This thesis examines the effect of drillhole diameter on blasting costs when different fragmentation targets are required. A mathematical model is developed to calculate blast design parameters and costs based on the required 80% fragment size needed for crusher operation. The model uses previously developed fragmentation models from literature. It examines how drillhole diameter affects blasting requirements to achieve fragmentation targets and calculates costs for diameters from 75 to 350mm. The total cost of drilling and blasting is analyzed to determine the optimal diameter selection given fragmentation targets and site conditions.

1. The Effect of Fragmentation Specification on
Blasting Cost
by
Muhammad Arshad Rajpot
A thesis submitted to the Department of Mining Engineering in conformity
with the requirements for the degree of
Master of Science (Engineering)
Queen's University,
Kingston, Ontario, Canada.
March 2009
Copyright © Muhammad Arshad Rajpot 2009

2. ii
In loving memory of my Father and Grandfather who wanted me to achieve the
highest echelon of my career. To my Mother and family: with great love and affection.

3. iii
ABSTRACT
Drilling and blasting are seen as sub-systems of size reducing operations in mining. To have
better design parameters for economical excavation of mineral production and
fragmentation, the comminution and fragmentation operations need to be studied and
optimized independently, as well as together, to create optimized use of energy and cost-
effective operation.
When there is a change in drillhole diameter or fragmentation specification, changes in the
blast design parameters are required affecting the cost of a drilling and blasting operation.
A model was developed to calculate blast design parameters and costs on the basis of the
required 80% fragment size needed for crusher operation. The model is based on
previously developed fragmentation models, found in the literature. The model examines
the effect of drilling diameter on blasting requirements to achieve certain fragmentation
targets and calculates blast design parameters and costs for a range of diameters from 75
to 350 mm.
To examine the effectiveness of this model, two different 80% passing sizes of fragments
have been considered. It was shown that cost optimization occurs at an intermediate
diameter, since there are opposing trends of the effect of diameter on powder factor and
accessories needed. To achieve a certain fragmentation target, the total cost of drilling and
blasting shows a clear trend allowing an optimum selection of diameter. The selected

4. iv
diameter also allows the examination of the suitability of the drill machine under the given
geological and operational conditions of the drilling site.

5. v
ACKNOWLEDGEMENTS
Supervisors
I am highly grateful to Dr. Charley Pelley for accepting me as a student for this M.Sc.Eng.
program, and providing financial, moral, and academic support to complete this thesis.
My special thanks go to Dr. Panagiotis Katsabanis, famous under the name Takis as a
research scholar in the global explosive industry for his constant academic guidance,
technical, financial and moral support to finalize this thesis work.
Resource Organizations and Persons
I am thankful to Atlas Copco, a major company manufacturing ITH drill machines,
particularly their managers Peter Edmonds and Ray Peterson, for providing practically
observed data for their products.
I am thankful in particular to the following for providing useful data and valuable advice:
Mauro Dobran, Manager R & D for Cubex
Karl Dufresne and Lester Kneen, Technical Sales Managers, ETI Canada Inc.
Doug McBeath - Accounts Manager, Orica Canada Inc. – Madoc, ON. and
Pat McLaughlin consultant, Suncor, Fort McMurray
Faculty & Research Staff

6. vi
I thank all faculty members and in particular Dr. Jonathan Peck former Chair and Dr.
Laeeque K. Daneshmend Chair Department of Mining Engineering at Queen's University,
for helping me to be a successful graduate.
I extend my special thanks to Dr. James F. Archibald who provided me with academic and
moral support to complete this study and always suggested consideration to integrate into
the Canadian mining industry. I am also very thankful to Dr. Sadan Kelebek and Professor
Garston H. Blackwell, who have been very kind and helpful to me whenever I needed their
help during my stay at Queen’s for this thesis work.
I am thankful to Dr. Christopher A. Pickles, Dr. Euler De Souza, Dr. Stephen D. McKinnon, Dr.
Wan-Tai Yen, and all other professors who have been helpful.
Graduate Students
I thank all caring grad students in the Department of Mining Engineering, who studied with
me as course mates and who have been very helpful in completing this thesis work.
Technical & Support Staff
I appreciate the sympathetic concern of Peter Auchincloss network administrator, for
helping me at a critical time of my life by providing me with all the support of computer
software and hardware.

7. vii
I thank Maritza Bailey for supporting me in the Department of Mining Engineering Labs
and providing necessary help whenever required.
I am indebted and thankful to Wanda Badger, Michelle Knapp, Jessica Hogan, Tina
McKenna, Kate Cowperthwaite, and all other staff members of the Department of Mining
Engineering, who had been very helpful and welcoming in completion of this thesis work.
Family and friends
Special thanks go to my daughters Maria, Bushra and Kinza, and son Mujtaba who accepted
me as a student Dad during their own study period. Very special thanks in particular to my
wife Talat without whose whole-hearted support I would never have been able to attend
Queen’s University at Kingston.
Finally I thank all my friends in Canada and in Pakistan who always wished me success and
helped me whenever and wherever I wanted them.
Muhammad Arshad Rajpot

8. viii
Table of Contents
ABSTRACT_______________________________________________________________________________________iii
ACKNOWLEDGEMENTS _________________________________________________________________________v
Table of Contents _____________________________________________________________________________ viii
List of Figures __________________________________________________________________________________ xv
List of Tables ___________________________________________________________________________________ xx
List of Symbols ________________________________________________________________________________ xxii
Chapter 1 __________________________________________________________________________________ 1
Introduction ______________________________________________________________________________________1
1.1. Preamble __________________________________________________________________________________1
1.2. Objective __________________________________________________________________________________5
1.2.1. Formulation or adoption of a mathematical model _______________________________________ 5
1.2.2. Calculating the effect of diameter on fragmentation______________________________________ 5
1.2.3. Selection of a diameter given certain fragmentation requirements _____________________ 5
1.2.4. Calculation of drilling and blasting costs to produce a certain fragmentation__________ 5
1.2.5. Effect of diameter on cost ___________________________________________________________________ 6
1.3. Outline_____________________________________________________________________________________6
Chapter 2 __________________________________________________________________________________ 8
Blast Design Parameters ________________________________________________________________________8

9. ix
2.1. Introduction_______________________________________________________________________________8
2.2. Uncontrollable factors ___________________________________________________________________9
2.2.1. Properties of rock____________________________________________________________________________ 9
2.2.2. Rock factor __________________________________________________________________________________10
2.3. Controllable factors ____________________________________________________________________ 10
2.3.1. Height of bench _____________________________________________________________________________12
2.3.2. Blasthole inclination________________________________________________________________________13
2.3.3. Stemming____________________________________________________________________________________14
2.3.4. Subdrilling___________________________________________________________________________________15
2.3.5. Burden and spacing ________________________________________________________________________16
2.3.6. Blasthole patterns __________________________________________________________________________17
2.3.7. Blasthole deviation _________________________________________________________________________18
2.4. Blasthole diameter _____________________________________________________________________ 20
2.4.1. Advantages associated with small diameter boreholes__________________________________21
2.4.2. Disadvantages associated with the small diameter boreholes __________________________21
2.4.3. Advantages associated with larger diameter boreholes_________________________________22
2.4.4. Disadvantages of using larger drillhole diameter ________________________________________22
2.5. Conclusion ______________________________________________________________________________ 22
Chapter 3 _________________________________________________________________________________24
Fragmentation Models Used __________________________________________________________________ 24
3.1. Introduction_____________________________________________________________________________ 24

10. x
3.2. Particle sizing ___________________________________________________________________________ 24
3.3. Kuz-Ram model_________________________________________________________________________ 29
3.4. Fines in the blast muckpile ____________________________________________________________ 31
3.4.1. Two-component model of blast fragmentation __________________________________________32
3.4.2. Swebrec function ___________________________________________________________________________34
3.5. Conclusion ______________________________________________________________________________ 35
Chapter 4 _________________________________________________________________________________36
Calculation of the 80% Passing Size__________________________________________________________ 36
4.1. Introduction_____________________________________________________________________________ 36
4.2. Calculation of blasting parameters on the basis of the 80% fragment size ________ 39
4.3. Correction for fines_____________________________________________________________________ 43
4.4. Selection of suitable drilling design parameters _____________________________________ 43
4.4.1. Effect of stemming length on burden _____________________________________________________43
4.4.2. Effect of subdrilling length on powder factor, uniformity index and burden __________45
4.4.3. Effect of stemming length on uniformity index, powder factor and average fragment
size___________________________________________________________________________________________48
4.4.4. Drillhole deviation effect on Uniformity Index ___________________________________________52
4.5. Effect of rock factor on burden ________________________________________________________ 52
4.6. Effect of explosive density on burden_________________________________________________ 53
4.7. Conclusion ______________________________________________________________________________ 55
Chapter 5 _________________________________________________________________________________56

