Mining, Metallurgy & Exploration (2021) 38:1059–1069

https://doi.org/10.1007/s42461-020-00374-8

Empirical Approach Based Estimation of Charge Factor

and Dimensional Parameters in Underground Blasting
Vivek Kumar Himanshu 1 & M. P. Roy 1 & Ravi Shankar 1 & A. K. Mishra 2 & P. K. Singh 1

Received: 2 February 2020 / Accepted: 17 December 2020 / Published online: 4 January 2021
# Society for Mining, Metallurgy & Exploration Inc. 2021

Abstract
Blasting with the aim to reduce oversize boulders in underground has many hurdles due to limited accessibilities and poor site
conditions. Optimized drilling and blasting parameters can help to achieve this objective. The major challenges of the blast
designers lie within deciding blast geometry, namely drill hole diameter, burden, and spacing. The general approaches covered
worldwide to determine burden-spacing are based on various rules of thumb, which are based on previous experiences of blasts
and the associated outcomes. However, many parameters influencing optimum burden-spacing to achieve desired fragment size
are site specific. Sometimes drill geometry is decided based on associated blasting hazards rather than rock fragmentation. The
Kuz–Ram model is a worldwide accepted rock fragmentation predictor. The parameters associated with this predictor also
include burden-spacing for a blast. Back calculation of burden-spacing from the Kuz–Ram model can be used to achieve desired
fragment size. This paper deals with burden-spacing determination by using an empirical approach for the underground stope ring
blasting.

Keywords Charge factor . Underground . Toe burden . Stoping . Ring . Rock fragmentation

1 Introduction the amount of explosive required for the breakage of one cubic
meter volume of the rock mass. The optimum charge factor
The productivity of excavation by blasting significantly de- results in the proper breakage of rock-strata with minimum
pends on cycle timing of excavators, which in turn are influ- nuisance and maximum productivity. The charge factor is a
enced by the fragment size of blasted rock [1]. The desired function of rock mass characteristics of the blast face, geolog-
fragment size from a blast can be successfully achieved pri- ical condition of the rock strata, and the excavation method-
marily by optimizing the appropriate explosive quantity. In ology. Additionally, the variations in explosive
addition, ample confinement of the explosive at the time of characteristics—detonation velocity, density, etc.—influence
blasting also influences the fragmentation [2]. However, im- the blasting outputs [3]. Therefore, it is also considered as a
proper confinement/coupling/impedance results in unneces- parameter influencing the charge factor. It is presumed that the
sary wastage of explosive energy thereby resulting in blasting charge factor used at a blast face is capable of achieving the
hazards viz. stemming ejections, vibration, and over breaks. burden movement. Thus, optimum charge factor may be de-
Therefore, a judicious design to distribute the explosives cided based on the required burden movement. Therefore, in
evenly plays an important role to obtain the optimum output brief, the scientific assessment of charge factor includes the
from the blast. This can be achieved by optimizing charge investigation of rock and explosive parameters. Further, vari-
factor and dimensional parameters based on the assessment ous researchers have studied and formulated rules of thumb
of in situ rock conditions. The charge factor can be defined as for defining the charge factor of a blast using different criteria.
In this context, Dyno Nobel (2010) [4] has classified the rocks
into four different types—hard, medium, soft, and very soft
* Vivek Kumar Himanshu
vivekbit07@gmail.com
rock types—for defining the charge factor (Table 1). Jemino
et al. (1995) [5] have suggested the charge factor based on the
1
rock mass properties of the blast face. The charge factor clas-
CSIR-Central Institute of Mining and Fuel Research (CSIR-CIMFR),
sification in this study has been used for different distances
Barwa Road, Dhanbad 826015, India
2
between natural fractures of the rock mass, different uniaxial
Indian Institute of Technology (Indian School of Mines),
compressive strength values, and rock density values. The
Dhanbad, India
1060 Mining, Metallurgy & Exploration (2021) 38:1059–1069

