Minerals Engineering 41 (2013) 115–120

Contents lists available at SciVerse ScienceDirect

Minerals Engineering

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

Grindability of binary ore blends in ball mills

Luís Marcelo Tavares a,⇑, Raquel D.C. Kallemback a,b

a Department of Metallurgical and Materials Engineering, Universidade Federal do Rio de Janeiro – COPPE/UFRJ, Rio de Janeiro, RJ, Brazilb Vale S.A., Porto de Tubrarão, Vitória, ES, Brazil

a r t i c l e i n f o

Article history:Received 1 September 2012Accepted 1 November 2012Available online 13 December 2012

Keywords:Bond ball millBlendsGrindingBinary mixtures

0892-6875/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.mineng.2012.11.001

⇑ Corresponding author. Tel.: +55 (21)2562 8538.E-mail address: tavares@ufrj.br (L.M. Tavares).

a b s t r a c t

The understanding of how blends of materials grind is of great relevance in both the minerals and thecement industries. If benefits and challenges associated to it are properly understood, then decisionscan be made on blending prior to grinding or grinding additives in separate during cement production,as well as different ores fed to mills in a processing plant. The paper investigates the size reduction ofblends of materials with different grindabilities in a Bond ball mill, as well as in a continuous pilot-scalemill. The accumulation of the harder (tougher) component in the mill charge as grinding progresses isanalyzed and a simple empirical model that describes this phenomenon has been proposed. It is foundthat the accumulation of hard component in the mill increases with the decrease in the ratio of Bondwork index values of the individual soft and hard components, and with the increase in the circulatingload ratio. It is also concluded that the Bond work index of the mixtures is often higher than theweighed-average value of the individual components in the mixture. As such, an expression is proposedfor calculating the value for blends based on this modeled accumulation effect and has been found toremove the bias from predictions made on the basis of the weighed-average values from the feed.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction A number of papers have addressed different aspects of the

The understanding of how blends of materials grind is of impor-tance in different areas. In cement grinding, size reduction of clin-ker and additives can be done separately or together. The later,called intergrinding, is beneficial because mills allow not onlythe size reduction but also the mixture of the components, simpli-fying the plant flowsheet (Öner, 2000). On the downside, this oftenleads to an increase in energy demand and in differential grindingof the components, which could have a negative impact on cementusage, since the harder components that are ground to coarsersizes may not react as readily with water during cement curing.

In the minerals industry, it is of relevance to understand howmills will respond to blends of ores with different grindabilitiescoming from different parts of the deposit. If blending does notprove to be beneficial from the standpoint of energy consumption,it may be possible to feed ores to parallel lines or different plants,whenever available. Further, it is relevant to understand how min-eralogical components of different hardness (although ‘toughness‘would be the most accurate term from a material science stand-point) respond to milling after their liberation has been reached,since their differential grinding response can lead to non-optimalparticle sizes in the flotation feed and to increases in slimes gener-ation (Malghan, 1986).

ll rights reserved.

problem, often demonstrating that neither grindability nor theBond work index obey the simple rule of mixtures (Hosten andAvsar, 1998; Yan and Eaton, 1994; Iglesias et al., 1999; Öner,2000; Ipek et al., 2005). For instance, Öner (2000) demonstratedthat the grindability resulting from mixtures of clinker and blastfurnace slag is systematically lower than the weighed-averagedvalues for the individual components. He also observed that thetougher material (slag) appears in the product with a coarser sizedistribution than the clinker. Hosten and Avsar (1998) also demon-strated that the Bond ball mill work index of the mixture of clinkerand trass is not the weighed-averaged values of the individualcomponents. Indeed, they showed that the work index of the mix-tures can be even higher than that of the hardest component. Sim-ilar results were found by Iglesias et al. (1999), who demonstratedthat small additions of gypsum in a mixture with cement clinkerresulted in nearly constant values of work index, in spite of the sig-nificantly lower Bond work index values of the gypsum samples.Similar results have been found by a number of researchers, as isillustrated in Fig. 1. Data in the figure has been plotted as a func-tion of the relative Bond ball mill work index of the blend, definedas

Relative BWiblend ¼BWiblend � BWisoft

BWihard � BWisoftð1Þ

Yan and Eaton (1994) attributed the higher values of Bond workindex of the mixtures in comparison to the weighed-averagedvalues to the fact that there is often an accumulation of hard

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 20 40 60 80 100Rel

ativ

e Bo

nd b

all m

ill w

ork

inde

x of

ble

nd

% weight of hard component in the feed blend

Yan and Eaton (1994)

Hosten and Avsar (1988)

Iglesias et al. (1999)

Iglesias et al. (1999)

Oner (2000)

Michaux (2012)

Fig. 1. Variation of the relative Bond ball mill work index of blends as a function ofthe proportion of hard component in the feed. Line represents the weighed-averagevalues. (See above-mentioned references for further information.)

