percentage ofavailable 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 showsthat only about 2–7% of sulphides grains will be exposed on therock surface. Therefore, assuming random breakage and randomdistribution of sulphide grains, a relatively small fraction of suchgrains can be relatively easily recovered from the rock. In suchcase, 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 arefurther highlighted by the modest grade of many major copperdeposits (�0.5%Cu). Considering that for chalcopyrite the coppercontent is 35%, and copper grade is 0.5%, for uniform distributionof copper minerals, each grain of chalcopyrite will be surroundedby 200 grains of gangue minerals. It will be difficult to expect thatthe 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 becomescoarse particle liberation? It is possible to assume that the requiredfinal size of fragments coming from comminution is dictated by therequirements of the next step in the process of mineral recovery. Inthe case of sulphide minerals, this is often flotation. In such case,ore is ground to, at least 300 lm, depending on the size of sulphidegrains. 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 fragmentsize.

Although the final fragment size of gangue particles could becoarser than 300 lm, the size of fragments containing valuable sul-phide grains should remain the same, i.e., under 300 lm (i.e., at thetop size that will maximise their subsequent recovery). Forinstance, if ore comminution to top size of 1 mm, would liberate(fully or partially), all valuable sulphide minerals grains by havingthem in the fragment size range up to �0.3 mm; then that wouldconstitute liberation at coarse fragment size. Obviously, it wouldbe highly advantageous if such liberation of sulphide mineralscan be achieved at a much coarser fragment size of gangue, forinstance 5 or 10 mm, or even coarser.

At best such early liberation may result in the product of SAGmilling or HPGR crushing, being composed of coarse, almost barrengangue fragments, and finely crushed sulphide rich fragments. Thiscreates an opportunity for avoiding highly energy intensive ballmilling or reducing such a need to a minimum. Strongly bimodalfragment size distribution coming from SAG mill or HPGR, can beseparated into a dominant coarse gangue part and highly enrichedfines (size less than �0.3 mm). In the context of a modest grade oftypical copper ores, it is worth noting that the amount of highgrade fines does not need to be large to contain almost all valuableminerals present in ore (<5% of total ore mass).

Consideration of the propensity for earlier substantial liberationof 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 rockare of critical significance in the evaluation of the propensity forearly liberation, Fig. 1. Related parameters such as strength (incompression and tension) can be approximated based on knowl-edge of elastic constants. Vickers hardness is frequently availableand can be used as proxy to elastic constants of minerals.

The most interesting aspect of the above figure is the differencebetween 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 pyriteand magnetite are much higher than those of the most commongangue minerals. Other main copper sulphides such as chalcociteand bornite, due to their much higher copper content and lack ofiron, have an even lower modulus of elasticity than chalcopyrite.

In the course of this work, strength properties as well as elasticproperties are determined through instrumented, computer con-trolled, micro-indentation testing. In contrast to traditional hard-ness testing, instrumented indentation testing allows the

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Fig. 3. Young’s modulus of elasticity of chalcopyrite measured at 11 samples fromsame ore.

Fig. 4. Relationship between grain boundary fracture toughness and transgranularfracture toughness for a range of minerals (modified after Tromans and Meech,2002).

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application of a specified force or displacement history. Force anddisplacement are measured continuously over a complete loadingcycle. In the case of homogenous minerals, testing produce anindent of highly reproducible size and shape, Fig. 2. From theunloading part of the load–deformation curve, elastic modulus ofthe indented surface can be calculated.

Elastic properties of the same mineral vary depending on thespecific history of mineralization, and presence of impurities withinminerals. However, within the same mineralization the mechanicalproperties of a particular mineral tend to vary in a relatively narrowrange. This is illustrated in the case of chalcopyrite, Fig. 3.

Beside elastic parameters, fracture mechanics parameters canalso 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 byTromans and Meech (2002) show that, on average, grain boundaryfracture toughness are lower than trans-granular fracture tough-ness. By fitting numerical values presented by these authors, weconcluded that grain boundary fracture toughness is lower onaverage by about 9% than trans-granular fracture toughness, ofthe same minerals, Fig. 4.

