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Modified Kuz—Ram fragmentation model and its use
at 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, Iran
b
Faculty of Mining Engineering, Geophysics and Petroleum, Shahrood University of Technology, Shahrood, Iran
c
Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Canada
article info
Article history:
Received 9 March 2008
Received in revised form
27 April 2009
Accepted 8 May 2009
Available online 21 June 2009
Keywords:
Rock fragmentation
Blasting
Kuz—Ram model
Image processing
Geomechanical properties
abstract
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 X
50.
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 X
50
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 rock
fragmentation size distribution by blasting [1,2]. Although it has
been used extensively in practice, it has some deficiencies; one is
timing effect, the other is lack in prediction of fines.
There are some models that proposed to improve the
Kuz—Ram’s model’s inability to predict the fragment size
distribution. The CZM [3] and TCM [4] models are two examples
of 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 fragments
consists of coarse and fine parts. According to CZM, two different
mechanisms control the rock fragments produced by blasting. The
coarse part is produced by tensile fracturing, and the Kuz—Ram
model is used to predict this part of the size distribution.
However, fines are produced by compressive fracturing in the
crushed zone, for which the Rosin–Rammler function gets a
different value of nand X
C
.
In the TCM model, two Rosin—Rammler functions are used for
ROM size distribution. TCM is a five-parameter model in which
two of the parameters are related to the coarse fraction, one is
related to the fines fraction, and the other two are related to fines
part of the distribution.
In addition, by replacing the original Rosin—Rammler equation
with the Swebrec function, the Kuznetsov—Cunningham—
Ouchterlony (KCO) model is arrived at to predict the ROM size
distribution [5]. Like Rosin—Rammler, it uses the median or 50%
passing value X
50
as the central parameter but it also introduces
an upper limit to fragment size X
max
. The third parameter, b,isa
curve-undulation parameter. The Swebrec function removes two
of Kuz—Ram’s drawbacks—the poor predictive capacity in fines
range and the upper limit cut-off of block size.
Spathis suggested that X
50
should have the prefactor
ðln 2Þ
1=n
=
G
½1þð1=nÞ. He claimed that the correction indicates
that the original implementation of Kuz—Ram will overestimate
the size of the rock fragments which may say that the original
Kuz—Ram underestimates the fines faction when the uniformity
index is 0.8–2.2 [6].
Riana et al. [7] presented a new method to determine the rock
factor Ain the Kuz—Ram model. This factor was correlated to
drilling 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 mean
fragment size and applied blast energy per unit volume of rock
ARTICLE IN PRESS
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/ijrmms
International Journal of
Rock Mechanics & Mining Sciences
1365-1609/$ - see front matter &2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijrmms.2009.05.003
Corresponding author. Tel.: +98 412344 4312; fax: +98 412344 4311.
E-mail address: babaei@sut.ac.ir (H. Aghababaei).
International Journal of Rock Mechanics & Mining Sciences 46 (2009) 967–973
(powder factor) has been developed by Kuznetsov [8] as a
function of rock type. He reported that initial studies had been
carried out with models of different materials and the results
were 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 and
prediction was shown and was to be expected as well. The model
predicts fragmentation from blasting in terms of mass percentage
passing through versus fragment size. Kuznetsov’s equation is [8]
X
m
¼AV
0
Q
e
0:8
Q
1=6
(1)
where X
m
is the mean fragment size (cm), Ais the rock factor,
(7 for medium hard rocks, 10 for hard highly fissured Rocks,13 for
hard, weakly fissured rocks), V
0
is the rock volume broken per
blast hole (m
3
), and Q
e
is the mass of TNT containing the energy
equivalent of the explosive charge in each blast hole (kg) and
the relative weight. The strength of TNT compared to ANFO
(ANFO ¼100) is 115. Hence, Eq. (1) based upon ANFO instead of
TNT can be written as
X
m
¼AV
0
Q
e
0:8
Qe
1=6
S
anfo
115
19=30
(2)
where X
m
is the mean fragment size (cm), Ais the rock factor, V
0
is
the rock volume broken per blast hole (m
3
), Q
e
is the mass
of explosive being used (kg), S
anfo
is the relative weight strength of
the explosive to ANFO (ANFO ¼100). Since
V
0
Q
e
¼1
K(3)
where Kis the powder factor (kg/m
3
), Eq. (2) can be rewritten as
X
m
¼AðKÞ
0:8
Q
1=6
e
115
S
anfo
19=30
(4)
Eq. (4) can now be used to calculate the mean fragmentation (X
m
)
for a given powder factor. Solving Eq. (4) for Kgives
K¼A
X
m
Q
1=6
e
115
S
anfo
19=30
"#
1:25
(5)
One can calculate the powder factor required to yield the desired
mean fragmentation. In his experiments, Cunningham indicated
that lower limit for Awas 8, even in very weak rock mass, whereas
the upper limit was A¼12.