Table 1Summary of the characteristics of the samples.

Sample Specific gravity(g/cm3)

A � b F80

(lm)F20

(lm)BWi(kW h/t)

Limestone #1 2.65 61.8 2460 915 9.05Limestone #2 2.72 609.8 2390 410 6.28Limestone #3 2.98 Na 2500 640 7.38Limestone #4 2.88 64.2 2710 1055 6.13Basalt 3.03 37.2a 2610 1265 13.78Copper ore 3.39 34.2 2730 1090 20.42

Na: not available.a Estimated from testing particle contained in size range 22.4 � 19.0 mm and

applying the correction equation proposed by Tavares and Silveira (2008).

116 L.M. Tavares, R.D.C. Kallemback / Minerals Engineering 41 (2013) 115–120

component in the mill hold-up. Unfortunately, this degree of accu-mulation is seldom estimated experimentally. Indeed, Fuerstenauand Venkataraman (1988) demonstrated, from a locked-cycledtest, that quartz, the hardest component in a binary mixturewith calcite, accumulates in the mill as grinding progresses. Thisaccumulation was found to be relatively slow, requiring up to 242-min cycles in order to reach equilibrium. They also demonstratedthat the breakage rates of individual components were indepen-dent of time, but varied with the composition of the mill hold upin each cycle. These findings suggest that a significant part of theliterature on grinding of mixtures in mills operating in batch modeis of relatively little relevance to explain what happens in indus-trial ball mills, which nearly always operate in closed circuit, andwill experience an accumulation of the harder component in thecharge. It also suggests that simplified methods of measuring theBond work index, such as the one proposed by Magdalinovic(1989), and that are based on the use of data from batch grindingtests, can lead to unrealistic results when dealing with ores thathave components with significantly different grindabilities.

In spite of the important developments in recent decades withimproved characterization, modeling and simulation approachesapplied to ball mills (Austin et al., 1984; Herbst and Fuerstenau,1980; Tavares and Carvalho, 2009), the Bond ball mill grindabilitytest retains a significant part of its original importance as a conve-nient and inexpensive method to assess the response of materialsto grinding in tumbling ball mills.

The present paper analyzes the Bond ball mill work index ofbinary ore mixtures, investigating the accumulation of the hardcomponent in the mill, as well as the different size distributionsof the components in the product.

2. Experimental

Samples of six rocks, four of which limestones, from deposits lo-cated in Brazil have been collected. They have been prepared fortesting by stage crushing, followed by removal of the material finerthan 300 lm by screening. Specific gravity of the samples has beendetermined by pycnometry and a summary of the results is shownin Table 1. It shows that grindabilities as well as single-particlebreakage strengths varied significantly for the samples, repre-sented by wide ranging values for both the Bond Work index andA � b values that characterize single-particle breakage by impact.

The Bond ball mill work index of each sample was measuredusing the standard equipment and procedure (Bergstrom, 1985)

using a constant closing sieve of 300 lm. In all tests, material pass-ing the closing sieve was removed from the feed, in an attempt tolimit the influence of variations in feed size distribution in the test.Experiments involving mixtures were conducted by first preparingindividual longitudinal piles of components that constitute eachbinary mixture, followed by adding to the mill quartered quantitiesof each material corresponding to additions of 25%, 50% and 75% involume (bulk). The Bond work index (BWi, in kW h/t) was calcu-lated using the expression (Bergstrom, 1985)

BWi ¼ 1:1 � 4:45

Am0:23G0:82bp 1=

ffiffiffiffiffiffiffiP80p

� 1=ffiffiffiffiffiffiffiF80p� � ð2Þ

where Am is the screen opening used in the test, Gbp is the net gramsper revolution of the mill in steady-state conditions, F80 is the feed80% passing size, while P80 is the 80% passing size of the product ofthe final locked-cycle. Selected tests were conducted in duplicateand only the averages of the measurements, which had deviationssmaller than 1 kW h/t, are reported.