11. xi
Drilling Considerations________________________________________________________________________ 56
5.1. Introduction_____________________________________________________________________________ 56
5.2. Drilling production _____________________________________________________________________ 56
5.2.1. Extrapolation of data for penetration calculation when diameter is changed _________58
5.2.2. Calculation for rotary-percussive and rotary drilling penetration _____________________58
5.2.3. Data from drilling machines selected for this study _____________________________________60
5.3. Drilling penetration rates and comparison in given and calculated UCS rock_____ 62
5.4. Effect of bailing velocity on penetration rate_________________________________________ 66
5.5. Effect of mechanical availability and utilization of drill machines _________________ 67
5.6. Conclusions _____________________________________________________________________________ 69
Chapter 6 _________________________________________________________________________________70
Cost Calculations_______________________________________________________________________________ 70
6.1. Introduction_____________________________________________________________________________ 70
6.2. Drilling costs ____________________________________________________________________________ 72
6.3. Cost estimates for surface mining drilling operations_______________________________ 79
6.3.1. Introduction_________________________________________________________________________________79
6.3.2. Cost estimate for surface drilling by top hammer (diameter smaller than 127mm) __80
6.3.3. Drilling cost estimates for diameters between 127mm and 250mm ___________________81
6.3.4. Drilling cost estimates for diameters above 250mm ____________________________________86
6.4. Comparative cost results from small to large size diameter ranges of drillholes
(surface mining)________________________________________________________________________ 87

12. xii
6.4.1. Influence of different rock UCS on drilling rate and cost of production________________89
6.4.2. Effect of bailing velocity on the cost of drilling___________________________________________90
6.5. Drilling operation for underground mining __________________________________________ 92
6.5.1. Cost calculations for underground drilling operation ___________________________________94
6.6. Blasting costs ___________________________________________________________________________ 96
6.7. Drilling cost per unit volume of rock blasted________________________________________102
6.8. Drilling blasting costs per unit volume of rock blasted with ANFO _______________102
6.9. Drilling blasting costs per unit volume of rock blasted with emulsion____________104
6.10. Conclusions___________________________________________________________________________106
Chapter 7 _______________________________________________________________________________ 108
Cost Comparisons and Optimization ________________________________________________________108
7.1. Introduction____________________________________________________________________________108
7.2. Optimization of drilling costs_________________________________________________________109
7.2.1. Assumptions for operating costs ________________________________________________________ 109
7.2.2. Assumptions for owning costs___________________________________________________________ 110
7.3. Discussion______________________________________________________________________________112
7.4. Optimization and comparison of drilling cost per unit volume of rock ___________118
7.5. Optimization and comparison of blasting costs_____________________________________123
7.5.1. Effect of rock factor ‘A’ on cost of blasting______________________________________________ 123
7.5.2. Effect of type of explosive on the cost per cubic meter of rock blasting______________ 124
7.5.3. Effect of fragment size on cost___________________________________________________________ 125

13. xiii
7.6. Optimization and comparison of drilling-blasting cost_____________________________126
7.6.1. Drilling-blasting costs under assumed conditions _____________________________________ 127
7.6.2. Drilling-blasting cost under realistic assumptions, a final discussion________________ 128
7.7. Conclusion _____________________________________________________________________________129
Chapter 8 _______________________________________________________________________________ 131
Cost Component Sensitivities ________________________________________________________________131
8.1. Introduction____________________________________________________________________________131
8.2. Assumptions made in this study _____________________________________________________132
8.3. Sensitivity analysis for drilling and blasting cost by changing the component costs
_______________________________________________________________________________________________133
8.3.1. Sensitivity of the blasting cost components ____________________________________________ 133
8.3.2. Sensitivity of drilling operation cost components to the cost of drilling and blasting.137
8.4. Sensitivity analysis for drilling and blasting cost by changing design parameters
_______________________________________________________________________________________________140
8.4.1. Sensitivity analysis of drilling and blasting cost by changing selected bench height 141
8.4.2. Sensitivity analysis of the effect of fragmentation specification on the drilling and
blasting cost_______________________________________________________________________________ 145
8.5. Final spider diagram and conclusion ________________________________________________146
Chapter 9 _______________________________________________________________________________ 149
Summary, Conclusions and Recommendations ____________________________________________149

14. xiv
9.1. Summary _______________________________________________________________________________149
9.2. Conclusions ____________________________________________________________________________151
9.3. Recommendations for further work _________________________________________________152
References______________________________________________________________________________ 153
Appendix A ____________________________________________________________________________________162
Blasting Costs, Summary __________________________________________________________________162
Appendix B ____________________________________________________________________________________164
Cost calculations using Table 6-2 as costing model _____________________________________164
Appendix C ____________________________________________________________________________________181
Price Quotations____________________________________________________________________________181
Appendix D ____________________________________________________________________________________187
Graph charts and figures _____________________________________________________________187

15. xv
List of Figures
Figure 1-1 A simple diagrammatic presentation of “Drill to Mill” fragmentation flow
sheet.................................................................................................................................................4
Figure 4-1 Burden vs diameter with different stemming lengths and 80% passing
fragment size of 80 cm........................................................................................................... 44
Figure 4-2 Burden vs diameter with different stemming lengths and 80% passing
fragment size of 30cm. ........................................................................................................... 45
Figure 4-3 Comparison of powder factor 'q' by changing subdrilling (SUB).......................... 46
Figure 4-4 Effect of subdrilling (SUB) on uniformity index 'n'..................................................... 47
Figure 4-5 Effect of subdrilling (SUB) length on burden 'B'.......................................................... 48
Figure 4-6 Effect of stemming length on uniformity index 'n' (i) when X80=30 cm and
(ii) X80=80 cm............................................................................................................................. 49
Figure 4-7 Effect of stemming length on powder factor with subdrilling=0.2B................... 50
Figure 4-8 Effect of stemming length on mean fragment size 'X50' with
subdrilling=0.2B when X80=30 cm and X80=80 cm. .................................................. 51
Figure 4-9 Change in uniformity index with changes in drillhole deviation when
stemming is equal to burden and subdrilling=0.2B.................................................... 52
Figure 4-10 Changes in burden length when drilled in rocks having different rock
factor............................................................................................................................................. 53
Figure 4-11 Effect of explosive density on burden.............................................................................. 54
Figure 5-1 Net production of various drill machines in different and similar UCS
rock................................................................................................................................................ 65

16. xvi
Figure 5-2 Net production rates of various drilling machines with different
availability and utilization.................................................................................................... 69
Figure 6-1 Cost per meter length of drilling and the cost trends with respect to
drillhole diameter for JH Tophammer. ............................................................................ 81
Figure 6-2 Cost per meter length of drilling by different machines for limestone at
different locations.................................................................................................................... 87
Figure 6-3 Cost per meter length of drilling by different machines for limestone of
different UCS at different locations................................................................................... 88
Figure 6-4 Cost per meter length of drilling by Driltech D75K in limestone at
different locations with different UCS.............................................................................. 90
Figure 6-5 Cost per meter length of drilling in limestone using different pressure
compressors............................................................................................................................... 91
Figure 6-6 Blasting cost of a drillhole charged with ANFO or emulsion at each
diameter size of selected range from 75 to 350 mm................................................101
Figure 6-7 Drilling and blasting cost per cubic meter of rock with different UCS and
X80=30 cm..................................................................................................................................103
Figure 6-8 Drilling and blasting cost per cubic meter of rock with different UCS and
X80=80 cm..................................................................................................................................104
Figure 6-9 Drilling cost per cubic meter of limestone by using emulsion/ANFO for
different UCS and X80=30 and 80 cm. .............................................................................105
Figure 6-10 Drilling and blasting cost per cubic meter of limestone by using
emulsion/ANFO for different UCS and X80=30 and 80 cm. ....................................106
Figure 7-1 Comparative cost per meter length of drilling in rocks of different UCS by
John Henry Tophammer Rockdrill. .................................................................................113

17. xvii
Figure 7-2 Comparative cost per meter length of drilling in rocks of different UCS by
Driltech D75K. .........................................................................................................................114
Figure 7-3 Comparative cost per meter length of drilling in rocks of different UCS by
various machines. ..................................................................................................................115
Figure 7-4 Comparative cost per meter length of drilling for the range of drilhole
diameters in rocks of different UCS by various machines......................................116
Figure 7-5 Cost per meter length of drilling in rocks of different UCS by various
machines with different percetages of availability (a) and utilization (u).....117
Figure 7-6 Drilling cost per cubic meter for rock fragments of X80=30 and 80 cm for
a range of drillhole diameters under similar conditions and UCS 126
MPa..............................................................................................................................................119
Figure 7-7 Drilling cost per cubic meter of limestone under given and assumed
conditions of UCS, availability (a) and utilization (u).............................................120
Figure 7-8 Drilling cost per cubic meter of limestone under assumed conditions of
UCS 126 MPa, availability (a) utilization (u) and X80=30 cm. ..............................122
Figure 7-9 Blasting cost per cubic meter of rock with different rock factor (A) and
fragment size of X80=30 cm. ...............................................................................................124
Figure 7-10 Blasting cost per cubic meter of rock having UCS 126 MPa, blasted with
ANFO or emulsion and fragment size of X80=30 and 80 cm. ................................125
Figure 7-11 Drilling and/or blasting cost per cubic meter of rock having UCS 126
MPa, fragment size of X80=30 cm. ....................................................................................126
Figure 7-12 Drilling and blasting cost per cubic meter of rock for fragment size of
X80=30 and 80 cm under assumed conditions of UCS, availability and
utilization. .................................................................................................................................128