At a rate of pressure application (strain rate), typical for commi-nution equipment, due to their small size, individual mineral grainswill not act as initial flaws from which fractures will be initiated. Insuch 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-raymicro-tomography, that some breakage along grain boundariesbetween chalcocite grain and gangue occurs only during a slowloading 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 forearly liberation during conventional comminution, only if they areclustered, forming much larger effective ‘‘grains’’. Such clusters or‘‘mega grains’’ will then be able to act as local weak zones, whichwill influence the initiation of cracks and/or their preferentialpropagation. Clustering could be with the same type grains, i.e.chalcopyrite; or could be with grains of some minerals which havedistinctive 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

Fig. 2. Size of indent for constant force, indicates that Galena is softer, less elastic,mineral than Sphalerite.

intense, high-strain rate loading to be able to induce micro-fracturing originating from individual sulphides mineral grains. Insuch a way, blasting may pre-condition ore, resulting in more effi-cient early liberation of valuable minerals in subsequent stages ofthe rock size reduction process.

Particularly tensile tail of the stress wave will be able to providestress loading conditions required for creation of micro-crackswithin 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 notresult in full crack coalescence (Nemat-Nasser and Horii, 1999).Micro cracks will be formed either simultaneous or before, creationof fragments forming macro-fractures. The created micro-crackswithin rock fragments will play significant role in subsequent com-minution, where fragments with enhanced density of micro-crack

Fig. 5. Modelled strain-rate time history for ANFO blast in amphibolite, showstensile straining (positive values) after initial high intensity compressive loading(negative initial peak).

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Fig. 7. Copper grade after blasting under same conditions. Homogenous sample ischaracterised with uniformly low grade (blue). (For interpretation of the referencesto color in this figure legend, the reader is referred to the web version of thisarticle.)

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will be crushed more easily (Nielsen and Malvik, 1999). Clearly,rock with stronger degree of heterogeneity, such as one causedby 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 willoriginate from the richer parts of the ore matrix, relative to thecoarser fragments. Blast induced breakage, particularly intensivebreakage, exhibits a preference for those parts of the ore that arerelatively rich in valuable, softer, minerals (Djordjevic, 2002).

Blasting of ore and waste with same the specific amount ofexplosive (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 relativelyhomogenous waste rock. This is further manifested in grade distri-bution, which for particular ore, is strongly biased toward thesmaller fragments, Fig. 7.

This is also in agreement with results presented by Ma et al.(2011). Through numerical modelling of the strain rate effect onthe failure pattern of heterogeneous material, the authors demon-strated that in the case of higher strain rate loading (50 and200 1/s), there is an increased tendency for the development of alarger number of smaller cracks within the rock sample.

The location of such micro-cracks is linked to the presence ofrock elements with reduced strength. Total deformation energyintroduced intro the sample, until complete loss of residualstrength, in the case of high strain rate loading is much higher thanin 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 withinthe rock in the case of higher strain rate loading.

Due to its unique nature, blast induced strain energy will fill thevoid which exists in conventional rock crushing and grinding. Dur-ing crushing and grinding, rock fragmentation occurs due to theapplication of force along the periphery of the rock fragments.Due to such geometry, spatial energy distribution tends to be astrong function of the shape of rock and position of the loadingpoints. The highest intensity being at contact points on the rocksurface and gradual decrease toward the interior. In many cases,the deformation pattern within rock is critically influenced bythe loading geometry and shape of rock, rather than internalstructure.

Blasting will result in a different pattern of deformation/fractur-ing, particularly at close distances from the blastholes (with �1 mfrom the blasthole). Due to high strain rate of loading, the blastinduced stress wave is able to introduce damage from within rockfragments. Considering that damage will be frequently initiatedfrom the grains of sulphide minerals, this could than stimulatepreferential fragmentation of higher grade fragments within the

Fig. 6. Fragment size distribution produced by blasting of two types of rock fromthe same deposit.

mineral processing circuit. Using HSBM code (Furtney et al.,2009) we modelled the occurrence of rock damage as a functionof explosive and rock properties.