Table 1 Charge factor dimensional parameters such as burden and spacing for un-
for different rock types Rock type Charge factor (kg/m3)
derground ring blasting have been related with hole diameter
as per Dyno Nobel quick
reference guide 2010 [5] Hard 0.7–0.8 by Rustan [9]. The suitability of hole diameter for under-
Medium 0.4–0.5 ground blasting is decided from the productivity as well as
Soft 0.25–0.35 safety perspective. The major factor from the productivity
Very soft 0.15–0.25 perspective consists of the planned hole depth to be blasted
in a round. The larger diameter of blast hole is more suitable
for the blast of deep holes, as the deeper holes tend to show
suggested charge factor as per Jemino et al. (1995) [5] is comparatively more deviation. The expected deviation will be
shown in Table 2. Broadbent [6] correlated the in situ p wave less while using the larger diameter of blast holes. However,
velocity with the charge factor for an open-pit copper mine. the smaller diameter blast hole may be preferred to control the
Further, the approach was used by Muftuoglu et al. (1991) [7] vibration for the safety of nearby structures [10].
for overburden strata in lignite/coal mines. Adhikari (2000) Different empirical models have been developed as rock
[8] reviewed some noteworthy approaches such as the transfer fragmentation predictors such as Kuz–Ram model, KCO
of energy approach, based on drilling data and assessment of model, Swebrec function, and various modifications of these
rock quality index, blastability index approaches for the as- models [11]. These models have correlated the fragment size
sessment of charge factor. The dimensional parameter for a from the blast output with the rock and explosive properties.
blast is indirectly related to the charge factor. It includes the The back calculation from these empirical models may be
blast geometry, viz. burden, spacing, explosive column approached to estimate the optimum charge factor and dimen-
length, stemming length, etc. Rules of thumb used by different sional parameters for a particular rock-explosive combination.
rock blasting practitioners have related the dimensional pa- However, the above empirical models have been generated for
rameters with hole diameter. Hole diameter is however, decid- the open-pit excavation. The scientific modification in the
ed based on the bench height. The assessment seems good model may be approached to suit the condition of under-
from the production planning perspective. However, the ground mining. The estimation of charge factor and dimen-
blasting practices with most sophisticated modern drilling sional parameters for ring blasting along with its experimental
equipment have surpassed the rule of thumb. The dimensional validation has been carried out at the Balaria underground
parameters in such cases must be decided on the basis of Lead–Zinc Mine. The mine is a part of the Zawar group of
assessment of rock mass and geo-mining conditions. The ge- mines and is operated by M/s Hindustan Zinc Limited of the
ometry of underground excavation is significantly different Vedanta group. It is located at a distance of approximately
from the general geometry of open-pit excavation. The deci- 40 km south of Udaipur, in the state of Rajasthan in India.
sion regarding dimensional parameter in underground exca-
vation focuses on reducing the boulder generation, accessibil- 1.1 Geology
ity of the excavators, maintaining the sequence of excavation,
as well as ensuring safety for people and machinery. The The region is one of the significant parts of the Aravalli
Supergroup that have been deposited in a Paleoproterozoic
Table 2 Charge factor classification based on the geotechnical rift setting [12]. The Archean metamorphic sequences of the
properties of the rock strata [6]
Banded Gneissic Complex form the basement of the Aravalli
Charge factor Mean distance Uniaxial Rock Supergroup [13]. The area in and around Udaipur constitutes
between natural compressive density the Aravalli Supergroup. The economically noteworthy lower
Class Average fractures in rock rock strength (t/m3) part of the Aravalli Supergroup is best exposed in the vicinity
limit (kg/ value mass (m) (MPa)
m3) (kg/m3)
of the Zawar region. This area incorporates four separate Pb–
Zn deposits, namely Balaria, Baroi, Mochia, and Zawarmala
0.12–0.18 0.150 <0.10 10–30 1.40–1.80 (Fig.1; modified after [14]). The mineralization in this region
0.18–0.27 0.225 0.10–0.25 20–45 1.75–2.35 has been found to be approximately 1700 Ma old as evident
0.27–0.38 0.320 0.20–0.50 30–65 2.25–2.55 from Pb–Pb model age [15]. Further, the major lithologies of
0.38–0.52 0.450 0.45–0.75 50–90 2.50–2.80 this region are dolomite (with varieties), phyllites, quartzite,
0.52–0.68 0.600 0.70–1.00 70–120 2.75–2.90 and conglomerates. The rocks of this area are steeply dipping
0.68–0.88 0.780 0.95–1.25 110–160 2.85–3.00 and are in the form of ridge and valley topography. The ridges
0.88–1.10 0.990 1.20–1.50 145–205 2.95–3.20 are of quartzite and dolomite, whereas the intervening basin
1.10–1.37 1.235 1.45–1.70 195–250 3.15–3.40 comprises different categories of slate and phyllites. The rocks
1.37–1.68 1.525 1.65–1.90 235–300 3.35–3.60 of this region have undergone three main phases of deforma-
1.68–2.03 1.855 >1.85 >285 >3.55 tion and have undergone metamorphism up to greenschist
facies [16]. The mineralization has taken place in the form
Mining, Metallurgy & Exploration (2021) 38:1059–1069 1061