18. xviii
Figure 7-13 Variation of drilling+blasting costs to produce fragmentation with 80%
product size of 30cm and 80cm in rock with UCS of 126 MPa.............................129
Figure 8-1 Cost trends of the total blasting cost, when cost of explosives or
accessories changed by 50%. ............................................................................................135
Figure 8-2 Change in total cost of drilling blasting when the cost of explosive or
accessories changes by 50% at a drillhole diameter of 89 mm. ..........................136
Figure 8-3 Change in total cost of drilling blasting when the cost of explosive or
accessories changes by 50% at adrillhole diameter of350 mm...........................137
Figure 8-4 Cost of drilling production $/m length by several machines with different
availability and utilization..................................................................................................138
Figure 8-5 Sensitivity analysis at drillhole diameter 350 mm to the total cost of
drilling and blasting when (i) availability and utilization of the machine
increases or decreases by 50% (ii) capital or opertion cost of drill
machines increases or decreases by 50%. ...................................................................140
Figure 8-6 Sensitivity analysis when the bench height changes by 50% at a drillhole
diameter of 350mm...............................................................................................................142
Figure 8-7 Sensitivity analysis when the bench height changes by 50% at a drillhole
diameter of 89mm. ................................................................................................................143
Figure 8-8 Cost of blasting when height of bench enlarged from 12 to 18 m or
reduced to 6 m.........................................................................................................................144
Figure 8-9 Drilling-blasting cost curves when 80% passing size reduced to 20, 15 or
10 cm...........................................................................................................................................145
Figure 8-10 Spider diagram for the sensitivity analysis at drillhole diameter 350 mm ....148

19. xix
Figure D-1 Drilling net production of Tophammer at various drillhole
diameters……………………………………………………………………………….......... 188
Figure D-2 Drilling net production of D75K at various drillhole diameters in
limestone………………………………………………………………………………........... 188
Figure D-3 Drilling net production of various machines at different drillhole
diameters in limestone………………………………………....................................... 189
Figure D-4 Drilling net production of Atlas Copco Drill Machine DM 45 with
different capacity compressors………………………………………...................... 189
Figure D-5 Drilling cost of production/m in underground mining by CUBEX-
Aries……………………………………………………………………………………….......... 190
Figure D-6 Cost trends of the total blasting cost, when cost of explosives or
accessories increased or decreased by 50%, for 80% passing size of
80cm. (Refer to Figure 8-.1)………………………………………………….............. 191
Figure D-7 Spider diagram for the sensitivity analysis and the effect of change
in cost component by increasing/decreasing 50% at drillhole
diameter 89 mm. (Refer to Figure 8-10)…………............................................ 192

20. xx
List of Tables
Table 5-1 Drilling net production rates of different machines................................................... 62
Table 5-2 Drilling production rates of different machines. ........................................................ 63
Table 5-3 Net production by D75K in limestone of UCS 140 and 126 MPa........................... 64
Table 6-1 Cost Index, an abstract from: Marshall & Swift Equipment quarterly cost
indices (see Appendix Table C-4 for detail)................................................................... 81
Table 6-2 Atlas Copco - DM45 900 drilling cost estimate .......................................................... 83
Table 6-3 Net production rate and costs at a range of drillhole diameter............................ 85
Table 6-4 CUBEX- ARIES-(ITH) drilling cost estimate for u/g production
information................................................................................................................................. 93
Table 6-5 CUBEX -ARIES-ITH drilling for drillhole length of 12 m........................................... 95
Table 6-6 Cost of explosives and blasting accessories.................................................................100
Table A-1 Blasting cost per cubic meter of rock with different stemming length
and explosives, and rock factor=7 (summary)…………………............................. 163
Table B-1 Atlas Copco - DM5 900 drilling cost estimate………………………….................. 165
Table B-2 Atlas Copco - DM45 1070 drilling cost estimate…………………………............ 167
Table B-3 Cubex- Aries-(ITH) drilling cost estimate (for u/g)……………………............... 169
Table B-4 Cubex- Aries-(ITH) drilling cost estimate (for u/g)……………………............... 171
Table B-5 Cost estimate to drill larger drillhole diameter…………………………................ 173
Table B-6 Drilling cost estimate for top drive hydraulic rotary, Driltech D75k
(track mounted)…………………………………………………………….............................. 174

21. xxi
Table B-7 Hydraulic Tophammer, John Henry Rockdrill (mounted on
excavator)……………............................................................................................................ 176
Table B-8 Drilling cost/m of hydraulic Tophammer, John Henry Rockdrill by
updating cost………………………………………………………………………………......... 178
Table B-9 Net production rates of various drill machine with different UCS,
availability and utilization………………………………………....................................... 179
Table B-10 Cost per meter cube of rock with different stemming length and
explosive……………………………………………………………………………………………. 180
Table C-1 Orica Canada Inc………………………………………………………………………………… 182
Table C-2 ETI Canada Inc……………………………………………………………………….................. 183
Table C-3 Average retail prices for diesel in 2005………………………………………............ 184
Table C- 4 Canadian Hydro…………………………………………………………………………………. 185
Table C- 5 Marshal & Swift Equipment Cost Index……………………………………………….. 186

22. xxii
List of Symbols
Legend Symbol
80% Passing size 80k
Ammonium Nitrate with fuel oil (explosive) ANFO/Anfo
Availability a
Bench height bH m
Bulk modulus K Pa
Burden B m
Charge length cl
Charge length above grade cbl
Charge mass Q kg
Depreciation dC
Depth/length of blasthole/drillhole ld m
Diameter of blasthole d m or mm
Drillhole inclination id cm or m
Drilling deviation dD m
Elastic modulus E Pa
Explosive density e kg/m3
Mean fragment size 50k

23. xxiii
Owning and operating cost OO
Particle size x cm
Penetration rate dV m/min
Powder factor q kg/m3
Rock factor A
Shear modulus G Pa
Spacing S m
Spacing to burden ration bm
Stemming length sl m
Subgrade drilling length SUB m
Total drilling cost tdC
Total quantity of explosive Q kg
Total volume of rock 0V
Trinitrotoluene (explosive) TNT
Uniaxial compressive strength cU
Uniformity coefficient or index n
Utilization u
Velocity of detonation VOD
Weight strength of explosive related to Anfo ANFOE

24. 1
Chapter 1
Introduction
1.1. Preamble
A blasted rock muckpile and the fragment sizes within it are very important for the
mining industry since they affect the downstream processes from hauling to grinding.
The size distribution of the blasted muckpile can be predicted by a variety of semi
empirical models which are based on blast design parameters, such as burden, spacing,
drillhole diameter, bench height and explosives consumption. It has been the
experience of many researchers that these models are quite successful in predicting the
mean fragment size; however they lack accuracy in predicting the 80% passing size
used in comminution calculations. Despite their limitations, models are commonly used,
since they provide reasonable trends to evaluate changes in blast design parameters.
The optimization of the final rock fragment/product size on a cost basis must result in
the minimum total cost that the drilling and blasting design parameters can generate.
Generally, the cost of drilling is the sum of two major components, capital and
operational cost, while the blasting cost consists of mostly the cost of explosives,
blasting accessories and labour.

25. 2
An important parameter, often linked to the distribution of explosive energy in the blast
is the drillhole diameter. It controls the distribution of energy in the blast and thus it
affects fragmentation. Large diameters are often associated with expansion of drilling
patterns; however large holes intersect fewer in-situ blocks of rock, resulting in more
oversize, especially in the case of jointed rock. Typically the drillhole diameter is
changed depending upon the rock or drill machine type. Similarly, changes in the bench
height when a new loading machine is introduced or for any other reason, affect
changes on all dependent parameters or on the blast muckpile size mix.
Modifications in a drillhole diameter or a bench height or a product size tend to change
all other relevant blast design parameters. In the present work, the effect of the
changes of blasting parameters, when the fragmentation output is specified, were
studied. Changes in the bench height or drillhole diameter, when the product size is
required to be kept constant due to market demand or crusher/grinder requirements,
result in changes in all other parameters and ultimately changes in the capital and
operational cost of drilling, and the cost of blasting. Comparative calculations in every
case allow the designer to determine the optimum cost parameters.
It is common for mine operators to seek the optimum drilling and blasting cost.
However, when no fragmentation specifications are provided, this is a vague target.
Similarly, it is quite common for mine operators to be concerned with fragmentation
only when difficulties in drilling and loading are encountered, or when a large amount

26. 3
of oversize is produced, resulting in a general loss of productivity in the crusher and/or
secondary blasting. The present work provides a solution to the existing situation by
optimizing the blasting cost when a specific fragmentation target is provided.
The flow sheet of Figure 1-1 shows the flow of fragments/particles from drill to mill.
Blast fragmentation is mostly sent to the milling section for further reduction of size for
metallurgical/chemical processing plants. Only in a few cases are the run of mine
fragments sent to the market. In most cases the material from the crusher is sent for
grinding to reduce it to the required size for processing. Clearly it is important to be
able to accurately calculate the 80% passing size from the mine, which is the 80% feed
size for the mill.
Bond, in 1961, presented his third law of comminution, formulating a mathematical
equation to calculate the amount of work done on the 80% passing particle feed size to
convert it into 80% passing particle product size, using a constant, called the Work
Index, to balance the equation. Bond’s Work Index is defined as the energy in Kwh per
short ton required to reduce the material from theoretically infinite feed size to 80%
passing an opening size of 100 microns. This law is still widely used and to date no
other law has proven to be better.
Thus the required 80% feed size at the crusher is the fragmentation specification for
the mine. This can be related to the blast design parameters, which in turn can be used
to calculate cost at each drillhole diameter assisting in the selection of a drill machine

27. 4
suitable to drill a required diameter size drillhole with a minimum cost of production.
In the following diagrammatic presentation X80 is the 80% size of blast fragmentation
P80 is the 80% size of the product of the crusher and F80 is the 80% size feeding the
mills.
Figure 1-1 A simple diagrammatic presentation of
“Drill to Mill” fragmentation flow sheet

28. 5
1.2. Objective
This thesis is aimed at correlating blast design to comminution particle size
requirements, predicting the 80% passing particle size for blast induced fragmentation
and subsequently optimizing the drilling and blasting processes. This work focussed on
the following objectives:
1.2.1. Formulation or adoption of a mathematical model
This model needs to calculate the 80% passing fragment size for run-of-mine
fragmentation based on blast design parameters.
1.2.2. Calculating the effect of diameter on fragmentation
The formulated model needs to study the effect of change of drillhole diameter on the
fragmentation.
1.2.3. Selection of a diameter given certain fragmentation requirements
The formulated model will serve as a tool to select drillhole diameter, when
fragmentation requirements are given.
1.2.4. Calculation of drilling and blasting costs to produce a certain
fragmentation
A costing model must be designed to calculate the cost of drilling and blasting once
fragmentation targets are provided.