For instance modelling of blast of ANFO (density 800 kg/m3)within strong amphibolite block, show that 15.8% of producedfragments are damaged, i.e. with reduced strength than intact rockof 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 intactrock matrix, Fig. 8.

Due to higher specific energy (as a result of higher density), thetotal 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 willbe reduced strength, while in the case of emulsion 21% of createdrock fragments will be with reduced strength. What is more inter-esting is that for emulsion blast, not only that more fragments arecrated but the fraction of fragments that have significant internaldamage is increased by 34% compared to ANFO blast. It is reason-able to expect that performance of the crushing and grinding willbe significantly improved in the case of blasting with highenergy/high density explosive (Michaux and Djordjevic, 2005).Volume of rock that will be affected by blast induced damagestrongly depends on the nature of blast design (number and prox-imity of free/unconstrained rock surfaces, mass of explosive perunit of rock volume, etc.). But in any case, envelope of rock damageextends beyond envelope of rock fragmentation, Fig. 9. In suchway, nominally part of solid rock which will remain in place, after

Fig. 8. Occurrence of damage within blasted rock fragments is function of explosivetype.

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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 � 10 � 10 m,with top face being free boundary.

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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 significantlylower elastic properties/strength than dominant gangue minerals,and that valuable minerals form a cluster of some kind, elementsof the rock volume which contain such clusters are likely to bemore efficiently fragmented than the adjoining rock volume, whichis 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 preferentialbreakage. Part of the ore matrix, with a larger concentration of thesofter inclusions (valuable minerals), is on average mechanicallyweaker than a similar matrix with fewer soft minerals. Rockstrength is proportional to its modulus of elasticity €, with highmodulus rock being of higher compressive strength (UCS). Theratio between two parameters (E/UCS) varies, depending onthe rock type. For rocks, like granite and similar, the ratio is inthe range 300–500 (Deere and Miller, 1966).

In the comminution process, rock size reduction, is achieved bystraining, to extent controlled by set, reduction ratio (crushers/HPGR). In other cases, fragmentation is controlled by intensity offorce and contact time (duration of force application). In both ofthese scenarios, the application of external force to rock continuesblindly, ignoring the state of mineral liberation or exposure. Thismay result in part of the rock with a high concentration of

Fig. 10. Increase heterogeneity of rock, due to presence of relatively soft grains, results inpurple – active tensile failure, green – elastic, but failed in past). (For interpretation of thethis article.)

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 boundaryof such pores, the application of external stress may result in stressconcentration sufficient for the initiation of micro-cracks. Anotherfrequent source of stress concentration is the heterogeneities in thedeformation of individual mineral grains. Due to different elasticproperties, and to some extent the shape, of the ore and gangueminerals, under load, differential deformation will result in thedevelopment of micro-cracks along the mineral boundaries, (Blairand Cook, 1998).

This behaviour was modelled using the FLAC finite differencecode (ITASCA, 2000). A relatively soft mineral was embedded intothe hard matrix. Samples were gradually loaded in compressionalong the vertical axis. The process of failure was gradual, withthe first failure occurring within the soft mineral. Due to heteroge-neous deformation along the boundary of the soft minerals andhard matrix, tensile stress concentration occurs in the matrix, nextto the failed soft mineral.

A further increase in external load causes extension of thecracks, resulting in macroscopic failure of the modelled rock sam-ple. In the case of multiple soft minerals, extension of the cracksis preferential: cracks first connect the soft inclusions, followedby the creation of the large shear cracks, Fig. 10. Formation of themacro shear fractures is also influenced by the shape of the rocksample. From the presented results it is clear that the average

improved fragmentation, under slow loading conditions (red – active shear failure;references to color in this figure legend, the reader is referred to the web version of

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Fig. 12. Progression of rock fracturing after set level of vertical strain is reached(chalcopyrite case).

