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International Journal of Rock Mechanics & Mining Sciences 46 (2009) 967–973

Contents lists available at ScienceDirect

International Journal ofRock Mechanics & Mining Sciences

1365-16

doi:10.1

� Corr

E-m

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

Modified Kuz—Ram fragmentation model and its useat the Sungun Copper Mine

S. Gheibie a, H. Aghababaei a,�, S.H. Hoseinie b, Y. Pourrahimian c

a Faculty of Mining Engineering, Sahand University of Technology, Tabriz, Iranb Faculty of Mining Engineering, Geophysics and Petroleum, Shahrood University of Technology, Shahrood, Iranc Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Canada

a r t i c l e i n f o

Article history:

Received 9 March 2008

Received in revised form

27 April 2009

Accepted 8 May 2009Available online 21 June 2009

Keywords:

Rock fragmentation

Blasting

Kuz—Ram model

Image processing

Geomechanical properties

09/$ - see front matter & 2009 Elsevier Ltd. A

016/j.ijrmms.2009.05.003

esponding author. Tel.: +98 412 344 4312; fax

ail address: babaei@sut.ac.ir (H. Aghababaei).

a b s t r a c t

Rock fragmentation, which is the fragment size distribution of blasted rock, is one of the most important

indices for estimating the effectiveness of blast work. In this paper a new form of the Kuz—Ram model

is proposed in which a prefactor of 0.073 is included in the formula for prediction of X50. This new

equation has a correlation coefficient that is greater than 0.98. In addition, a new approach is proposed

to calculate the Uniformity Index, n. A Blastability Index (BI) is used to correct the calculation of the

Uniformity Index of Cunningham, where BI reflects the uniformity of the distribution. Interestingly, this

correction also can be observed in the Kuznetsov—Cunningham—Ouchterlony (KCO) model, which uses

In situ block size as a parameter for calculating the curve-undulation in the Swebrec function. However,

it is in contrast to prediction of X50 as the central parameter in Swebrec and Rosin–Rammler distribution

functions. The new model is a two parameter fragmentation size distribution that can be easily

determined in the field. However, it does not consider the timing effect, or upper limit for sizes, as does

the original Kuz—Ram model. The model is used at the Sungun Mine, and it does a good job of

predicting the fines produced during blasting.

& 2009 Elsevier Ltd. All rights reserved.

1. Introduction

The Kuz—Ram model, which was proposed by Cunningham,has been used as a common model in industry for predicting rockfragmentation size distribution by blasting [1,2]. Although it hasbeen used extensively in practice, it has some deficiencies; one istiming effect, the other is lack in prediction of fines.

There are some models that proposed to improve theKuz—Ram’s model’s inability to predict the fragment sizedistribution. The CZM [3] and TCM [4] models are two examplesof extended Kuz—Ram models to improve the prediction of fines;they are known as JKMRC models.

In the CZM model, the size distribution of rock fragmentsconsists of coarse and fine parts. According to CZM, two differentmechanisms control the rock fragments produced by blasting. Thecoarse part is produced by tensile fracturing, and the Kuz—Rammodel is used to predict this part of the size distribution.However, fines are produced by compressive fracturing in thecrushed zone, for which the Rosin–Rammler function gets adifferent value of n and XC.

In the TCM model, two Rosin—Rammler functions are used forROM size distribution. TCM is a five-parameter model in whichtwo of the parameters are related to the coarse fraction, one is

ll rights reserved.

: +98 412 344 4311.

related to the fines fraction, and the other two are related to finespart of the distribution.

In addition, by replacing the original Rosin—Rammler equationwith the Swebrec function, the Kuznetsov—Cunningham—

Ouchterlony (KCO) model is arrived at to predict the ROM sizedistribution [5]. Like Rosin—Rammler, it uses the median or 50%passing value X50 as the central parameter but it also introducesan upper limit to fragment size Xmax. The third parameter, b, is acurve-undulation parameter. The Swebrec function removes twoof Kuz—Ram’s drawbacks—the poor predictive capacity in finesrange and the upper limit cut-off of block size.

Spathis suggested that X50 should have the prefactorðln 2Þ1=n=G½1þ ð1=nÞ�. He claimed that the correction indicatesthat the original implementation of Kuz—Ram will overestimatethe size of the rock fragments which may say that the originalKuz—Ram underestimates the fines faction when the uniformityindex is 0.8–2.2 [6].