29. 6
1.2.5. Effect of diameter on cost
Finally the effect of blasthole diameter on the drilling and blasting cost must be
analyzed.
1.3. Outline
Chapter one provides the introduction and the scope of the work performed; the second
chapter is a discussion on the blast design parameters, controllable and uncontrollable
factors related to rock-mass-explosive geometry combination and variables. Chapter
number three is an introduction to the engineering models, which have been used and
are being used to predict fragmentation by blasting. The chapter reviews previous work
done on the optimization requirement and cost calculation requirements.
Chapter number four is completely devoted to the formulation of an engineering model
giving due consideration to existing models and selection of design parameters for
calculating the effect of diameter on fragmentation. Chapter five discusses drilling
production, design parameters and practical implementation. In chapter six drilling and
blasting costs are calculated, and the influence of the blasthole diameter on cost is
analyzed for a range of drillholes.

30. 7
Chapter seven provides cost comparisons and factors based on which optimization is
possible for a range of drillhole diameters. Chapter eight is a sensitivity analysis based
on drilling blasting design parameters and cost components.
The study has included a few practical examples of drilling operations from drill
machine manufacturers and mining companies. The capital and operational costs of the
machines and components provided have been used to calculate the cost of drilling per
meter of drilling length. This cost, calculated in Canadian dollars per unit length of
drilling was ultimately converted to dollars per cubic meter /tonne of rock blasted. For
the blasting cost, calculations were based on the market values of the explosives and
components, which were obtained in the form of quotations. All relevant pieces of
information and useful calculation results have been attached as appendices at the end
of the thesis.

31. 8
Chapter 2
Blast Design Parameters
2.1. Introduction
Preliminary blast design parameters are based on rock mass-explosive-geometry
combinations, which are later adjusted on the basis of field feedback using that design.
The primary requisites for any blasting round are that it ensures optimum results for
existing operating conditions, possesses adequate flexibility, and is relatively simple to
employ. It is important that the relative arrangement of blastholes within a round be
properly balanced to take advantage of the energy released by the explosives and the
specific properties of the materials being blasted. There are also environmental and
operational factors peculiar to each mine that will limit the choice of blasting patterns.
The design of any blasting plan depends on the two types of variables; uncontrollable
variables or factors such as geology, rock characteristics, regulations or specifications
as well as the distance to the nearest structures, and controllable variables or factors.
The blast design must provide adequate fragmentation, to ensure that loading, haulage,
and subsequent disposal or processing is accomplished at the lowest cost.
Further to the cost, the design of any blast must encompass the fundamental concepts
of an ideal blast design and have the flexibility to be modified when necessary to

32. 9
account for local geologic conditions. The controllable and uncontrollable factors are
being discussed in this chapter and will be used in the blasting and costing models
wherever necessary.
2.2. Uncontrollable factors
Uncontrollable parameters concerning blast design are the rock mass properties and
the geological structure. These have to be considered in the blast design.
2.2.1. Properties of rock
A natural composite material, rock is basically neither homogeneous nor isotropic.
Inhomogeneity in rock is frequently discernible from its fabric, which includes voids,
inclusions and grain boundaries. Anisotropy is due to the directionally preferred
orientations of the mineral constituents, modifications in the changing environments
and characteristic of geological history, which may alter its behaviour and properties.
The intrinsic environmental factors that influence drilling are geologic conditions, state
of stress, and the internal structure of rock, which affect its resistance to penetration.
The following parameters affect rock behaviour to drilling:
Geology of the deposit: Lithology, chemical composition, rock types.
Rock strength and properties: Mechanical properties, chemical and physical
properties.
Structural geology: Presence of fractures, fissures, folds and faults.

33. 10
Presence of water: Depending on the source and quantity, it may be an uncontrollable
or a controllable factor.
These factors also influence the blast design parameters and the fragmentation
produced; thus their effects to blasting need to be quantified.
(Tandanand, 1973; Hustrulid, 1999)
2.2.2. Rock factor
An attempt to quantify the effect of rock parameters on fragmentation was made by
Cunningham (1987), who used Lilly’s (1986) “blastability index A”, and incorporated it
in his popular Kuz Ram model (Cunningham, 1983). He discussed that every
assessment of rock for blasting should at least take into account the density, mechanical
strength, elastic properties and fractures. He defined the rock factor A as;
A = 0.06*(RMD + JF + RDI + HF) --------------------- Equation 2-1
where RMD is the mass description, JF is the joint factor, RDI is the rock density
influence and HF is the hardness factor. Details on the model can be found in
Cunningham’s publication (Cunningham, 1987).
2.3. Controllable factors
For the purposes of blast design, the controllable parameters are classified in the
following groups:

34. 11
A- Geometric: Diameter, charge length, burden, spacing etc.
B- Physicochemical or pertaining to explosives: Types of explosives, strength,
energy, priming systems, etc.
C- Time: Delay timing and initiation sequence.
Geometric parameters are actually influenced by uncontrollable and controllable
factors, which are also design parameters and can be grouped as follows:
(i) Diameter (d) and Depth of Drillhole ( ld ).
(ii) Inclination ( id ) and Subdrilling Depth ( SUB) of Drillhole.
(iii) Height ( sl ) and Material of Stemming.
(iv) Bench Height ( bH ).
(v) Spacing to Burden Ratio ( bm ).
(vi) Blast Size, Direction and Configuration.
(vii) Initiating Sequence and System.
(viii) Buffers and Free Faces.
(ix) Explosive Type, Energy and Loading Method.
(x) Powder Factor q =Q/Vo where Q is the total quantity of explosive per
borehole and Vo is the total volume of rock blasted.
(Jimeno, 1995; Hustrulid, 1999)

35. 12
2.3.1. Height of bench
Usually the working specifications of loading equipment determine the height of the
bench. The bench height limits the size of the charge diameter and the burden. (Ash
1968), states that when the bench height to burden ratio is large, it is easy to displace
and deform rock, especially at the bench centre. The optimum ratio ( BHb / ) is larger
than 3. If BHb / = 1, the fragments will be large, with overbreak/backbreak around
holes and toe problems. With BHb / = 2, these problems are attenuated and are
completely eliminated when BHb / >3.
The condition BHb / >3, is usually found in quarries and coal strip mining operations.
In metal mining the bench height is conditioned by the reach of the loading machine
and the dilution of the mineral as well.
When bH is small, any variation in the burden B or spacing S has a great influence on
the blasting results. When bH increases, with B kept constant, spacing can increase to
maximum value without affecting fragmentation. If the bench height is very large, there
can be problems of blasthole deviation, which will not only affect rock fragmentation
but will also increase risk of generating strong vibrations, flyrock, and overbreak
because the drilling pattern and subsequently the explosives consumption will not
remain constant in the different levels of the blasthole.

36. 13
2.3.2. Blasthole inclination
According to Jimeno et al (1995) the benefits of inclined drilling are better
fragmentation, displacement and swelling of the muckpile, less subdrilling and better
use of the explosive energy, lower vibration levels and less risk of toe appearance.
The disadvantages of inclined holes are the following:
(i) Increased drilling length and deviation when drilling long blasthole.
(ii) More wear on the bits, drill steel and stabilizers.
(iii) Less mechanical availability of the drilling rig.
(iv) Poor flushing of drill cuttings due to friction forces, requiring an increase
in air flow.
There are few management factors which are disadvantageous with the inclined
holes and are as follows:
(i) Difficulty in positioning of the drills.
(ii) Necessity of close supervision which creates work lapses.
(iii) Lower drill feed, which means that in hard rock the penetration rate is
limited in direct proportion to the angle of inclination of the mast.
(iv) Less productivity with rope shovels due to lower height of the
muckpile.

37. 14
(v) Problems in charging the explosive, especially in blastholes with
water. (Jimeno et al., 1995)
2.3.3. Stemming
If stemming is insufficient, then there will be a premature escape of the gases into the
atmosphere which will produce airblast and dangerous flyrock. On the other hand, if the
stemming is excessive, there will be a large quantity of boulders coming from the top
part of the bench, poor swelling of the muckpile and an elevated vibration level.
To determine stemming, the following must be taken into consideration:
(i) The type and size of the material to be used
The type of stemming material and amount of stemming used will definitely influence
the degree of confinement and the efficiency of the blast. In order to extract the
maximum energy from the expanding gases, the stemming plug should never blow out
and allow the gases to escape prematurely.
Literature (Konya, 1990 and Jimeno et al., 1995) suggests an optimum bore diameter to
stemming particle diameter ratio of about 17:1. It is common practice to use drill
cuttings, owing to their availability near the collar of the blasthole. However, it has been
observed that coarse angular material, such as crushed rock, is more effective and the
resistance to ejection of the stemming column increases when the humidity content is
lowered.