The Blastability Index, which was first proposed by Lilly [9],
has been adapted for Kuznetsov’s model (Table 1), in an attempt
to better quantify the selection of rock factor A[2]. Cunningham
stated that the evaluation of rock factors for blasting should at
least take into account the density, mechanical strength, elastic
properties and structure. The equation is
A¼0:06 ðRMD þJF þRDI þHFÞ(6)
The Rosin–Rammler formula is then used to predict the fragment
size distribution. It has been generally recognized as giving
a reasonable description of fragmentation in blasted rock. This
equation is [10]:
R
m
¼1e
ðX=X
C
Þ
n
(7)
where R
m
is the proportion of material passing the screen, Xis the
screen size (cm), X
C
is the characteristic size (cm), and nis the
index of uniformity. The characteristic size X
C
is one through
which 63.2% of the particles pass. If the characteristic size X
C
and
the index of uniformity nare known, a typical fragmentation
curve can be plotted. Eq. (7) can be rearranged to yield the
following expression for the characteristic size:
X
c
¼X
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
lnð1R
m
Þ
n
p(8)
Since the Kuznetsov formula gives the screen size X
m
for which
50% of the material would pass, substituting the values X¼X
m
and R¼0.5 into Eq. (8) gives
X
c
¼X
m
ffiffiffiffiffiffiffiffiffiffiffiffiffi
0:693
n
p(9)
A useful indirect check on the index of uniformity has
been performed by Cunningham [2]. He based his prediction
of fragmentation on the Kuznetsov equation and used the
relationship between fragmentation and drilling pattern to
calculate the blasting parameter of the Rosin–Rammler formula.
The blasting parameter, n, is estimated by
n¼2:214 B
D
1
2þS
2B
0:5
1W
B
L
H
(10)
where Bis the burden (m), Sis the spacing (m), Dis the borehole
diameter (mm), Wis the standard deviation of drilling accuracy
(m), Lis the total charge length (m) and His the bench height (m).
Where there are two different explosives in the hole (bottom
charge and column charge), Eq. (10) is modified to:
n¼2:214 B
D
1W
B
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
2þS
2B
s
0:1þabs BCL CCL
L
0:1
L
H
(11)
where BCL is the bottom charge length (m) and CCL is the column
charge length (m). When using a staggered pattern, this equation
must be multiplied by 1.1. The value of ndetermines the shape
of the Rosin–Rammler curve. High values indicate uniform sizing.
Low values, on the other hand, suggest a wide range of sizes
ARTICLE IN PRESS
Table 1
Rock factor parameters and rates.
RMD Rock mass description
Powdery/friable 10
Vertically jointed JF*
Massive 50
JPS Vertical joint spacing
o0.1m 10
0.1m 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 ¼25 RD*50 RD; rock density (t/m
3
)
HF Hardness factor (GPa)
Y/3 If Yo50
UCS*/5 If Y450
* Meaning Unit
MS Oversize m
DP Drilling pattern size m
YYoung’s modulus GPa
UCS Uniaxial compressive strength MPa
JF ¼JPS+JPA
S. Gheibie et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 967–973968
including both oversize and fines. This combination of the
Kuznetsov and Rosin—Rammler equation results in what has
been called the Kuz—Ram fragmentation model.
3. Research method
3.1. Prediction of ROM size distribution
Based on a modified blastability index, the geomechanical
properties of ten blast sites were collected prior to blasting.
Several laboratory tests were carried out according to ISRM
standards to determine the mechanical and physical parameters
such as Young’s modulus, density and uniaxial compressive
strength and the overall results of these tests and collection have
been shown in Table 2. The flowchart (Fig. 1) shows the steps
in 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 of
blasting at the Sungun Mine, image processing studies were
carried out for 10 blast sites muck piles. All blasts results were
analyzed after conducting blasting operation at three positions of
muck pile (soon after blasting, after loading around half of muck
pile and end of muck pile). For image processing, 15 digital
photographs were taken from each muck pile position and then
processed by the Goldsize program. The analyzed photo results
were 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 results
obtained by image analysis are always different from those of by
sieving. Fines correction usually is the common deal to overcome
this problem in practice. Some methods that can be used to
correct fines have been discussed in the literature [5,11,12].