Fig. 1 Geological map of Zawar

Group of mines, HZL, Rajasthan
(Modified after Mookharjee [13])

of fine bedding in carbonaceous phyllite lithologies and as The optimum thickness of the orebody to employ transverse
structurally controlled, epigenetic form in different varieties long-hole stoping is based on the strength properties of the
of dolomites [17]. host rock. The main access to the orebody at different mines
of the Zawar group is through a shaft or decline. The main
1.2 Mining Method Employed at the Experimental access is connected to a footwall drive through cross-cuts on
Site each stoping level. The orebody under excavation is exposed
by driving drivages such as footwall drive and extraction
The lead-zinc orebody at Zawar group of mine is excavated drive. Drivage/drift is defined as a horizontal or inclined
using the long-hole stoping method, which is a variant of the heading/roadway [18]. In metalliferous mining terminology,
Sublevel open stoping method. Further, the long-hole stoping the drivages are generally made parallel to the ore body. The
method has two main variants—longitudinal and transverse horizontal opening across the ore body is termed a cross-cut.
long-hole stoping methods. The selection of longitudinal or Connection to the drivages are made through cross-cuts. The
transverse long-hole stoping method is significantly based on excavation between the cross-cuts are made by opening slot
the width of the orebody. The transverse long-hole stoping is raises. The plan and sectional view of mining method used at
approached for the wider orebody, whereas the longitudinal Zawar group of mines is shown in Fig. 2.
long-hole stoping method is used for narrow orebodies. In Slot raises are opened through the cross-cut for the final
addition to this, the strength properties of rock are also a de- excavation of stopes. The slot opening encompasses the box-
ciding factor for selection of these long-hole stoping method. cut blasting with movement of blasted muck along the free
1062 Mining, Metallurgy & Exploration (2021) 38:1059–1069

Fig. 2 Plan and sectional view showing the sequence of stope excavation at Zawar group of mines

face in lower drive as well as along empty reamer holes. The oversize boulders can be expected from a blast if spacing of
slot opening is further extended to make a slot cross-cut. Ring joint sets are nearly of drilling pattern size. Joints dipping out
holes are drilled to further excavate the stope. The movement of the face will result in finer fragmentation; however, joint
of blasted muck from ring holes takes place along the free face sets dipping in to the face will result in courser fragments.
generated by the slot cross-cut. Density and hardness of the rock mass also have influence
on rock fragment size. Low density rocks will result in finer
fragments at the same charge factor compared to the high-
1.3 Estimation of Charge Factor density rocks.

The charge factor estimation approach using the empirical A ¼ 0:06  ðRMD þ JF þ RDI þ HFÞ ð1Þ
Kuz–Ram model encompasses the assessment of rock and
Where,
explosive properties. Kuznitsov’s equation under the empiri-
cal Kuz–Ram model describes the mean fragment output from A rock factor
a blast on the basis of rock and explosive properties. RMD rock mass description
The rock factor in the empirical model are dependent on the JF joint factor
nature of in situ rock, rock mass strength, hardness of the rock, RDI rock density index
and nature of discontinuities in the periphery of rock mass. HF hardness factor
The factor consists of parameters such as rock mass descrip-
Joint factor can be further represented as Eq. (2).
tion, joint factor, rock density index, and hardness factor. The
relationship for computation of rock factor in Lilly’s JF ¼ JPS þ JPA ð2Þ
blastability index is shown in Eq. (1) [19]. The rock mass
description in rock factor has been further classified as pow- Where,
dery/friable, vertically jointed, and massive. The vertically JPS vertical joint spacing
jointed rock mass is classified on the basis of joint sets present JPA joint plane angle
in the in situ rock mass. The term is named joint factor, and it
can be further classified as vertical joint spacing and joint The parameters shown in Eqs. (1) and (2) have been
plane angle, as per Eq. (2) [19]. Based on the equation and assessed for the experimental stope based on the rating of
detailed assessment of rating under blastability index, more Lilly’s blastability index. The experimental stope had closely
Mining, Metallurgy & Exploration (2021) 38:1059–1069 1063