Riana et al. [7] presented a new method to determine the rockfactor A in the Kuz—Ram model. This factor was correlated todrilling index for two different types of Indian rock types,sandstone and coaly shale [7].

2. Review of blast fragmentation models

An empirical equation for the relationship between the meanfragment size and applied blast energy per unit volume of rock

ARTICLE IN PRESS

Table 1Rock factor parameters and rates.

RMD Rock mass description

Powdery/friable 10

Vertically jointed JF*

Massive 50

JPS Vertical joint spacing

o0.1 m 10

0.1 m to MS 20

MS* to DP* 50

JPA Joint plane angle

Dip out of face 20

Strike perpendicular to face 30

Dip into face 40

RDI Rock density influence

RDI ¼ 25 RD*�50 RD; rock density (t/m3)

HF Hardness factor (GPa)

Y/3 If Yo50

UCS*/5 If Y450

* Meaning Unit

MS Oversize m

DP Drilling pattern size m

Y Young’s modulus GPa

UCS Uniaxial compressive strength MPa

JF ¼ JPS+JPA

S. Gheibie et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 967–973968

(powder factor) has been developed by Kuznetsov [8] as afunction of rock type. He reported that initial studies had beencarried out with models of different materials and the resultswere later applied to both open pit mines and an atomic blast.Considering the nature of mining and the variability of rock,a degree of scatter between fragmentation measurements andprediction was shown and was to be expected as well. The modelpredicts fragmentation from blasting in terms of mass percentagepassing through versus fragment size. Kuznetsov’s equation is [8]

Xm ¼ AV0

Qe

� �0:8

Q1=6 (1)

where Xm is the mean fragment size (cm), A is the rock factor,(7 for medium hard rocks, 10 for hard highly fissured Rocks, 13 forhard, weakly fissured rocks), V0 is the rock volume broken perblast hole (m3), and Qe is the mass of TNT containing the energyequivalent of the explosive charge in each blast hole (kg) andthe relative weight. The strength of TNT compared to ANFO(ANFO ¼ 100) is 115. Hence, Eq. (1) based upon ANFO instead ofTNT can be written as

Xm ¼ AV0

Qe

� �0:8

Qe1=6 Sanfo

115

� ��19=30

(2)

where Xm is the mean fragment size (cm), A is the rock factor, V0 isthe rock volume broken per blast hole (m3), Qe is the massof explosive being used (kg), Sanfo is the relative weight strength ofthe explosive to ANFO (ANFO ¼ 100). Since

V0

Qe¼

1

K(3)

where K is the powder factor (kg/m3), Eq. (2) can be rewritten as

Xm ¼ AðKÞ�0:8Q1=6e

115

Sanfo

� �19=30

(4)

Eq. (4) can now be used to calculate the mean fragmentation (Xm)for a given powder factor. Solving Eq. (4) for K gives

K ¼A

XmQ1=6

e

115

Sanfo

� �19=30" #1:25

(5)

One can calculate the powder factor required to yield the desiredmean fragmentation. In his experiments, Cunningham indicatedthat lower limit for A was 8, even in very weak rock mass, whereasthe upper limit was A ¼ 12.

The Blastability Index, which was first proposed by Lilly [9],has been adapted for Kuznetsov’s model (Table 1), in an attemptto better quantify the selection of rock factor A [2]. Cunninghamstated that the evaluation of rock factors for blasting should atleast take into account the density, mechanical strength, elasticproperties and structure. The equation is

A ¼ 0:06 � ðRMDþ JF þ RDI þ HFÞ (6)

The Rosin–Rammler formula is then used to predict the fragmentsize distribution. It has been generally recognized as givinga reasonable description of fragmentation in blasted rock. Thisequation is [10]:

Rm ¼ 1� e�ðX=XC Þn

(7)

where Rm is the proportion of material passing the screen, X is thescreen size (cm), XC is the characteristic size (cm), and n is theindex of uniformity. The characteristic size XC is one throughwhich 63.2% of the particles pass. If the characteristic size XC andthe index of uniformity n are known, a typical fragmentationcurve can be plotted. Eq. (7) can be rearranged to yield the

following expression for the characteristic size:

Xc ¼Xffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

� lnð1� RmÞnp (8)