38. 15
(ii) The length of the stemming column
Jimeno et al. (1995) proposes the optimum lengths of stemming increase as the quality
and competence of the rock decrease, varying between 20D and 60D, where D is the
diameter of the borehole. Whenever possible, a stemming length of more than 25D
should be maintained in order to avoid problems of airblast, flyrock, cutoffs, and
overbreak. Ash (1968) concluded that the amount of stemming or collar should be used
as a direct function of the burden. Theoretically, in isotropic homogeneous materials
the two dimensions should be equal for stress balance in the solid rock (Konya, 1990).
Both options, stemming proportionate to the diameter with a certain multiplication
factor or to the burden will be examined in the following chapters to optimize the blast
design.
2.3.4. Subdrilling
If the subdrilling is small, then the rock will not be completely sheared off at floor level,
which will result in toe appearance and a considerable increase in loading costs.
However, if subdrilling is excessive, the following will occur:
 An increase in drilling and blasting costs.
 An increase in vibration level.

39. 16
 Excessive fragmentation in the top part of the underlying bench, causing drilling
problems of the same and affecting slope stability in the end zones of the open
pit.
 Increase in risk of cutoffs and overbreak, as the vertical component of rock
displacement is accentuated.
In order to reduce subdrilling, explosives which give a high concentration of energy per
unit length in the bottom part of the charge and the drilling of inclined blastholes are
recommended. For vertical blastholes when a bench is massive, the subdrilling distance
suggested by Ash (1968), Gustafsson (1973), Jimeno et al. (1995) should be
approximately equal to 30% of the burden. Hustrulid (1999), on the other hand
proposes that the drilled distance of the hole to the toe elevation (the subdrilling
distance) should be equal to 8 diameters.
2.3.5. Burden and spacing
The burden is the minimum distance from the axis of a blasthole to the free face, and
spacing is the distance between blastholes in the same row. These parameters depend
basically upon the drilling diameter, the height of the bench and the desired degree of
fragmentation and displacement.
Numerous formulas have been suggested to calculate the burden, which take into
account one or more of the indicated parameters; however, their values all fall in the
range of 20 to 40 D, depending fundamentally upon the properties of the rock mass.

40. 17
It is very important to be certain that the size of the burden is adequate. Errors in
burden size could be due to marking and collaring, inclination and directional deflection
during drilling, and irregularities in the face of the slope.
Excessive burden resists penetration by explosion gases to effectively fracture and
displace the rock and part of the energy may become seismic intensifying blast
vibrations. This phenomenon is most evident in pre splitting blasts, where there is total
confinement and vibration levels can be up to five times those of bench blasting.
Small burden lets the gases escape and expand with high speed towards the free face,
pushing the fragmented rock and projecting it uncontrollably, provoking an increase in
overpressure of the air, noise and flyrock.
Spacing is calculated as a function of burden, delay timing between blastholes and
initiation sequence. Very small spacing causes excessive crushing between charges and
superficial crater breakage, large blocks in front of the blastholes and toe problems.
Excessive spacing between blastholes causes inadequate fracturing between charges,
along with toe problems and an irregular face. (Jimeno, et al. 1995)
2.3.6. Blasthole patterns
In bench blasting, the normal blasthole patterns are either square or rectangular, owing
to the ease with which the collaring points can be marked out. However, the most
effective are staggered patterns, especially those drilled on an equilateral triangular

41. 18
grid, as they give optimum distribution of the explosive energy in the rock and allow
more flexibility when designing the initiation sequence and the break direction.
2.3.7. Blasthole deviation
Associated with fragmentation is blasthole deviation. There are four causes of blasthole
deviation as follows:
 Structural properties of the rock, such as schistosity planes, fissures, loose open
joints filled with soft materials, lithological changes, etc. This group is especially
important when the drilling direction is oblique to these planes.
 If the chosen bit diameter is too large in comparison with the diameter of the
drill steel, a deviation of the blasthole is produced due to lack of bending
resistance in the drill string and premature wear of the same.
 Collaring errors in which deviations are frequently more than 10 cm or typically
about one hole diameter.
 Alignment errors, which are the most common in drilling operations and depend
on method of drilling, length of hole and types of machines used. Tophammer
drills have the highest possibilities of drillhole deviation (5-10%) while the
effect reduces in the case of in the hole (ITH) drills (usually <2%) Atlas Copco
(1).
Alignment errors are usually caused by improper setting of the feeds. In normal manual
setting the error is 4 – 7% and can be reduced to 3 – 5% by careful working (stable

42. 19
required alignment of machine and drill feed according to the rock conditions, and
training of the driller). In case of feed with indicator the error is reduced to 0.5 – 1.0%
and further to 0.2 – 0.5% with careful working. Hence this error is more related to
human care and training of the operating personnel (Atlas Copco, (1).
Gustafsson (1973) suggested 3 cm /meter drill hole as an acceptable number for the
faulty drilling or drillhole deviation. Bhandari (1997) suggested that an important
component of drillhole deviation is error in collaring, which can be eliminated by
adopting proper surveying. Atlas Copco (1) presented the company’s most recent
findings and states that the most severe causal factor is in-hole deviation during
drilling, usually because of geological conditions. The drillhole tends to deviate to a
direction perpendicular to the jointing. The longer the holes, the more accentuated is
the deflection. It is often claimed that the deviation is proportional to the depth to the
power of two.
To illustrate various causes of hole deviation, Atlas Copco (1) states that experience
shows that the approach of the drillbit towards the bedding is crucial. There seems to
be a tendency for the bit to follow parallel to the bedding, where the angle of approach
is smaller than 15 degrees. Drilling through homogeneous rock, such as isotropic
granite with sparse jointing, causes little or no in hole deviation. [Atlas Copco (1)]

43. 20
Similarly the method of drilling is also responsible for drillhole deviation. Atlas Copco
(2), comparing different products, explains that the main drawback with top hammer
drilling is the in-hole deviation that limits the practical hole length. As the magnitude of
deviation is exponential to the hole length, top hammer holes are normally restricted to
30 m.
Penetrating structured rock with strong foliation and bedding properties can cause
deviations of up to 5-10%. As a result, many mines avoid drilling holes deeper than 20
m, unless guide rods are added directly behind the bit, or drill tubes are used. In these
cases, the deviation can be expected to decrease to 3-5%.
ITH (In The Hole) rock drills drill comparatively straight holes and in the hole deviation
is maintained within +/-0.5% to +/- 1%. Mines drill 75 m, long holes with negligible
deviation. Atlas Copco (1)
In summary deviation depends on the different drilling methods and ranges between 5-
10% for tophammer and +/-0.5 to +/- 1% for ITH drill machines, and their tophammer
with guide tube falls in-between somewhere.
2.4. Blasthole diameter
Drillhole diameter plays an important role in the distribution of explosives in a blast.
Intuitively, it has a major impact on fragmentation. Drillhole diameter is selected on the

44. 21
basis of the available machine and the factors controlling blasting. The ideal drilling
diameter for a given operation depends upon the following factors:
(i) Properties of the rock mass to be blasted.
(ii) Degree of fragmentation required.
(iii) Bench height and configuration of charges.
(iv) Cost of drilling and blasting,
2.4.1. Advantages associated with small diameter boreholes
Due to a better distribution of energy in blasting, smaller diameter boreholes result in a
lower powder factor. In the case of jointed rock, the use of small diameter boreholes is
imperative, otherwise fragmentation could be unacceptable if the joints and
discontinuities are widely separated and form blocks in situ.
In these cases it is recommended that the spacing between blastholes be smaller than
the mean separation distance between discontinuities, which necessitates smaller
holes.
2.4.2. Disadvantages associated with the small diameter boreholes
The costs of drilling, priming and initiation are high.
Charging and stemming of drillholes, and connecting them in a blasting circuit is time
consuming.

45. 22
2.4.3. Advantages associated with larger diameter boreholes
Large diameter boreholes have the following advantages:
 The explosive detonates more reliably away from its critical diameter.
 Higher shock energy can be delivered to the rock mass, aiding
fragmentation.
 Lower overall costs of drilling and blasting (assumed).
 Loading of the explosive charge is mechanized.
 Higher drilling productivity (m3 blasting/m drilled)
2.4.4. Disadvantages of using larger drillhole diameter
If fragmentation is to remain constant and the diameter is increased, it will be
necessary to increase the powder factor as the charges are not as well distributed in the
rock mass.
The stemming length also increases with the drilling diameter, and the collar of the
blasthole could become a potential source of boulder formation.
2.5. Conclusion
In this chapter parameters affecting drilling and blasting have been discussed. Blasters
have a fairly good idea of the effect of these parameters on fragmentation. However

46. 23
optimization of blasting and costing of fragmentation require quantifying these
parameters.