In this paper, for correcting the fines a representative sample
was provided from muck pile. The sample was analyzed by sieving
and image processing. There were some differences between the
sieving and imaging methods. Actually, image analysis did not
include particles below 40 mm in this sampling and the fines ratio
was nearly 7%. Since the distribution of sizes below 40 mm at
the 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]:
P
fines
ðxÞ%¼x
k
n
(12)
where P
fines
(x) is the passing percent for fines, Xis the size of
particles, Kis the Top size or rock fragments, and nis the material
constant.
After merging the fines and coarse size distributions obtained
by Eq. (12) and image analysis, as a result Fig. 2 shows the
corrected size distribution which is almost closer to sieving
result. By assuming that the rock fragmentation size distribution
follows the Rosin—Rammler distribution, thus, the two formulas
proposed by Chung and Katsabanis can be used to calibrate the
distribution [13]:
X
c
¼e
ð0:565LnX
m
þ0:435LnX
80
Þ
(13)
n¼0:842=ðLnX
80
LnX
m
Þ(14)
where X
m
is the sieve size at 50% material passing (cm), X
80
is the
sieve size at 80% material passing (cm), X
C
is the sieve size at
63.2% material passing (cm), and nis the uniformity index. The
values obtained from Eqs. (10) and (11) can be seen in Table 2.
As Table 3 shows, the Kuz—Ram model overestimates the size
distribution. This confirms that the mean fragment size (X
m
)
and uniformity index (n) as the model’s inputs are not true
(obtained from image analysis) values. Thus, the Kuz—Ram model
is modified in this paper with the aim of having a better
prediction of ROM size distribution. Results obtained at the
Sungun Mine show that Kuznetsov’s model underestimates the
mean fragment size (Table 3). Also, the predicted uniformity
indexes for each blast site were different from those obtained by
image analysis.
4. Proposed model
By analyzing the data from Sungun the two equations below
areproposedtopredictROMsizedistribution.TheRosin—Rammler
function is used as the size distribution with X
m
as central
parameter and n, as the uniformity index for:
X
m
¼0:073BI V
0
Q
e
0:8
Qe
1=6
S
anfo
115
19=30
(15)
n
0
¼1:88 nBI
0:12
(16)
All parameters in Eq. (15) are similar to those described in Eq. (2),
where n
0
is the modified uniformity index, nis the uniformity
index (Cunningham) and BI is the blastability index. The r
2
values
for 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 fines
correction discussed in the Section 3.3 were carried out in the
verification study. Results show that the proposed model has
the acceptable ability to predict the ROM size distribution at the
Sungun Copper Mine (Table 5). Fig. 3 shows the reliability of the
results.
6. Discussion
As mentioned in previous sections, Kuznetsov’s model is based
on geomechanical, geometrical parameters as well as explosive
properties. In this research, 10 blast sites were chosen with
comparable blast geometry and explosive type. Only the geome-
chanical properties of rock masses were variable. Rock mass
properties are defined by BI in Kuznetsov’s equation.
ARTICLE IN PRESS
Table 2
Rating of geomechanical parameters collected from field.
Blast site BI n
00
(Modified model) n
0
(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
S. Gheibie et al. / International Journal of Rock Mechanics & Mining Sciences 46 (2009) 967–973 969
Rock masses are an anisotropic and inhomogeneous media,
with different physical and mechanical behaviors in different
directions. There are many parameters used in the technical
description of rock masses, of which the blastability index uses
some, such as rock mass description, joint spacing, joint plane
angle, etc. Therefore, geomechanical properties as the most
important parameters in rock blasting are not considered
explicitly [14,15]. Therefore, it seems that Kuznetsov’s equation,
theoretically and practically, will not predict the mean fragment
size accurately.
ARTICLE IN PRESS
−
−
−
−
−
−
−
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
As the blast geometry and the explosive used were equal for all
blasts, it can be concluded that these differences arise from the
incomplete description of rock mass properties.
The blastability index is representative of rock mass properties
in the Kuznetsov’s equation. Paying attention to the parameters
used in the BI system, it is known that RMD, JPS, JPA, etc., alone
are not able to describe rock mass properties completely. As an
example, joint aperture is one of the important properties
of joints, which affects the rock mass blastability [14,16], but is
not considered in the BI system. Joint aperture controls the
outgoing gases and energy retention time in rock mass. If this
parameter as an increasing parameter in BI system is considered,
the BI value will increase, and the mean fragment size will be
closer to true value. Since the correction of BI and insertion of any
effective parameter or development of a new classification system
requires extensive researches in different mines and conditions,
these corrections are beyond the scope of this paper.