Since the Kuznetsov formula gives the screen size Xm for which50% of the material would pass, substituting the values X ¼ Xm

and R ¼ 0.5 into Eq. (8) gives

Xc ¼Xmffiffiffiffiffiffiffiffiffiffiffiffiffi0:693np (9)

A useful indirect check on the index of uniformity hasbeen performed by Cunningham [2]. He based his predictionof fragmentation on the Kuznetsov equation and used therelationship between fragmentation and drilling pattern tocalculate the blasting parameter of the Rosin–Rammler formula.The blasting parameter, n, is estimated by

n ¼ 2:2� 14B

D

� �1

2þ

S

2B

� �0:5

1�W

B

� �L

H

� �(10)

where B is the burden (m), S is the spacing (m), D is the boreholediameter (mm), W is the standard deviation of drilling accuracy(m), L is the total charge length (m) and H is the bench height (m).Where there are two different explosives in the hole (bottomcharge and column charge), Eq. (10) is modified to:

n ¼ 2:2� 14B

D

� �1�

W

B

� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

2þ

S

2B

� �s

� 0:1þ absBCL� CCL

L

� �� �0:1 L

H

� �(11)

where BCL is the bottom charge length (m) and CCL is the columncharge length (m). When using a staggered pattern, this equationmust be multiplied by 1.1. The value of n determines the shapeof the Rosin–Rammler curve. High values indicate uniform sizing.Low values, on the other hand, suggest a wide range of sizes

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S. Gheibie et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 967–973 969

including both oversize and fines. This combination of theKuznetsov and Rosin—Rammler equation results in what hasbeen called the Kuz—Ram fragmentation model.

3. Research method

3.1. Prediction of ROM size distribution

Based on a modified blastability index, the geomechanicalproperties of ten blast sites were collected prior to blasting.Several laboratory tests were carried out according to ISRMstandards to determine the mechanical and physical parameterssuch as Young’s modulus, density and uniaxial compressivestrength and the overall results of these tests and collection havebeen shown in Table 2. The flowchart (Fig. 1) shows the stepsin the ROM size distribution prediction, image processing,modification and validation of the modified model.

3.2. Fragmentation assessment

After estimating the ROM size distribution for each case ofblasting at the Sungun Mine, image processing studies werecarried out for 10 blast sites muck piles. All blasts results wereanalyzed after conducting blasting operation at three positions ofmuck pile (soon after blasting, after loading around half of muckpile and end of muck pile). For image processing, 15 digitalphotographs were taken from each muck pile position and thenprocessed by the Goldsize program. The analyzed photo resultswere merged to get a better analysis of the photo analyses.

3.3. Fines correction and distribution calibration

Since there are some fine particles that are hidden, the resultsobtained by image analysis are always different from those of bysieving. Fines correction usually is the common deal to overcomethis problem in practice. Some methods that can be used tocorrect fines have been discussed in the literature [5,11,12].

In this paper, for correcting the fines a representative samplewas provided from muck pile. The sample was analyzed by sievingand image processing. There were some differences between thesieving and imaging methods. Actually, image analysis did notinclude particles below 40 mm in this sampling and the fines ratiowas nearly 7%. Since the distribution of sizes below 40 mm atthe Sungun was a straight line in log–log plot, therefore, a Gaudin-Schuhman distribution can be adopted to plot the size distribu-tion curve [11]:

PfinesðxÞ% ¼x

k

� �n

(12)

Table 2Rating of geomechanical parameters collected from field.

Blast site BI n00 (Modified model) n0 (Image analysis) n (Uniformity index)

Mo-1 54.5 1.459 1.469 1.25

Mo-2 57 1.452 1.45 1.25

Mo-3 56.5 1.451 1.447 1.25

Mo-4 60 1.443 1.441 1.25

Mo-5 60 1.44 1.437 1.25

Di-1 63 1.437 1.433 1.25

Di-2 70.67 1.416 1.42 1.25

Di-3 72.42 1.411 1.414 1.25

Di-4 76.7 1.402 1.4 1.25

Di-5 82 1.39 1.39 1.25

where Pfines(x) is the passing percent for fines, X is the size ofparticles, K is the Top size or rock fragments, and n is the materialconstant.