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fragment size in the case of multiple inclusions will be smaller thanthe 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 thatexpected in comminution machines. As observed, through X-raytomography (Garcia et al., 2009), during very slow loading rate ofrock samples, there is a clear tendency for cracks to propagate pref-erentially, along the interface of soft and hard minerals. The rate ofloading during comminution is much faster. Under such condi-tions, the developed fracture will have be with much higherenergy, and their propagation will be mostly governed by theshape of the rock sample and the loading configuration, rather thanthe small scale heterogeneity of internal composition.

This issues is further investigated, using image based modellingof rock failure process. The significance of the difference in elasticproperties between sulphide grains and host matrix is illustratedin the case of chalcopyrite and pyrite ended in k-feldspar richmatrix. 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 theimage 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 inthe second case properties of pyrite were used. Although pyriteand chalcopyrite may have tendency to be with different spatialdistribution in-situ, intention of modelling is to show effect ofdifferent mechanical properties, under otherwise identicalconditions.

The sample was loaded along vertical direction, with the basebeing fixed. After deforming the sample in vertical direction, to aprescribed level, the pattern of failure was observed. Modelling shas been performed with, object oriented, OOF finite element code(Langer et al., 2001). In both cases failure of the rock, is localisedwithin the matrix. However, in the case of chalcopyrite rich matrix,only minor failure of the matrix was noticed, at selected level ofstrain, while in sample with pyrite, extensive failures of the matrixoccurred. The extent of matrix failure, associated with pyrite, issuch that in real life it would result in the disintegration of thesample, Figs. 11 and 12.

These modelling results, refers to a relatively small area of therock, within which clustering of sulphide minerals occurred

Fig. 11. Progression of rock fracturing after set level of vertical strain is reached(pyrite case).

(fragment size �1–5 mm). Based on modelling results, feldsparmatrix which includes pyrite will be fragmented earlier and morecompletely than rock matrix which contains chalcopyrite.

Within comminution equipment, due to uncontrolled loadingconditions, in the scale of individual rock fragments, load is appliedto the rock, until rock fail. Therefore the dynamics of the failureprocess, in the scale of individual rock fragment, is of relevancefor 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 strengthfeldspar. The effect of magnetite will be similar. Due to the similarelastic 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 damagecaused by the presence of pyrite, may result in liberation of chalco-pyrite. Based on the elastic properties, a similar effect will be alsocaused by magnetite (Djordjevic, 2013a,b).

6. Modelling elastic properties of mineral clusters

Using the concept of effective medium theory (Garboczi andBarryman, 2001; Mavko et al., 2009), it is possible to estimate whatis the effective ‘‘average’’, modulus of elasticity of the unit of rockvolume, populated to a certain extent with sulphide grains. Basedon 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 theshape of chalcopyrite grains, based on the published value for elas-tic properties of chalcopyrite and quartz, it is possible to determinethe effective properties of ore made mostly of quartz or feldsparwith embedded chalcopyrite grains. In this case the best that canbe done is to calculate the upper and lower bounds of elastic prop-erties as a function of the relative concentrations. The best boundsfor linear elastic, isotropic material, without specifying any shapeparameters of individual components are Hashin–Shtrikmanbounds (Hashin and Shtrikman, 1962). A more general form issometimes called Hashin–Shtrikman–Walpole bounds (Walpole,1969).

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Fig. 15. Effective elastic modulus of quartz as function of fraction of withembedded soft sulphide grains.

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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 ofthe rock being fragmented first and more efficiently, than theenriched part of the rock.

Under such conditions, at moderate loading rate, the first stageof comminution may result in the enriched part being liberatedfrom the gangue, and ending in the coarse size fraction. Final liber-ation of copper sulphides may occur in the second stage, whenhigh grade progeny become subjected to pressure. Using the pub-lished values of elastic constants for some material, and measuredfor chalcopyrite (Table 1), we calculated the effective elastic con-stants for two types of host matrix, one predominantly in the formof 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 spatialheterogeneity in terms of elastic properties of rock. Assuming thatchalcopyrite is closely associated with pyrite, part of the rock with

Table 1Elastic constants of minerals.