In addition, exponent nin the Rosin—Rammler model is the
uniformity of fragmentation distribution. The uniformity index
proposed by Cunningham depends on blast geometrical para-
meters. As Eq. (10) shows, there is no parameter to describe the
rock mass properties. Although the uniformity index is deter-
mined by blast geometry, in some methods, such as those
proposed by Lilly [17] and Moomivand [16], blast geometries are
determined on the basis of rock mass properties.
As the only variable in all 10 blasts is the rock mass
geomechanical parameters, it seems that there may be a relation
between rock fragmentation uniformity and rock mass properties.
Certainly, assessment of rock mass properties effects on size
distribution of rock fragments is difficult. Existence of disconti-
nuities with different properties, anisotropy and inhomogeneity of
rock mass media, adds to the blasting mechanisms complexity.
This complexity indicates that separation of gas pressure and
shock wave efficiencies is difficult. Thus, achievement of a relation
in this case requires more researches.
In Sungun Mine, there are several joint sets, which create
uniform 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 and
then liberate the insitu blocks. In some sites at the Sungun Mine,
blasting creates just few new fracture surfaces; it just produces
blocks whose external surfaces are altered. These results strength-
en the theory of rock mass properties effects on uniformity of size
distribution of rock fragments.
In this research, a relation between real uniformity of rock
fragments and blastability index was obtained. Through decreas-
ing the joints spacing, the size of insitu blocks becomes more
uniform. By releasing adequate gas particles, the blocks will
liberate. Boulder formation is common in widely spaced jointed
rock mass blasting [15]. Bhandari concluded that blasts in rock
masses with parallel or perpendicular joints to bench face, leads
to a uniform fragmentation [15]. Certainly, BI may not be
completely proper to make a relation with uniformity; therefore,
ARTICLE IN PRESS
100
80
60
40
20
0
%
1 10 100 1000 10000
X (mm)
Image
Analysis
Fines
corrected
distribution
Fines Ratio = 7%
End fine size 40 mm
Fig. 2. Fragment size distribution obtained by image analysis, fines and fines
corrected distribution.
Table 3
Predicted and actual size distribution for each blast site.
Blast site X
30
(cm) X
m
(cm) X
80
(cm)
MO-1
Kuz-Ram 10 17 33.4
Image analysis 13.8 22 38.7
Proposed model 13.5 21.3 38
MO-2
Kuz-Ram 10.6 18 35.3
Image analysis 14 22 39.6
Proposed model 13.9 22 39.3
MO-3
Kuz-Ram 10.6 18 35.3
Image analysis 15.2 24 42.8
Proposed model 15.1 23 43
MO-4
Kuz-Ram 11.2 19 37.3
Image analysis 15 24 43.2
Proposed model 14.7 23.3 42
MO-5
Kuz-Ram 11.2 19 37.3
Image analysis 16 25.5 45.5
Proposed model 15.2 24 44.4
DI-1
Kuz-Ram 11.8 20 39.3
Image analysis 16.7 26.5 48
Proposed model 16.1 25.8 47
DI-2
Kuz-Ram 12.9 22 43.2
Image analysis 17 27 49.2
Proposed model 17.38 27.3 48.4
DI-3
Kuz-Ram 13.5 23 45
Image analysis 18.8 28.5 51.7
Proposed model 17.7 28 50.9
DI-4
Kuz-Ram 14 24 47
Image analysis 18 29 53
Proposed model 18.3 29.5 53.8
DI-5
Kuz-Ram 15.3 26 51
Image analysis 19.8 32 58.7
Proposed model 19.7 31.7 58.1
Table 4
Rating of geomechanical parameters collected from field for validation.
Blast site BI n
00
(Proposed model) n
0
(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
development of a new index of rock mass properties to be related
with uniformity is suggested. The authors have experimented that
at the Sungun Mine, there are other parameters which affect the
fragmentation uniformity which are not considered in BI system.
It seems that when joint aperture is smaller, the retention time
of gas energy in rock mass gets higher and the gas pressure’s
efficiency increases. Thus, explosive energy leads to better
fragmentation. In some sites of the Sungun Mine, rock masses
consist of hard ferro-oxides filled with an irregular distribution of
tight joints. Ferro-oxides are stronger than the host rock itself,
which is monzonite. Fragmentation in these kinds of blast sites is
non-uniform. To extend that rock masses with BIo60 leads to a
mixture of more fines and boulders.