47. 24
Chapter 3
Fragmentation Models Used
3.1. Introduction
To associate fragmentation specifications, imposed by crushing, to blasting, it is
imperative to associate fragmentation distribution to blasting parameters. The present
section describes the models available for this purpose.
3.2. Particle sizing
Crucial in the present investigation is the ability to calculate the 80% product size of the
blasted rock. The most common fragment distribution functions are the Gates-Gaudin–
Schumann, Rosin-Rammler and Swebrec functions.
A commonly used form of the Gates-Gaudin-Schumann function is the following:
n
sk
x
y 






--------------------------------------------------------Equation 3-1
Where y is the fraction of the muckpile with particle size smaller than x, ‘n’ is a
distribution parameter and ‘ks’ is the maximum particle size.
Another equation used is the Rosin-Rammler equation, which is expressed as:

48. 25
n
bx
ey 
1 ------------------------- Equation 3-2
where ‘b’ is a constant.
The Rosin-Rammler equation has been used by Cunningham for blasting analysis in the
following form:
n
cx
x
eR









 ----------------------- Equation 3-3
where R is the fraction of material retained on a screen, x is the screen size, is a
constant, called the characteristic size, and ‘n’ is the uniformity index.
The uniformity index, typically, has values from 0.6 to 2.2. The value of ‘n’ determines
the shape of a curve. A value of 0.6 means that the muckpile is non uniform (dust and
boulders) while a value of 2.2 means a uniform muckpile with the majority of fragments
close to the mean size (Clark, 1987).
These equations are often used in combination with Kuznetsov’s equation, which is
expressed in terms of the quantity of explosive per blasthole, eQ and the relative to
ANFO weight strength of explosives, ANFOE and the powder factor, q = Q/Vo. Kuznetsov’s
equation is typically written as:
cx

49. 26
------------------------- Equation 3-4
This is the most useful format, especially when absolute weight strengths are not given
by manufacturers. (Clark, 1987)
Kuznetsov’s equation has been reliable and accurate for predicting the average
fragment size (Chung and Katsabanis, 2000). The issue is to be able to predict the entire
fragmentation distribution in order to obtain the 80% passing size. For this purpose
Cunningham (1983) proposed the use of the Rosin–Rammler equation with an
empirically calculated uniformity index. Several forms of this uniformity index can be
found in the literature suggesting the difficulty in encapsulating the effect of all blasting
parameters in the blast by a single constant. The following parameters are related to
muckpile uniformity.
(i) Distribution of explosive in the blast (burden, spacing to burden ratio,
borehole diameter, collar, subgrade, bench height)
(ii) Firing accuracy of detonators used
(iii) Timing of detonators used
30
19
6
1
8.0 115
)( 





 
ANFO
eav
E
QqAx

50. 27
(iv) In situ fragmentation due to geological discontinuities
Cunningham addressed some of the above issues; however the original intent of the
model was to be a tool to predict reasonable changes when blast design parameters are
modified and does not accurately predict sizes. However operators are using the model
placing a great amount of confidence in its predictions.
Originally, Cunningham expressed the uniformity index ‘n’ by the following equation:
--------------- Equation 3-5
(Cunningham, 1983)
where ‘B’ is the burden in m, ‘d’ is the hole diameter in mm, ‘ tD ’ is the standard
deviation of drilling accuracy in m, ‘ bm ’ is the spacing to burden ratio, ‘ cbl ’ is the charge
length above grade level in (m) and ‘ bH ’ is the bench height in (m).
In 1987 Cunningham modified this equation and presented the following:
-------------Equation 3-6
where BL is the bottom charge length above grade (m), CL is the column charge length
(m), and cbl is the total charge length above grade. (Cunningham, 1987)
 
b
cbbt
H
lm
B
D
d
B
n 




 













2
1
1*1142.2
b
cbbt
H
l
CLBL
CLBLm
B
D
d
B
n
1.05.0
1.0*
2
11142.2 




























51. 28
The above uniformity indices have been tested against experimental data and have not
been found to be reliable (Chung and Katsabanis, 2000). Lately Cunningham (2005),
produced a new version of the uniformity index, expressed as follows:
)())(1(
2
130
2 3.0
nC
H
l
B
Dm
d
B
nn
b
btb
s 

 --------- Equation 3-7
where )(nC is a correction factor used to calibrate the model if data are available and
sn is a factor incorporating scatter of the delay times used in the blast. The factor sn
can be expressed as follows:
8.0
)
4
1(206.0 s
s
R
n 
----------------------------- Equation 3-8
where sR is the scatter ratio and is expressed as:
x
t
s
T
R

6 ------------------------------------------------- Equation 3-9
with t being the standard deviation of the initiation system and xT the desired delay
time between holes.

52. 29
3.3. Kuz-Ram model
If one uses Kunetsov’s equation for the 50% passing size, where avxx  one can get an
expression for the characteristic size from the Rosin-Rammler equation in terms of the
uniformity index and the 50% passing size. Thus the Rosin-Rammler equation can
become:
n
x
x
eR







 50
*693.0
--------------------------------- Equation 3-10
This is a commonly used form of the Kuz-Ram model.
Once the rock is blasted it becomes feed to the milling unit (crushing and grinding)
process. Calculations for crushing circuits are based on the 80% passing particle feed
size and thus fragmentation specifications for blasting are based on this particular size.
It is however important to remember that one size does not describe the entire
fragmentation distribution. For example the quantity of fines cannot be estimated by
the 80% passing size. In reality fines may be useful or a detriment to the operation and
their quantity must be specified as well. The problem, with the previous models, is that
fines cannot be estimated in a reliable fashion. The Kuz Ram model typically
underestimates fragments, while attempts have been made in the last few years to
correct this. The correction is based on the modification of the Rosin – Rammler
fragmentation distribution, adding another Rosin – Rammler distribution to describe

53. 30
the fines, or on the basis of the Swebrec function (Ouchterlony, 2005), which is a new
function describing fragmented rock.

54. 31
3.4. Fines in the blast muckpile
An occasional problem lies in the realistic assessment of fines. It is felt that these can be
generated both by the equipment loading the rock, and through weak binding material
between mineral grains in addition to the intensive crushing of rock around the
boreholes during blasting. It is interesting to note that fine materials have varied
utilization. Sometimes fines are considered for further metallurgical and chemical
processing, while at other times fines are rejected and become waste. Within the
research project, “Less fines production in aggregate and industrial minerals industry”,
which was funded by the European Union, Moser (2004) states that Europe is
consuming 2.25 billion tons of blasted rock, 80% being building industry aggregate and
industrial minerals (Moser, 2004). Out of this blasted material 10-15% cannot be sold,
being too fine i.e. smaller than 4 mm.
In favour of fines to benefit the SAG (Semi Autogeneous grinding) mill throughput,
Grundstrom et al. (2001) state that the blast fragmentation affects mill throughput and
finer ROM (Run of Mine) from modified blasts increased the mill throughput
substantially. Similarly, Kanchibotla et al. (1998) witnessed primary crusher product
size reduction and significant increase in throughput due to the generation of more
fines, achieved by changing the powder factor.
Scott (1998), states that ores which contain significant quantities of very fine clay
material within the rock matrix, are found to generate considerable amounts of fines.

55. 32
Kanchibotla et al. (1998) pointed out that the Kuz-Ram model underestimates the
contribution of fines. This deficiency of the model can be overcome by introducing a
second uniformity index to describe the fines distribution, below the mean size. In the
case of the finer fractions, it is hypothesized that they are produced by the pulverizing
or crushing action of the explosive in a blasthole. The crushing zone radius around each
blasthole is determined based on the peak blasthole pressure and the strength of the
rock.
Kojovic et al. (1998) state that rock in the crushed zone is assumed to be completely
pulverised to generate fines, which are assumed to be less than 1mm in size. The coarse
part of the distribution is predicted using the conventional uniformity index based on
blast design parameters proposed by Cunningham (1987) while the finer part is based
on the percentage assumed pulverized around the borehole. The model is presented in
the following section.
3.4.1. Two-component model of blast fragmentation
To address the coarse as well as the fine portion of the muckpile, Djordjevic (1999)
states that the major portion of the muckpile is the result of tensile failure while the fine
size fragments in the muckpile are because of shear and compressive stresses
surrounding the borehole. Prediction of fragmentation by blasting is often based on the
assumptions that a single-distribution of pre-existing discontinuities is present within a
blasted rock volume and that the underlying mechanism of failure is tensile failure.

56. 33
Djordjevic discussed the two component model utilizing experimentally determined
parameters from small scale blasting. If one assumes that small particles are generated
close to the borehole and large particles away from the borehole, the muckpile is the
blend of two size distributions, tc PandP , both following the Rosin Rammler equation as
follows:
P(x) = F*Pc(x)+(1-F)*Pt(x) ------------------------- Equation 3-11
The two-component model suggests that the entire muckpile is described by the
distribution P(x), tc PandP are the passing percentages for size (x) for the compressive,
and tensile failure zones respectively and F is the fraction of fines produced in the
muckpile. (Djordjevic, 1999)
The volume which is crushed is calculated from small tests and cratering theory. The
volume affected is proportional to the mass of explosive used. The radius of shear
failure can be calculated from the Djordjevic equation as well.
This new model demonstrates potential for prediction of the complete fragment size
distribution curve, regardless of the type of rock and amount of fines generated. The
method is relatively simple to use and has the potential to predict ROM blast
fragmentation even at the feasibility stage of mine design. (Djordjevic, 1999)

57. 34
3.4.2. Swebrec function
Another model used in the prediction of fines and subsequently in improving the
prediction of the distribution of fragments is the Swebrec function. This was developed
by Ouchterlony in Sweden (2005). The details of the model are outside of the scope of
this thesis. However the Kuz Ram connection has implications in the present work. The
Swebrec function essentially replaces the Rosin-Rammler distribution. The Swebrec
function is expressed as:



























b
x
x
x
x
xP
50
maxmax
ln/ln1/1)( ------------ Equation 3-12
where P(x) is the fraction smaller than size x, maxx is the minimum in situ size and 50x
is the 50% passing size. The b exponent can be connected to the uniformity index in the
Kuz-Ram function through the following equation:
n
x
x
b 






50
max
ln2ln2 -------------------- Equation 3-13
The model has been called the Kuznetsov – Cunningham – Ouchterlony (KCO) model.
(Ouchterlony, 2005)

58. 35
3.5. Conclusion
Engineering models have been developed to relate fragment distribution to blast
design. Among the models used, Kuz Ram is the popular one and was selected for the
current work. Although its accuracy for the prediction of the 80% passing size has been
questionable, it provides a reasonable method to relate trends in fragmentation to blast
design variables. When a better alternative replaces the Rosin-Rammler equation the
same methodology can be used using the improved equation.