Mineral Bulk modulus(GPa)

Shear modulus(GPa)

Young’s modulus(GPa)

‘‘Average’’feldspar

37.5 15 40.5

Quartz 37 44 93.2Pyrite 147.4 132.5 309.5Chalcopyrite 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.

more copper will appear as ‘‘stronger’’. As a result in the initialstage of rock crushing, that the sulphide rich part may becomedetached 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 onthe effective elastic modulus within the rock, Fig. 14. This is resultof relatively similar values of Young’s modulus of chalcopyrite andquartz, as per Table 1.

Therefore, only the presence of hard minerals such as pyrite (ormagnetite, garnet) will influence the early liberation of chalcopy-rite, when embedded in rock rich in quartz. Where sulphide grainsare significantly softer than quartz, their presence will noticeablyreduce 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 forchalcopyrite.

7. Conclusions

Assuming the random distribution of sulphide minerals andrandom rock breakage, a relatively small percentage of sulphidegrains will be exposed on the rock surface. The percentage of valu-able sulphide minerals that will have some exposure on the surfaceof the rock is a function of size of grains vs. size of the rock frag-ment. Early liberation of sulphide grains needs to be consideredin terms of the mechanical properties of such grains relative tothe properties of the host matrix.

Depending on the nature of mineral associations, crushing ofrocks will result in different outcomes. Where clustering is ofmostly very soft copper minerals, with the host rock being moder-ately strong feldspars or quartzite’s, the copper rich parts of rockare likely to fragment first, resulting in relatively small size frag-ments being rich in copper minerals. The remaining, copperdepleted gangue will be of much coarser size. In the case of mod-erately strong chalcopyrite, the difference in elastic propertiesbetween chalcopyrite and feldspar or quartz rich rock, will notbe significant enough to cause a propensity for early liberation,while crushing macro rock fragments at loading rates relevantfor 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 invaluable minerals. During crushing of such rock, the sulphides richzones will fragment in a different way than gangue. Depending onthe loading configuration, such zones may end up in an initiallycoarser 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,

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138 N. Djordjevic / Minerals Engineering 64 (2014) 131–138

which will act as stress amplifier. Stress concentration withinpyrite (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) willbe of critical significance in the evaluation of the propensity forcoarse liberation of copper sulphide minerals. An absence of closespatial associations will significantly reduce the possibility of earlyliberation of copper sulphides. This would not be the case wherecopper sulphides are predominantly on the surface of rock frag-ments, or very close. In such cases simple abrasive action withinmills, will quickly transfer copper sulphides into fines, leavingcoarse fragment essentially barren.

During blasting in-situ ore is exposed to sufficiently intense,high-strain rate loading to be able to induce micro-fracturingoriginating from individual sulphides mineral grains as well astheir clusters. Due to the high rate of loading, a substantialamount of energy can be dissipated with rock fragment, beforemacro-failure of rock, which will relieve rock of blast inducedstress. The extent of blast induced rock preconditioning will bedirectly proportional to the amount of energy delivered into therock during blasting. Spatial energy density within the blast canbe to certain extent modulated, through precise control of explo-sive initiation times. However, due to the short duration of highintensity dynamic loading, the length of crated micro cracks arelikely to be limited.

Created micro-cracks will play a significant role in subsequentcomminution, where rock fragments with enhanced density ofmicro-cracks will be crushed more easily. Extensive micro-crack-ing is also likely to play a significant role during heap or dumpleaching, stimulating infiltration/diffusion of leaching fluids intothe interiors of rock fragments.

Acknowledgments

The author would like to thank Julius Kruttschnitt MineralResearch Centre and Sustainable Minerals Institute, University ofQueensland for financial support and permission to publish thispaper. I would like to acknowledge assistance of Dr. Luke Keeney(CRCORE) who performed micro-indentation testing. Thanks arealso due to Mrs. K. Holtham for editing help.

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