The composition of the hold up and final product from the testswith blends involving mixtures with basalt and copper ore hasbeen analyzed by partially dissolving the limestone phase, leavingan insoluble residue, from which the basalt and copper ore con-tents were estimated. Details on the experimental procedure usedin the analyses, conducted in duplicate, can be found elsewhere(Kallemback, 2012).

Additional tests were conducted with a pilot scale mill workingboth in open circuit and in closed circuit with an air classifier, and acomplete description of the testwork may be found elsewhere(Kallemback, 2012).

3. Results and discussion

3.1. Product size distributions

Upon conclusion of each Bond ball mill grindability test, prod-ucts have been analyzed in respect to size distribution and compo-sition. Fig. 2 summarizes results from these analyzes for eachindividual component in a blend of basalt and limestone #1. It sug-gests that the product size distribution of the hard component (ba-salt) did not vary if it was ground together or separately fromlimestone, whereas limestone became only marginally finer inthe presence of basalt.

3.2. Accumulation of hard component in the mill

In order to investigate the accumulation of the hard componentin the mill hold-up, its proportion in the passing product from eachlocked-cycle period was measured during standard Bond grindabil-ity tests of artificial blends and typical results are shown in Fig. 3. Itis evident that the basalt content of the fine product that leaves themill is initially lower than in the feed, since it is enriched with the

30

40

50

60

0 20 40 60 80 100

% p

assi

ng 7

5 m

icro

n si

eve

% weight of hard component in the feed blend

Basalt

Limestone #1

Fig. 2. Effect of proportion of basalt in the mixture on the percentage passing the75 lm sieve of each individual component.

0

20

40

60

80

100

0 1 2 3 4 5 6 7 8 9

% w

eigh

t of b

asal

t in

prod

uct

Grinding period

75% basalt50% basalt25% basalt

Fig. 3. Basalt content in the passing product from each grinding period for Bond ballmill grindability tests with mixtures of basalt and limestone #1. Horizontal linesrepresent the percentages of hard component in the mixtures fed to the mill.

0

20

40

60

80

100

0 1 2 3 4 5 6 7 8 9

% w

eigh

t bas

alt i

n m

ill ho

ld-u

p

Grinding period

75% basalt50% basalt25% basalt

Fig. 4. Basalt content (weight) in the mill hold up as a function of its content in thefeed for mixtures with limestone #1.

0.2

0.4

0.6

0.8

1.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Wei

ght f

ract

ion

of h

ard

com

pone

nt in

mill

hold

up

Weight fraction of hard component in the feed

Basalt & limestone #1

Copper ore & limestone #1

Fig. 5. Relationship between percent of hard component in the feed and in the millhold up in the Bond ball mill test for selected binary mixtures (symbols representexperimental data and solid lines the fit to Eq. (3)).

1

2

3

4

5

6

7

8

9

10

0.2 0.4 0.6 0.8 1

α

BWisoft/BWihard

Experimental data fitted to Eq. 3

Equation (4)

Fig. 6. Relationship between model parameter a and the ratio of Bond work indexof the soft and of the hard material.

L.M. Tavares, R.D.C. Kallemback / Minerals Engineering 41 (2013) 115–120 117

softer component (limestone). For the blend studied, these valuesbecome approximately the same after about several locked-cycleperiods. For other blends involving greater differences in grindabil-ity of the components, the same general behavior was observed.

Using data such as those from Fig. 3 and mass balancing the re-sults from the test, it was then possible to estimate the basalt con-tent of the mill hold-up just before running each locked-cycleperiod. These results are illustrated in Fig. 4, which shows thatthe basalt content in the mill hold-up increased with the numberof periods in the Bond test, reaching equilibrium after about 5–9

grinding periods for different feed blends. This equilibrium wasreached more rapidly for higher contents of the hard componentin the feed and with blends composed of ores with similargrindablities.

Aiming to describe quantitatively the accumulation of the hardphase under steady-state conditions in the mill during the Bondgrindability test, results for selected blends were plotted in Fig. 5as a function of the proportion of hard phase in the feed. This accu-mulation of the hard component in the mill could be describedusing the empirical expression

/WH ¼17

5a/W

1� /W þ a/Wþ 2/W

� �ð3Þ

where /WH and /W are the weight fractions of hard component inthe mill hold up and in the feed, respectively. a is the only modelparameter that requires fitting. Eq. (3) takes into account the factthat the maximum accumulation in the mill is limited by the250% circulating load ratio standardized in the Bond test.