59. 36
Chapter 4
Calculation of the 80% Passing Size
4.1. Introduction
Blasted rock has to be hauled for further processing. Downstream processes are
crushing and grinding before delivering a material to a processing plant. According to
Currie (1973), crushers are classified according to the size of material treated with
some sub-division in each size according to the way forces are applied. A primary or
coarse crusher crushes mine feed with a maximum size of 1520 mm (60 in boulder)
down to sizes of 200 mm to 50 mm. Although it can accept large fragments, its
productivity depends on fragment size. Furthermore smaller size input allows the
modification of the close setting of the crusher allowing savings and productivity
improvements in subsequent operations.
Discussion on fragmentation started long ago, and Mackenzie’s (1967) cost curves for
drilling and blasting concluded that for a given type of drilling and explosive, the cost
per cubic yard or ton will remain constant or increase with the degree of fragmentation.
Tunstall et al. (1997), discussing the influence of fragmentation on crushing, states that
the maximum size of the blasted rock should not exceed the maximum feed size for the
type of primary crusher employed. The maximum feed size for a given type of crusher is
a function of the feed opening, and the most favourable maximum recommended feed

60. 37
size for primary crushers is 75% to 85% of the opening for jaw crushers and 80% of the
opening for gyratory crushers.
Eloranta (1995) showed that overall costs declined while shovel and crusher
productivity rose by about five per cent when the powder factor rose by 15 per cent.
Nielsen and Kristiansen, (1996) described and presented the results of several
industrial and laboratory blasting, crushing, and grinding tests and experiments
investigating how blasting can influence the subsequent crushing and grinding
operations. They described that blasting plays a wider role than just fragmenting the
rock. It is the first step of an integrated comminution process leading from solid ore to a
marketable product. Nielsen (1999) performed a series of laboratory blasting and ball
mill grinding tests on four different types of hard and competent rocks. The results
show that exposing these rock types to a higher level of explosive energy enhanced
their grindability.
Elliot et al. (1999) carried out a study to attain a 90% passing size of 0.2 m from the
existing 90% fragmentation level for production blasts of 0.6 m at Lafarge’s Exshaw
cement operation. This study was aimed at replacing the 1372 mm (54-inch) primary
gyratory crusher. Exshaw’s 1372 mm crusher was nearing the end of its operating life
and replacement required a significant capital outlay. Replacement with a smaller
crushing system would result in significant cost savings. Smaller size of fragmentation

61. 38
was considered as an increase of the operating cost to avoid acquisition of more
crushers requiring significant capital and installation expenditures. (Elliot et al., 1999)
It is clear now that the effect of blasting is far reaching and may even affect the grinding
stages as well. If one focuses on crushing, it is possible to eliminate the primary crusher
or increase the crushing efficiency controlling the 80% feed size delivered from run-of-
mine fragmentation. The issue is, if drilling and blasting can deliver a required 80%
passing size economically, then, if possible, why not deliver fragmentation directly to
the secondary crusher to save cost? To eliminate a primary crusher, it might be
appropriate to use a heavy duty secondary crusher, which may accept a larger fragment
as a feed size. In case where mines cannot eliminate primary crushers completely, then
light duty primary crushers would be recommended.
In this current study two fragment sizes, 30 and 80 cm, have been selected as 80%
passing sizes. This range covers most common sizes required by crushing installations.
An 80 cm size as an 80% passing fragment is a good size for heavy duty crushers to
increase crushing efficiency and productivity. Similarly, a 30 cm run of mine 80%
passing fragment size is a good feed size for a light duty crusher. It can save cost on the
downstream processes in the grinding department by reducing crushing and grinding
time, and increase the efficiency and throughput of the crusher and grinder as well.
Hence 30 cm and 80 cm fragment sizes have been selected to work with and to show
the results of the calculations of the 80% passing particles.

62. 39
4.2. Calculation of blasting parameters on the basis of the 80%
fragment size
Using the Kuz-Ram model one can calculate the blasting parameters needed to satisfy
the milling unit requirement of the 80% passing fragment size. The 80% passing size
can be expressed as follows:






 n
xx
1
5080 )4306.0( ------------------- Equation 4-1
From Kuznetsov’s equation:
---------------------------- Equation 4-2
where , is the quantity of explosive and, 0V is the rock volume to be blasted. The
value of 0V can be substituted as a multiplication of bench height, spacing, burden and
the spacing-burden ratio, then this equation can be presented as:
 
























30
19
30
19
28.06.1
50
115
**
4
**
ANFO
cbb
E
ldmHABx 

------ Equation 4-3
where  is the density of explosive.
eQ
30
19
6
1
8.0
0
0
50
115
)( 






ANFO
e
E
Q
Q
V
Ax

63. 40
Jimeno proposed the stemming length should be more than 25D (Jimeno et al., 1995).
Taking dlc 30 and sub-drilling ‘SUB’ equal to 8d (Katsabanis, 2003), the column
charge becomes as follows:
ddHl bc 308  ----------------------Equation 4-4
Substituting cl in Kuznetsov’s equation we have:
where
6.1
50 * BFx b -------------------------Equation 4-5
 
























30
19
30
19
28.06.1
50
115
*)22(*
4
**
ANFO
bbb
E
dHdmHABx 

----------Equation 4-6
If stemming ‘ sl ’ is assumed equal to the burden and sub-drilling SUB is equal to 8d,
the column charge becomes:
BdHl bc  8 -------------------------------Equation 4-7
Substituting this value of cl in equation 4-3, bF can be written calculated in terms of
burden and diameter.
Let us examine a case scenario when stemming is equal to burden length and subgade
length SUB is 20% of burden, then column charge can be written as follows:
BHl bc 8.0 ----------------------------------------Equation 4-8

64. 41
Now substituting the value of cl from Equation 4-8 in equation 4-6, then bF becomes:
 
























30
19
30
19
28.0 115
*)8.0(*
4
*
ANFO
bbbb
E
BHdmHAF 

------------------------Equation 4-9
To predict other than the 50% sizes one needs the uniformity index:
------------------------Equation 4-10
where cbl is the charge length which is above grade; hence, cbl can be equal to bench
height minus 22 times drillhole diameter or stemming length ( dHb 22 ) or ( BHb  ) .
(Cunningham, 1983)
The value of drilling deviation tD varies from 1% to 5% of bH and can be modified
according to the requirements. It is defined according to the type of machine in use, the
location and the training of the crew. In the present case, the deviation is taken as 2%
plus one drillhole diameter of bH . Let us rewrite the equation in the following format:
----------------------- Equation 4-11
where IF is equal to:
b
cbb
I
H
lm
F 




 

2
)1(
1 ------------------------------- Equation 4-12
 
b
cbbt
H
lm
B
D
d
B
n 




 













2
1
11142.2
I
t
F
B
D
d
B
n *1142.2 













65. 42
Combining the two equations 4-1 and 4-5, the following equation is obtained:
  80
1
6.1
*4306.0* xBF n
b  ------------------------------------
Equation 4-13
Using the value of ‘n’ from equation 4-11, equation 4-13 is further developed as follows:
  0*^4306.0* 80
*1*142.2
1
6.1
1









































xBF
F
B
d
d
B
b
i
-------- Equation 4-14
which relates to the 80% passing size of blast particle, explosive quantity and rock type
(Fb), distribution of charge (FI), and burden and diameter. Implications of the Kuz Ram
are the implications of this model as well.