spaced vertical joints having a dip of 70° to 80°. The joint the drill level and extraction level of the stope. Therefore, the
plane was dipping inside the blast face. The rock density index charge factor computation based on a single hole cannot be
and hardness factor for the stope has been assessed based on justified for the ring blasting pattern. Accordingly, a hypoth-
the assessment of geotechnical parameters for the stoping esis is made considering the “total explosive charge in a ring”
block. The computed Lilly’s blastability index for the exper- in place of “the total explosive charge in a hole” for the com-
imental stope of the Balaria underground mine is shown in putation of charge factor, and an algorithm has been made
Table 3. The dependency of quality and quantity of explosive based on the back calculation from the empirical Kuz–Ram
charge on mean fragment size of the blasted rock has also been model for the estimation of charge factor. The algorithm is
described in Kuznitsov’s equation [20]. The relative weight shown in Fig. 3. The charge factor to achieve different mean
strength (RWS) of the explosive in the equation is a measure fragment size has been computed based on this algorithm.
of the energy available per weight of explosive as compared to Relative weight strength of ANFO and emulsion explosive
an equal weight of ammonium nitrate fuel oil (ANFO) explo- has been considered as 100 and 115, respectively, for the
sive. It is calculated by dividing the absolute weight strength computation. The computed charge factor for two types of
(AWS) of the explosive by the AWS of ANFO and multiply- explosives for different expected mean fragment sizes is
ing by 100. Equation (3) is Kuznetsov’s equation showing the shown in Table 4. The RWS parameter considered for the
relationship among mean fragment size of blasted rock, rock explosive is based on the energy and thereby related to the
factors, and explosive parameters. detonation pressure exerted by the explosive. However, in
fractured strata, gaseous energy also plays an important role.
The estimated charge factor using ANFO explosive in such
Xm ¼ AK−0:8 Q1=6 ð115=RWSÞ19=20 ð3Þ strata may be higher to achieve the expected mean fragment
size.
Where,
Xm mean particle size, cm
A rock factor 1.4 Estimation of Dimensional Parameters
K charge factor, Kg/m3
Q quantity of explosive per hole, Kg The geometry of the underground ring blast varies between
the drill level and extraction level. The burden and spacing in
Kuznitsov’s equation has been developed for the prediction such cases are split as collar burden/spacing and toe burden/
of fragment size from the open pit blasting. Underground ring spacing. The blast holes in the ring blasting pattern are drilled
blasting differs from open pit blasting as the blast holes are from a drill drivage/cross cut. The holes are drilled in inclined
inclined in the former case. The inclined blast holes in under- fashion to excavate the complete ore body. The inclination of
ground ring blasts create varying blast hole spacing between the blast holes is such that it looks to be converging at the

Table 3 Computation of Lilly’s blastability index for experimental stope at the Balaria underground mine [17]

Parameters affecting rock fragmentation Variants of parameters Rating Rating suggested for
Balaria underground mine

Rock mass description (RMD) Powdery/ friable 10 JF

Vertically jointed Joint factor (JF)
Massive 50
Joint factor (JF) Vertical joint spacing (JPS) < 0.1 m 10 10
0.1 m − 1.0 m 20
1.0 m to Drill pattern size 50
Joint plane angle (JPA) Dip out of the face 20 40
Strike perpendicular to face 30
Dip into face 40
Rock density index (RDI) 25 × RD-50 RD- rock 25 × 2.84–50 = 21
density (tonne/cu-m)
Hardness factor (HF) If Y < 50 GPa, Y = Young’s modulus Y/3 Y = 15 GPa
UCS = 90 MPa
Y > 50 GPa UCS/5 Rating = 15/3 = 5
UCS = Uniaxial compressive strength (in MPa)
Calculated rock factor 4.56
1064 Mining, Metallurgy & Exploration (2021) 38:1059–1069