Fig. 5 suggests that the variation of parameter a may be par-tially explained by the difference in Bond ball mill work index val-ues for the soft and hard components in the blend. Although it isrecognized that the accumulation of the hard component will beinfluenced by other factors, such as the feed size distributions ofthe individual components and the size-dependent strength of par-ticles (Tavares and King, 1998), it is proposed that the parameter a

Pred

icte

d fra

ctio

n of

har

d co

mpo

nent

in

hol

d up

(wt.)

Measured fraction of hard component in hold up (wt.)

Fig. 7. Comparison of measured and predicted values of the proportion of hard component in the mill hold up.

118 L.M. Tavares, R.D.C. Kallemback / Minerals Engineering 41 (2013) 115–120

in Eq. (2) may be described exclusively as a function of the ratio ofwork indices of the individual components with the expression

a ¼ 3:05� 2:09

1þ 0:67BWisoft=BWihard� �9:5 ð4Þ

A comparison between experimental data and fitting results ispresented in Fig. 6, which demonstrates the fidelity of the model.An evident outlying point exists in the graph, which correspondsto the mixtures of basalt and limestone #2, which resulted inexceptionally large accumulations of the hard component in themill hold up.Although empirical, Eqs. (3) and (4) give sensible val-ues for the range of conditions that are encountered in practice,that is 0 6 /W 6 1 and 0 6 BWisoft=BWihard 6 1, so their use extrap-olating the limits contained in the fitting data will not lead to phys-ically unreasonable predictions.

Fig. 7 compares measured and predicted results using themodel, which demonstrates the good fit, except for the datacorresponding to the blend of basalt and limestone #2, whichwas already identified as an outlier in Fig. 6. It is not yet clearthe reasons for the exceptional accumulation of hard material intests involving this blend, but it could be related to the very lowstrength of limestone #2 (high A � b value) and its comparativelyhigh proportion of fines contained in feed (F20), as demonstratedin Table 1. The figure also shows validation data from Csöke

0

50

100

150

200

250

300

350

400

450

0 20 40 60 80 100

% c

ircul

atin

g lo

ad ra

tio

% weight of hard component in the feed blend

Blend

Basalt

Limestone #1

Fig. 8. Circulating load ratios in the Bond ball mill grindability test for mixtures ofbasalt and limestone #1.

et al. (2012), which were not used in model fitting, thus demon-strating the validity of the model.

The Bond ball mill grindability test is conducted as to reach250% circulating load ratio under steady-state conditions. How-ever, when components with different grindabilities are fed tothe mill, their circulating load ratios can differ. This is illustratedin Fig. 8, which shows that the circulating load ratio for basaltwas as high as 400%, whereas limestone, the softer component,did grind more readily and reached circulating loads as low as110% in the blend with 75% basalt. From these it may be inferredthat, in an industrial mill, in which classifiers such as hydrocy-clones and screw classifiers are used, circulating loads can differeven more if the harder component also has higher specific gravity.Fig. 8 also shows that the circulating load ratio of the hard compo-nent increases as its proportion decreases in the feed.

It is possible to predict the circulating load ratios for the hardcomponent in a blend in the Bond grindability test, considering250% circulating load ratio, by

Circulating load ratio of hard componentð%Þ ¼ 1007/WH

2/W� 1

� �

ð5Þ

using the values of fraction of hard component in the mill hold up/WH predicted using Eqs. (3) and (4). These predictions are also

0.9

1

1.1

1.2

1.3

Batch Pilot open circuit(0% CL)

Pilot closed circuit(100% CL)

Locked cycle -Bond (250% CL)

Rat

io o

f bas

alt i

n ho

ld-u

p an

d fe

ed

Fig. 9. Effect of mode of conducting the test and circulating load ratio (CL) on theaccumulation of hard component in milling tests, in which the feed is composed,approximately, of equal proportions of basalt and limestone #1.

5

10

15

20

5 10 15 20

Pred

icte

d BW

i (kW

h/t)

Measured BWi (kWh/t)

Fig. 11. Comparison between measured values of Bond ball mill work index formixtures depicted in Figs. 1 and 10, and data from Csöke et al. (2012), to predictionsusing Eq. (6).