Since the KCO [5] is a more practical model for prediction
of ROM size distribution, it is better to compare it with newly
proposed model. The first considerable difference is that the KCO
uses Swebrec function instead of Rosin—Rammler for description
of size distribution. Also, it has an upper limit parameter, X
max,
which makes the prediction more reliable. Moreover, KCO model
uses a prefactor of g(n)¼1orðln 2Þ
1=n
=
G
½1þð1=nÞ for prediction
of the mean fragment size, X
50
; however, the newly proposed
model has the different prefactor of 0.073. But maybe it rises from
different geological aspects of blast sites.
On the other hand, KCO uses a parameter, b, which is called
curve-undulation parameter. According to the KCO, bis the function
of Cunningham’s uniformity index, X
max
and X
50
.X
max
is defined as
the minimum of insitu block size, Sor B. Equally, in newly proposed
model n
0
as the modified uniformity index is adopted Cunningham’s
uniformity, nand BI as representative of rock mass. Interestingly,
BI and the insitu block size are related to each other. Therefore, it is
believed that it has a challenging concept in rock fragmentation size
distribution which was revealed in both the KCO and the newly
proposed model in this paper.
7. Conclusion
In this research, the size distribution of rock fragmentation
at the Sungun Copper Mine was predicted by Kuz—Ram
model. Results of image processing show that Kuz—Ram model
overestimates the ROM size distribution. Therefore, the X
m
(mean
fragment size) and n(uniformity index), as model’s inputs, are not
true values. Kuznetsov’s model predicts the mean fragment size
to be lesser the than true values. Since the blast geometry
and explosive type were the same, it was concluded that these
differences rose from disability of rock mass description. Blast-
ability Index does not consider some effective parameters such
as joint aperture and joint filling material. For modification of
Kuznetsov, 0.073 is proposed instead of the 0.06 multiplier.
Results confirm that the uniformity of size distribution of rock
fragmentation is a function of rock mass geomechanical parameters.
The proposed equation to calculate modified the uniformity index is
in the form of a power model. Increasing the BI (resistance of rock
mass against blasting), uniformity decreases. Finally, a new form of
Kuz—Ram fragmentation model was proposed.
Moreover, the new form of Kuz—Ram has some differences
and similarities with KCO model. Firstly, it uses Rosin—Rammler
function but KCO adopts Swebrec function. The prefactor that
are applied to mean fragment size are also different. However, it
may rise from different blast sites. Interestingly, curve-undulation
parameter, b, is somehow related to newly used term in uni-
formity index, BI. Because, both of them consider insitu block size
as an influential parameter in exponent of distribution functions.
However, the proposed model does not consider the timing
effect and upper limit for sizes as the original Kuz—Ram does. It is
good to mention that it can also predict the fines produced in the
blasting at the Sungun Mine. Five other blast sites were used to
verify the newly proposed model at the Sungun; results show its
reliability in prediction of rock fragmentation size distribution.
Acknowledgments
The authors wish to sincerely acknowledge the full financial
support provided by Sungun Copper Mine and Sahand University
of Technology. Grateful thanks are recorded to Dr. Moomivand,
Dr. Qanbari, Mr. Hajiloo, Mr. Karbasi and Mr. Mahammadzada for
their continuous support in during of the project.
References
[1] Cunningham CVB. The Kuz—Ram model for prediction of fragmentation from
blasting. In: Proceedings of the first international symposium on rock
fragmentation by blasting, Lulea, Sweden, 1983. p. 439–54.
[2] Cunningham CVB. Fragmentation estimations and the Kuz—Ram model. In:
Proceedings of the second international symposium on rock fragmentation by
blasting, Keystone, Colo, 1987. p. 475–87.
ARTICLE IN PRESS
Table 5
ROM size distribution of image processing and modified model at the Sungun for
validation.
Blast site X
30
X
50
X
80
M-1
Proposed model 18.5 27.3 45
Image analysis 20 30 49
M-2
Proposed model 14.85 27.9 62.1
Image analysis 16 30 65.5
M-3
Proposed model 19.95 33.5 64.7
Image analysis 20.84 35 66.9
M-4
Proposed model 17.33 31.7 68
Image analysis 18.33 33 69.56
M-5
Proposed 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 %
100101102
X (cm)
Corrected Model
Image Proc
M-2
Fig. 3. Comparison of ROM size distribution of image processing and modified
model.
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