Fig. 3 Algorithm for estimation of charge factor for underground ring blasting

collar point. Accordingly, the actual spacing between the two spacing of the holes suggested by Rustan is 1.5 to 2.0 times
blast holes is at the toe of the ring. The spacing at the collar the toe burden.
point of the blast holes is much less. The spacing between the
blast holes at any point between toe and collar is different. In Burdenðin mÞ ¼ 11:8  Φ0:63 ð4Þ
such case, the explosive charge in the blast holes is distributed
Where,
to meet the required explosive energy demand at a point. The
charging is done in the alternate holes at a point where the Φ blast hole diameter (in m)
spacing between blast holes is less than half of the toe spacing. The suggested empirical relation is very general in nature,
Such charging practice is known as differential charging. A which does not consider the rock parameters. Therefore, an al-
view of the differential charging of the blast holes for a ring is gorithm has been made using the uniformity index equation and
shown in Fig. 4. Rosin–Rammler equation of the Kuz–Ram model. The combi-
The widely applicable empirical relation for the computa- nation of these equations along with the Kuznitsov’s equation
tion of burden-spacing in underground stope blast is designed gives the desired passing percentage of the rock fragment from a
as suggested by Rustan [9]. The relation gives the toe burden defined screen size of specific equivalent diameter. The unifor-
for the ring blast for different diameters of the blast hole. The mity index equation uses various blast hole geometrical param-
suggested empirical relation is shown in Eq. (4). The toe eters, namely burden, spacing, charge column length, deck
length, bench/stope height, and drill deviation. The uniformity
Table 4 Computed charge factor for different expected mean fragment index relation is shown in Eq. (5). The uniformity index equation
size for ring blasting at the Balaria underground mine has further been correlated with the estimated mean fragment
size and expected fragment size (X). The relation is known as
Mean fragment size (in mm) Powder factor (in kg/ m3)
the Rosin–Rammler equation, as shown in Eq. (6).
ANFO explosive Emulsion explosive v0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
u

u S


 0:1
14B uB 1 þ B C
u W BCL−CCL L
200 0.73 0.61 n¼ 2:2− t @ A 1− abs þ 0:1
d 2 B L H
250 0.55 0.46
300 0.44 0.37 ð5Þ
Mining, Metallurgy & Exploration (2021) 38:1059–1069 1065

Fig. 4 Differential charging

pattern for blast holes of a ring

Where, the experimental site. The estimation of “n” is done by

back calculation from Rosin–Rammler’s equation. For
n uniformity index
example, suppose the expected mean fragment size out-
B burden (m)
put from a blast is 20 cm (Xm = 20). Let us assume that
S spacing (m)
90% of the blasted fragment is expected to pass through
d hole diameter (mm)
a screen of 50 cm (X = 50). Thus, in this case 10% of
W standard deviation of drilling precision (m)
the rock fragment will be retained on the screen of size
L charge length (m)
50 cm (Rx = 0.1). After putting the values of Xm, X, and
BCL bottom charge length (m)
R x in Eq. (6), we get the value of “n” as 1.31.
CCL column charge length (m)
Similarly, the value of “n” is computed under different
H stope height (m)
combinations of mean and expected fragment size to
pass through a screen.
The algorithm has been developed using the empiri-

n 
X cal relations under the Kuz–Ram model to estimate the
Rx ¼ exp −0:693 ð6Þ
Xm dimensional parameter of the ring blast. The algorithm
is shown in Fig. 5. The presented algorithm is based on
Where, the presumption that there is no deviation in the drill
Rx mass fraction retained on screen opening X holes for the blasting face. Burden-spacing estimation
Xm mean fragment size (in cm) for different available drill hole diameters has been
n uniformity index done for the Balaria underground mine using the algo-
rithm. The stope height at the mine is 20 m. The avail-
The values of the uniformity index generally vary able drilling machine at the mine has diameters of
between 0.8 and 2.2 (Cunninghum 1983) [21]. Its high 70 mm, 76 mm, 89 mm, and 115 mm. For example,
value indicates the uniform sizing, while low values suppose we want to compute the optimum burden for a
result in a higher proportion of both fines and oversize. ring blast with the objective to obtain mean and 90%
The normal range of n for blasting fragmentation in fragment size from the blast as 20 cm and 50 cm, re-
reasonably competent ground is 0.75 to 1.5. The more spectively. The diameter of the drilling machine avail-
competent rocks have higher values (Cunninghum 1987) able with the mine management is 70 mm. The stope to
[22]. The computed “n” value for the estimation of di- be excavated has a height of 20 m. Let us assume
mensional parameters at the experimental site lies be- spacing/burden as 1.1. Further assume that the maxi-
tween 0.7 and 2. The wide range of the computed uni- mum length of the charged blast hole is 14 m.
formity index is due to the variations in combinations Therefore, for this example, the burden can be comput-
of expected mean fragment size and 90% passing size ed as per Eq. (7). Considering no deck charging in the
 
to identify the best suitable dimensional parameter for blast-holes, the value of abs BCL−CCL L will be 1.
1066 Mining, Metallurgy & Exploration (2021) 38:1059–1069