5

10

15

20

5 10 15 20

Pre

dict

ed B

Wi (

kWh/

t)

Measured BWi (kWh/t)

Fig. 12. Comparison between measured values of Bond ball mill work index formixtures depicted in Figs. 1 and 10, and data from Csöke et al. (2012), to predictionsusing the proposed model (Eqs. (3), (4), and (7)).

L.M. Tavares, R.D.C. Kallemback / Minerals Engineering 41 (2013) 115–120 119

shown in Fig. 8, which demonstrates the good agreement betweenmodel and experiments and, thus, the validity of the model.It isworth noting that the accumulation of hard material in the mil isalso likely to be influenced by the mode of grinding as well as thecirculating load ratio. Fig. 9 compares the ratio of the basalt contentin the mill hold up and in the feed (/WH=/W ) measured experimen-tally for a series of tests in which the feed content was maintainedat, approximately, 50% of hard component. In these tests, describedelsewhere (Kallemback, 2012) and conducted in a pilot-scale 0.3 mdiameter mill and in dry mode, the ratio increases from batch, to anopen circuit, and then to a closed-circuit test at low circulating loadratio, with the highest ratio obtained for the Bond test, conducted at250% circulating load and in locked-cycle mode. While there is,obviously, no accumulation in the mill in batch mode, it alreadyappears in the case of a mill that is operating in open circuit. Thisis because the harder component, which is coarser inside the mill,is not as readily discharged.

3.3. BWi of blends

A summary of results from grindability tests of the blends stud-ied in the present work is presented in Fig. 10, using the definition,presented earlier in Eq. (1), of relative Bond work index of blends.Although it also shows significant deviations between measuredand weighed-average values, data for, at least three mixtures, fitreasonably well to the line. As such, it is worthwhile comparingthe measured values to those calculated assuming that the Bondball mill work index varies with the weigh fraction of the compo-nents, that is

BWiblend ¼ /W BWihard þ ð1� /W ÞBWisoft ð6Þ

Results are shown in Fig. 11, which demonstrates that a signifi-cant scatter exists and a bias in the equation towards underestimat-ing the Bond ball mill work index of the blend. This is confirmed byan average of�7.7% in the relative errors between the predicted andmeasured values. The absolute relative error was equal to 7.9%,whereas the maximum relative absolute error, 22.8%.

On the other hand, if it is considered that the Bond ball millwork index could be more appropriately described by not directlyconsidering the weigh fractions of the components in the feed, butin the mill hold up, as proposed by Yan and Eaton (1994), then itwould be predicted using

BWiblend ¼ /WHBWihard þ ð1� /WHÞBWisoft ð7Þ

where the weight fraction of the hard component in the mill hold up/WH could be predicted using Eqs. (3) and (4). Fig. 12 compares model

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 20 40 60 80 100Rel

ativ

e Bo

nd b

all m

ill w

ork

inde

x of

ble

nd

% weight of hard component in the blend

Basalt and Limestone #1

Basalt and Limestone #2

Basalt and Limestone #3

Limestone #2 and Limestone #3

Copper ore and Limestone #4

Copper ore and Limestone #1

Fig. 10. Variation of the relative Bond ball mill work index of blends as a function ofthe proportion of the tougher component in the feed for the mixtures studied in thepresent work. Line represents the weighed-average values.

predictions to experimental results, demonstrating that the bias in thepredictions, observed in Fig. 11, disappear, which is also demonstratedby an average relative error of only �0.3%. The scatter in the graph isalso significant, although the relative absolute error is marginally low-er (6.5%) and the maximum relative absolute error is 26.6%.

Evidently, some of the scatter in the graphs is associated to thefact that neither one of the current approaches are able to predict ahigher value of Bond work index for the mixture than the valuesmeasured for the individual components. This is the case for sixof the mixtures depicted in Figs. 1 and 10 and has been describedas the results of a number of effects, including the softer compo-nent coating the grinding media (Iglesias et al., 1999) or the softcomponent shielding the harder particles from being nipped inthe mill (Hosten and Avsar, 1998). Other explanations are probablyrelated to specifics of ore mineralogy and breakage characteristicsof the components in such blends. In these cases, which cannot beidentified so far exclusively on the basis of grindability data foreach individual component, the only alternative to estimate theBond work index of the blends is to conduct physical tests withblends containing different proportions of soft and hard material.