After merging the fines and coarse size distributions obtainedby Eq. (12) and image analysis, as a result Fig. 2 shows thecorrected size distribution which is almost closer to sievingresult. By assuming that the rock fragmentation size distributionfollows the Rosin—Rammler distribution, thus, the two formulasproposed by Chung and Katsabanis can be used to calibrate thedistribution [13]:

Xc ¼ eð0:565LnXmþ0:435LnX80Þ (13)

n ¼ 0:842=ðLnX80 � LnXmÞ (14)

where Xm is the sieve size at 50% material passing (cm), X80 is thesieve size at 80% material passing (cm), XC is the sieve size at63.2% material passing (cm), and n is the uniformity index. Thevalues obtained from Eqs. (10) and (11) can be seen in Table 2.

As Table 3 shows, the Kuz—Ram model overestimates the sizedistribution. This confirms that the mean fragment size (Xm)and uniformity index (n) as the model’s inputs are not true(obtained from image analysis) values. Thus, the Kuz—Ram modelis modified in this paper with the aim of having a betterprediction of ROM size distribution. Results obtained at theSungun Mine show that Kuznetsov’s model underestimates themean fragment size (Table 3). Also, the predicted uniformityindexes for each blast site were different from those obtained byimage analysis.

4. Proposed model

By analyzing the data from Sungun the two equations beloware proposed to predict ROM size distribution. The Rosin—Rammlerfunction is used as the size distribution with Xm as centralparameter and n, as the uniformity index for:

Xm ¼ 0:073BIV0

Qe

� �0:8

Qe1=6 Sanfo

115

� ��19=30

(15)

n0 ¼ 1:88 � n � BI�0:12 (16)

All parameters in Eq. (15) are similar to those described in Eq. (2),where n0 is the modified uniformity index, n is the uniformityindex (Cunningham) and BI is the blastability index. The r2 valuesfor Eqs. (15) and (16) were 0.98 and 0.96, respectively.

5. Validation of proposed model

To validate the proposed model, five blast sites were studied(Table 4). All the steps in the flowchart (Fig. 1) including finescorrection discussed in the Section 3.3 were carried out in theverification study. Results show that the proposed model hasthe acceptable ability to predict the ROM size distribution at theSungun Copper Mine (Table 5). Fig. 3 shows the reliability of theresults.

6. Discussion

As mentioned in previous sections, Kuznetsov’s model is basedon geomechanical, geometrical parameters as well as explosiveproperties. In this research, 10 blast sites were chosen withcomparable blast geometry and explosive type. Only the geome-chanical properties of rock masses were variable. Rock massproperties are defined by BI in Kuznetsov’s equation.

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−

−

−

−

−−

−

Fig. 1. Steps of Run of Mine (ROM) size distribution prediction, Kuz—Ram modification and validation.

S. Gheibie et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 967–973970

Rock masses are an anisotropic and inhomogeneous media,with different physical and mechanical behaviors in differentdirections. There are many parameters used in the technicaldescription of rock masses, of which the blastability index usessome, such as rock mass description, joint spacing, joint plane

angle, etc. Therefore, geomechanical properties as the mostimportant parameters in rock blasting are not consideredexplicitly [14,15]. Therefore, it seems that Kuznetsov’s equation,theoretically and practically, will not predict the mean fragmentsize accurately.

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100

80

60

40

20

0

%

1 10 100 1000 10000X (mm)

ImageAnalysis

Fines

correcteddistribution

Fines Ratio = 7%

End fine size 40 mm

Fig. 2. Fragment size distribution obtained by image analysis, fines and fines

corrected distribution.

Table 3Predicted and actual size distribution for each blast site.

Blast site X30 (cm) Xm (cm) X80 (cm)