Fig. 5 Algorithm for estimation

of dimensional parameters for
underground ring blasting

Accordingly, 1.10.1 has come in the denominator of “n” 8 0 0 119

>
> !
 >
>
in Eq. (7). The computation of burden with all the as- < B 1:31 20 B 1 CC= 70
sumed parameters is shown in Eq. (8). The value of B¼ 2:2−B
@ 1:10:1 
B rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi AA * C
>
> 14 @ 1 þ 1:1 >
> 14
burden computed using Eq. (8) is 1.9 m. The spacing : ;
will be 1.9 × 1.1 ≈ 2.1. 2
8 0 0 119 ð8Þ
>
> >
>
>
> B B CC> >
>
> B B C C >
> Similarly, the computation of toe burden has been done
>
> B !
B C C >
>
< B n H B 1 CC= d with variation in the following parameters:
B
B ¼ 2:2−B  0:1  B vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C C
L B rffiffiffiffiffiffiffiffiffiffiffiffi CC>* 14
>
>
> B 1:1 Buu CC>
>
> B B u 1 þ S CC> >
>
(i) Variations in charging length of the stope.
>
> @ @ t B AA> > (ii) Variations in spacing to burden ratio.
>
: >
;
2 (iii) Variations in expected 90% passing size of the rock
ð7Þ fragment.
Mining, Metallurgy & Exploration (2021) 38:1059–1069 1067

Table 5 Optimized burden-spacing for different drill hole diameters for

blasting at the experimental stope of the Balaria underground mine

Hole diameter (in mm) Toe burden (in m) Toe spacing (in m)

70 1.8 1.9
76 2.0 2.1
89 2.3 2.4
115 3.0 3.1

Different combinations have been studied to suggest the

optimum burden-spacing for the experimental stope. The best
suited combination of burden-spacing from the analysis is
presented in Table 5. The stope height of 20 m was charged
up to 14 m to achieve the result. The mean fragment size of the
rock was 200 mm and the 90% passing size of the fragment Fig. 6 A view of blasted muck pile in the Balaria underground mine,
HZL, Rajasthan
was 500 mm. The ratio of spacing to burden was 1.05 in the
optimized computation.
mean and 90% passing fragment size have been com-
1.5 Experimental Trials and Validation of Optimized pared. The predicted and output fragment sizes for the
Blasting Parameters blasts carried out at the experimental stope are summa-
rized in Table 6. The results show that the actual mean
Six blasts were carried out at the experimental stope of fragment size of the rock is lower compared to the
the Balaria underground mine. The blasts were carried predicted mean fragment size. However, the actual
out for the drill hole diameters of 70 mm, 76 mm, and 90% passing size of the rock fragments is much higher
115 mm. The mean fragment size and 90% passing compared to the predicted rock fragment size.
fragment size were predicted for these blasts using the The further development in the Kuz–Ram model sug-
empirical Kuz–Ram model. The actual fragment analysis gests that the mean fragment size is also a function of
for the blasted stope was also carried out using image the blasting geometry. The models have been presented
analysis (Fig. 6). WipFrag software was used for the in the form of a modified Kuz–Ram model. The recent
fragmentation analysis. The image of the blasted muck fragmentation prediction models such as KCO have also
was taken from each blasted face. The images from a discussed that mean fragment size is not the acceptable
particular blast face were taken after each round of re- descriptor, and it may be replaced by the 50% passing
moval of muck by a low profile dump truck (LPDT). size. However, the over prediction of mean fragment
The histogram showing the passing percentage of rock size using the Kuz–Ram model is acceptable from the
fragments of different size was plotted (Fig. 7). The mine productivity point of view.