4. Conclusions

� The size distribution of the product of the Bond grindability testchanged with the proportion of hard component in the mixture.However, the size distribution in the product of individual

120 L.M. Tavares, R.D.C. Kallemback / Minerals Engineering 41 (2013) 115–120

components remained relatively unchanged, being only mar-ginally finer for limestone #1 when ground in a mixture withbasalt, the hard component.� An accumulation of the hard component in the mill hold-up was

observed and was directly related to the ratio of the BWi valuesof the soft and hard components. An empirical model describingthis phenomenon has been proposed.� The circulating load for the hard component was found to be

higher than for the soft component and a model to predict thatin the Bond test was proposed.� The accumulation of the hard component increased with the

circulating load ratio, as well as the milling operation is shiftedfrom open to closed-circuit.� Experimental results show that small additions of soft material

to a predominantly hard feed to a ball mill do not usually resultin an equivalent improvement in grindability, and even a dele-terious effect can be observed on grindability as a result of it.� An empirical model for calculating the Bond work index of bin-

ary blends has been proposed and is based on the predictedfraction of hard material contained in the mill hold up, ratherthan in the feed. It was able to eliminate the bias observed whenthe weighed-average values of the Bond work indices of theindividual components in the feed are used. A significant scatterstill exists in the predictions, which are, at least in part,explained by cases in which the Bond work index of blendswas higher than the values obtained for the individualcomponents.

Acknowledgements

The authors would like to thank the financial support to thisinvestigation from the Brazilian research agencies CNPq andCAPES, as well as from VALE and AMIRA, through the P9O andP9P project. The suggestions from Mr. Rodrigo M. de Carvalho

during the course of this work and the assistance of Mr. MalobaTshela from the University of Cape Town in conducting the contin-uous grinding tests were appreciated. The authors also acknowl-edge Dr. Simon Michaux for providing valuable unpublished data.

References

Austin, L.G., Klimpel, R.R., Luckie, P.T., 1984. Process Engineering of Size Reduction.AIME.

Bergstrom, B.H., 1985. Crushability and Grindability, in: SME Mineral Processing,Handbook, vol. 2, pp. 30-65–30-68.

Csöke, B., Rácz, A., Mucsi, G., 2012. Determination of the Bond work index ofcomposite materials. Proc. XXVI Int. Min. Proc. Congr. 371, 985–998.

Fuerstenau, D.W., Venkataraman, K.S., 1988. The comminution of multicomponentfeeds under batch and locked-cycle conditions: kinetics, simulation and energydistribution. Int. J. Miner. Process. 22 (1–2), 105–118.

Herbst, J.A., Fuerstenau, D.W., 1980. Scale-up procedure for continuous grindingmill design using population balance models. Int. J. Miner. Process. 7, 1–31.

Hosten, C., Avsar, C., 1998. Grindability of mixtures of cement clinker and trass.Cem. Concr. Res. 28 (11), 1519–1524.

Iglesias, J.G., Álvarez, M.M., Rodríguez, J.E., 1999. Influence of gypsum’smineralogical characteristics on its grinding behaviour applied to cementfabrication. Cem. Concr. Res. 29 (5), 727–730.

Ipek, H., Ucbas, Y., Hosten, C., 2005. The Bond work index of mixtures of ceramic rawmaterials. Miner. Eng. 18, 981–983.

Kallemback, R.D.C., 2012. Investigação da moagem de misturas binárias emmoinhos de bolas. M.Sc. thesis, Universidade Federal do Rio de Janeiro (inPortuguese).

Magdalinovic, N., 1989. A procedure for rapid determination of the Bond workindex. Int. J. Miner. Process. 27 (1–2), 125–132.

Malghan, S.G., 1986. Treatment methods for difficult-to-float copper porphyry ores.Min. Eng. September, 905–910.

Michaux, S., 2012. Personal communication.Öner, M., 2000. A study of intergrinding and separate grinding of blast furnace slag

cement. Cem. Concr. Res. 30 (3), 437–480.Tavares, L.M., King, R.P., 1998. Single particle fracture under impact loading. Int. J.

Miner. Process. 54, 1–28.Tavares, L.M., Carvalho, R.M., 2009. Modeling breakage rates of coarse particles in

ball mills. Miner. Eng. 22, 650–659.Tavares, L.M., Silveira, M.A.C.W., 2008. Comparison of measures of rock crushability.

In: Meftuni Yekeler. (Org.). Fine Particle Technology and Characterization,Kerala: Research Signpost, pp. 1–20.

Yan, D., Eaton, R., 1994. Breakage properties of ore blends. Miner. Eng. 7,185–199.