MO-1Kuz-Ram 10 17 33.4

Image analysis 13.8 22 38.7

Proposed model 13.5 21.3 38

MO-2Kuz-Ram 10.6 18 35.3

Image analysis 14 22 39.6

Proposed model 13.9 22 39.3

MO-3Kuz-Ram 10.6 18 35.3

Image analysis 15.2 24 42.8

Proposed model 15.1 23 43

MO-4Kuz-Ram 11.2 19 37.3

Image analysis 15 24 43.2

Proposed model 14.7 23.3 42

MO-5Kuz-Ram 11.2 19 37.3

Image analysis 16 25.5 45.5

Proposed model 15.2 24 44.4

DI-1Kuz-Ram 11.8 20 39.3

Image analysis 16.7 26.5 48

Proposed model 16.1 25.8 47

DI-2Kuz-Ram 12.9 22 43.2

Image analysis 17 27 49.2

Proposed model 17.38 27.3 48.4

DI-3Kuz-Ram 13.5 23 45

Image analysis 18.8 28.5 51.7

Proposed model 17.7 28 50.9

DI-4Kuz-Ram 14 24 47

Image analysis 18 29 53

Proposed model 18.3 29.5 53.8

DI-5Kuz-Ram 15.3 26 51

Image analysis 19.8 32 58.7

Proposed model 19.7 31.7 58.1

Table 4Rating of geomechanical parameters collected from field for validation.

Blast site BI n00 (Proposed model) n0 (Image processing) n (Uniformity index)

M-1 81.75 1.932 1.898 1.8

M-2 73.75 1.136 1.223 1.032

M-3 80 1.606 1.612 1.400

M-4 78.75 1.525 1.552 1.400

M-5 92.5 1.506 1.482 1.554

S. Gheibie et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 967–973 971

As the blast geometry and the explosive used were equal for allblasts, it can be concluded that these differences arise from theincomplete description of rock mass properties.

The blastability index is representative of rock mass propertiesin the Kuznetsov’s equation. Paying attention to the parametersused in the BI system, it is known that RMD, JPS, JPA, etc., aloneare not able to describe rock mass properties completely. As anexample, joint aperture is one of the important propertiesof joints, which affects the rock mass blastability [14,16], but isnot considered in the BI system. Joint aperture controls theoutgoing gases and energy retention time in rock mass. If thisparameter as an increasing parameter in BI system is considered,the BI value will increase, and the mean fragment size will becloser to true value. Since the correction of BI and insertion of anyeffective parameter or development of a new classification systemrequires extensive researches in different mines and conditions,these corrections are beyond the scope of this paper.

In addition, exponent n in the Rosin—Rammler model is theuniformity of fragmentation distribution. The uniformity indexproposed by Cunningham depends on blast geometrical para-meters. As Eq. (10) shows, there is no parameter to describe therock mass properties. Although the uniformity index is deter-mined by blast geometry, in some methods, such as thoseproposed by Lilly [17] and Moomivand [16], blast geometries aredetermined on the basis of rock mass properties.

As the only variable in all 10 blasts is the rock massgeomechanical parameters, it seems that there may be a relationbetween rock fragmentation uniformity and rock mass properties.Certainly, assessment of rock mass properties effects on sizedistribution of rock fragments is difficult. Existence of disconti-nuities with different properties, anisotropy and inhomogeneity ofrock mass media, adds to the blasting mechanisms complexity.This complexity indicates that separation of gas pressure andshock wave efficiencies is difficult. Thus, achievement of a relationin this case requires more researches.

In Sungun Mine, there are several joint sets, which createuniform blocks. The explosive type used at the Sungun is ANFO,which has high gas energy (EB) and produces high gas pressures.The gas particles passing the joints activate the elder joints andthen liberate the insitu blocks. In some sites at the Sungun Mine,

blasting creates just few new fracture surfaces; it just producesblocks whose external surfaces are altered. These results strength-en the theory of rock mass properties effects on uniformity of sizedistribution of rock fragments.

In this research, a relation between real uniformity of rockfragments and blastability index was obtained. Through decreas-ing the joints spacing, the size of insitu blocks becomes moreuniform. By releasing adequate gas particles, the blocks willliberate. Boulder formation is common in widely spaced jointedrock mass blasting [15]. Bhandari concluded that blasts in rockmasses with parallel or perpendicular joints to bench face, leadsto a uniform fragmentation [15]. Certainly, BI may not becompletely proper to make a relation with uniformity; therefore,

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Table 5ROM size distribution of image processing and modified model at the Sungun for

validation.

Blast site X30 X50 X80

M-1Proposed model 18.5 27.3 45

Image analysis 20 30 49

M-2Proposed model 14.85 27.9 62.1

Image analysis 16 30 65.5

M-3Proposed model 19.95 33.5 64.7

Image analysis 20.84 35 66.9

M-4Proposed model 17.33 31.7 68

Image analysis 18.33 33 69.56

M-5Proposed model 24.35 39.3 74.5

Image analysis 25.2 42 80.3

100

90

80

70

60

50

40

30

20

10

0

R %

100 101 102

X (cm)

Corrected ModelImage Proc

M-2

Fig. 3. Comparison of ROM size distribution of image processing and modified

model.