Table 6 Predicted and output fragment size for the blasts carried out at the experimental stope

Blast No. Hole Hole Burden × No. Average Explosives Predicted fragment size Average fragmentation
No. of dia. depth spacing of uncharged using empirical Kuz– output
holes [mm] [m] [m] × [m] deck length per hole Ram model
[m]
Charge Total Mean 90% passing Mean 90% passing
factor explosives fragment fragment size fragment fragment size
[kg/m3] detonated size [mm] [mm] size [mm] [mm]
[mm]

1. 17 70 3–19 1.9 × 1.9 Nil 6.0 0.61 600 196 500 125 900
2. 14 70 6–24 1.9 × 1.9 Nil 6.0 0.67 700 187 476 105 822
3. 18 76 10–22 1.9 × 1.9 Nil 6.0 0.59 704 207 519 100 955
4. 15 115 18.5–21 2.8 × 2.8 Nil 7.0 0.60 1253 225 602 85 1000
5. 15 70 1.8–22.4 1.9 × 1.9 Nil 7.0 0.61 450 187 512 87 885
6. 10 70 3.5–18.5 1.9 × 1.9 Nil 6.0 0.67 375 168 429 100 850
1068 Mining, Metallurgy & Exploration (2021) 38:1059–1069

Fig. 7 Histogram and cumulative size curve view of fragmented block sizes for the blast conducted at the Balaria underground mine, HZL, Rajasthan

The variation in the 90% passing fragment size may be 2 Conclusions

reduced after considering 50% passing fragment size in place
of mean fragment size in the Rosin–Rammler equation. The Blast dimensional parameters determination for underground
variation may also be due to the effect of delay interval be- blasting is very crucial because it will influence the perfor-
tween the holes in actual blasting of a ring. Because the pre- mance of downstream processes according to charge factor.
diction has been made with the presumption that there is no The predicted blast fragmentation level and its estimation
deviation in the drill holes, the inaccurate drilling may also have been approached using different methods. Rock blasting
have caused the variation between predicted and measured practitioners worldwide use rules of thumb to determine
values of 90% passing fragment size. The linear regression burden-spacing for a blast face. The Kuz–Ram model is de-
analysis was carried out to compare the trend of variations fined by three equations combining the Kuznitsov equation,
between measured and predicted values of 90% passing frag- uniformity index equation, and Rosin–Rammler equation.
ment size (Fig. 8). The relationship shows coefficient of de- Back calculation from the Kuz–Ram model has been used in
termination (R) of 0.87. However, the measurement of drilling this study to compute burden-spacing for a blast based on
accuracy is necessary in the future to obtain more accurate predefined fragment size. The computed burden-spacing was
prediction. Because the prediction has been done considering validated with the experimental blasts, which suggests that the
the complete blast of a ring in a single round, the impact of actual mean fragment size of the rock is lower compared to the
delay has been neglected in this prediction. The suitable cor- predicted mean fragment size. However, the actual 90% pass-
rection factor for impact of delay on fragment size distribution ing size of the rock fragments is much higher compared to the
can be added in the future. predicted rock fragment size. The main reason for this discrep-
ancy may be due to the effect of the delay interval between the
holes in actual blasting of a ring or inaccuracy in drilling
1200
parameters. This discrepancy may be eliminated in the future
Measured 90 % fragment size (in mm)

R² = 0.7583
1000 by further development of the algorithm and addition of a
800
suitable correction factor.
The algorithm suggested in this paper can be useful for
600
optimization of dimensional parameters for underground ring
400 blasting. The discussed methodology can replace the conven-
tional rule of thumb with the aim to meet the production de-
200
mand. The latest fragmentation prediction models, such as the
0 modified Kuz–Ram model, KCO model, and Swebrec func-
400 450 500 550 600 650
Predicted 90 % fragment size (in mm)
tion, can be used in the future to develop an algorithm for
more accurate predictions of the blast induced rock fragment
Fig. 8 Plot between measured and predicted 90% passing fragment size size. The impact of delay between the holes for a ring may also
Mining, Metallurgy & Exploration (2021) 38:1059–1069 1069

be added in the fragmentation model. A separate rock frag- 10. Himanshu VK, Roy MP, Mishra AK, Paswan RK, Panda D, Singh
PK (2018) Multivariate statistical analysis approach for prediction
mentation model for ring blasting can also be developed in the
of blast-induced ground vibration. Journal of Arabian Geoscience
future. 11:460
11. Silva JD, Amaya J, Basso F (2017) Development of a predictive
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that are relevant to the content of this article. Rajasthan, India. Econ Geol 59:656–677
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