S. Gheibie et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 967–973972

development of a new index of rock mass properties to be relatedwith uniformity is suggested. The authors have experimented thatat the Sungun Mine, there are other parameters which affect thefragmentation uniformity which are not considered in BI system.It seems that when joint aperture is smaller, the retention timeof gas energy in rock mass gets higher and the gas pressure’sefficiency increases. Thus, explosive energy leads to betterfragmentation. In some sites of the Sungun Mine, rock massesconsist of hard ferro-oxides filled with an irregular distribution oftight joints. Ferro-oxides are stronger than the host rock itself,which is monzonite. Fragmentation in these kinds of blast sites isnon-uniform. To extend that rock masses with BIo60 leads to amixture of more fines and boulders.

Since the KCO [5] is a more practical model for predictionof ROM size distribution, it is better to compare it with newlyproposed model. The first considerable difference is that the KCOuses Swebrec function instead of Rosin—Rammler for descriptionof size distribution. Also, it has an upper limit parameter, Xmax,

which makes the prediction more reliable. Moreover, KCO modeluses a prefactor of g(n) ¼ 1 or ðln 2Þ1=n=G½1þ ð1=nÞ� for predictionof the mean fragment size, X50; however, the newly proposed

model has the different prefactor of 0.073. But maybe it rises fromdifferent geological aspects of blast sites.

On the other hand, KCO uses a parameter, b, which is calledcurve-undulation parameter. According to the KCO, b is the functionof Cunningham’s uniformity index, Xmax and X50. Xmax is defined asthe minimum of insitu block size, S or B. Equally, in newly proposedmodel n0 as the modified uniformity index is adopted Cunningham’suniformity, n and BI as representative of rock mass. Interestingly,BI and the insitu block size are related to each other. Therefore, it isbelieved that it has a challenging concept in rock fragmentation sizedistribution which was revealed in both the KCO and the newlyproposed model in this paper.

7. Conclusion

In this research, the size distribution of rock fragmentationat the Sungun Copper Mine was predicted by Kuz—Rammodel. Results of image processing show that Kuz—Ram modeloverestimates the ROM size distribution. Therefore, the Xm (meanfragment size) and n (uniformity index), as model’s inputs, are nottrue values. Kuznetsov’s model predicts the mean fragment sizeto be lesser the than true values. Since the blast geometryand explosive type were the same, it was concluded that thesedifferences rose from disability of rock mass description. Blast-ability Index does not consider some effective parameters suchas joint aperture and joint filling material. For modification ofKuznetsov, 0.073 is proposed instead of the 0.06 multiplier.

Results confirm that the uniformity of size distribution of rockfragmentation is a function of rock mass geomechanical parameters.The proposed equation to calculate modified the uniformity index isin the form of a power model. Increasing the BI (resistance of rockmass against blasting), uniformity decreases. Finally, a new form ofKuz—Ram fragmentation model was proposed.

Moreover, the new form of Kuz—Ram has some differencesand similarities with KCO model. Firstly, it uses Rosin—Rammlerfunction but KCO adopts Swebrec function. The prefactor thatare applied to mean fragment size are also different. However, itmay rise from different blast sites. Interestingly, curve-undulationparameter, b, is somehow related to newly used term in uni-formity index, BI. Because, both of them consider insitu block sizeas an influential parameter in exponent of distribution functions.

However, the proposed model does not consider the timingeffect and upper limit for sizes as the original Kuz—Ram does. It isgood to mention that it can also predict the fines produced in theblasting at the Sungun Mine. Five other blast sites were used toverify the newly proposed model at the Sungun; results show itsreliability in prediction of rock fragmentation size distribution.

Acknowledgments

The authors wish to sincerely acknowledge the full financialsupport provided by Sungun Copper Mine and Sahand Universityof Technology. Grateful thanks are recorded to Dr. Moomivand,Dr. Qanbari, Mr. Hajiloo, Mr. Karbasi and Mr. Mahammadzada fortheir continuous support in during of the project.

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