66. 43
4.3. Correction for fines
In case fines are undesirable, a correction factor for fines has to be applied. The two
component model Djordjovic Equation 3-11 in Chapter 3 is the best tool available so far
to predict fines. In cases where fines have to be discarded a correction factor is
available to be considered.
4.4. Selection of suitable drilling design parameters
To examine the predictions of the model, the model was run on MS-EXCEL, with a rock
factor 7, a value meant for medium strength rocks.
4.4.1. Effect of stemming length on burden
Stemming is usually more than 25 diameters (Jimeno et al., 1995), depending on the
rock type, the explosive used and particular factors of blasting. Often, stemming is also
taken as equal to or a multiple of burden (Pfleider, 1972). In the present work,
stemming length has been examined using both approaches. Initially stemming length
was set equal to 25d and calculations were performed with a specification of 80%
passing size equal to 80cm (Figure 4-1). The resulting burden when hole diameters
vary from 75mm to 225 mm showed a constant rising trend. After a certain diameter
size, burden lengths started retreating, showing impractical values. A similar trend was
observed with the second trial, which was run with a stemming length equal to 30d. In

67. 44
this case burden values dropped just after the 200 mm diameter. The result is due to
the borehole length which is incompatible with charge diameter. When the diameter is
large, a large proportion of the hole is uncharged. This affects charge distribution in the
borehole, which also affects the uniformity index of the blast. However modifying
stemming without considering the burden of the blast is unreasonable. Flyrock, if this is
a concern, does not result only from the horizontal face of the blast but also from the
other faces. Thus, it is reasonable to relate collar to the burden. The third trial was run
with burden equal to stemming clB  and produced more reasonable results as is
evident in Figure 4-1. The trend of burden vs. diameter of the blast is nearly constant
and the burden increases with increasing diameter, which is acceptable in practice. As a
result, this solution has been adopted for calculation of the blast design parameters.
Figure 4-1 Burden vs diameter with different stemming lengths and 80%
passing fragment size of 80 cm.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
50 100 150 200 250 300 350
Burdeninm
Diameter in mm
Stemming=25d Stemming=30d Stemming=B

68. 45
Similar results were obtained for the case in which the 80% passing size of the
muckpile was 30cm. The results are shown in the following Figure 4-2:
Figure 4-2 Burden vs diameter with different stemming lengths and 80%
passing fragment size of 30cm.
Clearly having a short bench with large diameter holes is not practical. The increase of
burden is not proportional to the diameter indicating that expansion of drilling patterns
is less effective in larger diameters.
4.4.2. Effect of subdrilling length on powder factor, uniformity index and
burden
Typically subdrilling is set equal to 8 borehole diameters. As suggested by Gustafson
1973, subdrilling is required to be 30% of the maximum burden, but according to
Pfleider (1972), under certain conditions, very little or no subdrilling may be required.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
50 100 150 200 250 300 350
Burdeninm
Diameter in mm
Stemming=25d Stemming=30d Stemming=B

69. 46
For vertical blastholes when the rock is massive, the subdrilling should be at least one
third of the burden.
The length of subdrilling was examined in the present work. Thus subdrilling lengths
equal to eight blast hole diameters as well as subdrilling lengths equal to 20% of the
burden of the blast were examined. Figure 4-3 shows the powder factor required to
produce 80% passing fragment sizes of 30 and 80 cm when drillhole diameter
changes.
Clearly the effect of subdrilling on powder factor is substantial and shows that the
simple adoption of an unchecked value may be very costly to an operation. It is
therefore important to optimize subgrade length, especially in large diameter holes.
Figure 4-3 Comparison of powder factor 'q' by changing subdrilling (SUB).
According to Cunningham, to calculate the uniformity index the column charge is taken
above grade. Therefore a change in subdrilling does not show any significant effect on
0.0
0.5
1.0
1.5
2.0
75 100 125 150 175 200 225 250 270 300 325 350
kg/m^3
Diameter in mm
SUB=8d, X80=30 SUB=0.2B, X80=30 SUB=8d, X80=80 SUB=0.2B, X80=80

70. 47
the uniformity index ‘n’ which largely controls the value of the 80% passing size. This is
clear in the following column chart of Figure 4-4.
Figure 4-4 Effect of subdrilling (SUB) on uniformity index 'n'.
The values of the uniformity index ‘n’ calculated with the different subdrilling lengths
show little difference for the same fragment size and the same diameter. The small
difference is due to a small change in burden. However, the change in diameter affects
the uniformity index as well.
The uniformity index is different for the various specified 80% passing sizes. Due to the
small burden required to obtain small fragment sizes, the uniformity of the piles having
smaller particle sizes is higher.
Subgrade changes the powder factor as well as the distribution of explosive in the blast.
Both factors change the fragmentation distribution. As a result the choice of subgrade
drilling affects the calculated burden of the blast.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
75 100 125 150 175 200 225 250 270 300 325 350
UniformityIndex
Diameter in mm
SUB=0.2B, X80=30cm SUB=8d,X80=30cm SUB=0.2B, X80=80cm SUB=8d, X80=80cm

71. 48
The graph of Figure 4-5 shows the change in burden length at each drillhole diameter
when the value of subgrade drilling is changed.
Figure 4-5 Effect of subdrilling (SUB) length on burden 'B'.
The difference in the length of burden when different subgrade values are adopted is
not very significant at the smaller diameters, but it becomes more significant with the
increase in the drillhole diameter.
4.4.3. Effect of stemming length on uniformity index, powder factor and
average fragment size
Stemming length creates a significant effect on the blasting results. The curves of Figure
4-6 show the uniformity indices for 75 to 350 mm diameters’ fragment sizes. The value
1
2
3
4
5
6
7
8
50 100 150 200 250 300 350
Burdeninm
Diameter in mm
X80=30cm, SUB=8d X80=30cm, SUB=0.2B
X80=80cm, SUB=8d X80=80cm, SUBB=0.2B

72. 49
of n for this ranges from 1.27 to 0.96 and 1.02 to 0.67 for 30cm and 80 cm sizes of
fragments.
Figure 4-6 Effect of stemming length on uniformity index 'n' (i) when X80=30
cm and (ii) X80=80 cm.
Figures 4-7(a) and 4-7(b) show the effect of stemming length on the powder factor
when certain feeds are specified. Apparently for large diameters the rule of
proportionality between stemming length and diameter produces unrealistically high
powder factor values due to the short length of the explosive column. Such high values
of powder factor would require charges to be placed close to each other and close to the
free face of the blast. These solutions can create flyrock problems during the blast and
malfunction of charges. Selecting stemming equal to burden produces a more realistic
solution as far as the distribution of charge is concerned.
Nevertheless, it is obvious that use of large diameter boreholes requires additional
amounts of explosive energy. Thus there are several opposing trends as far as the cost
0.1
0.3
0.5
0.7
0.9
1.1
1.3
50 150 250 350
UniformityIndex'n'
Diameter in mm X80=30cm
Stemming=25d Stemming =30d
Stemming =B
0.1
0.3
0.5
0.7
0.9
1.1
1.3
50 100 150 200 250 300 350UniformityIndex'n'
Diameter in mm X80=80 cm
Stemming=25d Stemming=30d
Stemming=B

73. 50
of drilling and blasting is concerned. The cost of the drilling of a blast with larger
diameters may be smaller; however increased powder factor means increased
explosive consumption.
(a) X80=30 cm and
(b) X80=80 cm
Figure 4-7 Effect of stemming length on powder factor with subdrilling=0.2B.
0
2
4
6
8
50 100 150 200 250 300 350
Powderfactor(kg/m^3)
Diameter in mm Stemming=ls in m X80=30 cm
ls=25d ls=30d ls=B
0
2
4
6
8
10
12
14
16
50 100 150 200 250 300 350
Powderfactor(kg/m^3)
Diameter in mm Stemming=ls in m X80=80 cm
ls=25d ls=30d ls=B

74. 51
Also there is a drastic change of the small size material to maintain a certain 80%
passing size. The graph of Figure 4-8 shows the average fragment sizes at each drillhole
diameter with respect to the stemming lengths.
Figure 4-8 Effect of stemming length on mean fragment size 'X50' with
subdrilling=0.2B when X80=30 cm and X80=80 cm.
Clearly to achieve a certain 80% passing size when a drillhole diameter is increased, the
average fragment size must be reduced. This means that production of fines will
increase. If fines are unwanted, this increase may present a problem. In the case of most
mines, production of fines may result in higher productivity.
0
5
10
15
20
25
30
35
40
50 100 150 200 250 300 350
Averagefragmentsizeincm
Diameter in mm
Stemming=25d Stemming=30d Stemming=B
X80=80cm
X80=30cm

75. 52
4.4.4. Drillhole deviation effect on Uniformity Index
Drilling deviation affects fragmentation. In this study, the deviation is taken as 2% of
the hole length plus a set up error of 1 hole diameter. This can be changed according to
the type of drill and the operator’s experience. Atlas Copco (1) claims that their
machines ensure less than 1% deviation for ITH and less than 3% deviation for
Tophammer drill machines. Figure 4-9 shows the changes in the uniformity index
values when the value of deviation is 1% to 3% of the bench height.
Figure 4-9 Change in uniformity index with changes in drillhole deviation
when stemming is equal to burden and subdrilling=0.2B.
4.5. Effect of rock factor on burden
A change in geology and rock mechanics properties of rocks affects blast design .
Kuznetsov’s equation accounts for the geological and rock mechanics properties
through index ‘A’, typically called a rock factor.
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
75 100 125 150 175 200 225 250 275 300 325 350
UniformityIndex'n'
Diameter in mm
Deviation= 0.01 Deviation= 0.02 Deviation= 0.03
X80=30cm
X80=80cm

76. 53
To examine the effect of rock factor, two different values (5 and 13 of rock factor ‘A’)
were used in the calculations corresponding to soft and very hard rocks, respectively.
The calculated burdens for the two selected passing sizes of 30 and 80 cm have been
plotted in Figure 4-10.
Figure 4-10 Changes in burden length when drilled in rocks having different
rock factor.
It is clear that the rock factor is important. It is also apparent that differences in burden
are larger as diameter increases.
4.6. Effect of explosive density on burden
The density of commercial explosives varies between 0.8 to 1.4 g/cm3. ANFO and
emulsion have been used to predict burdens as a function of diameter used for the two
fragmentation cases. The total quantity of explosive used per borehole is based on
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
75 100 125 150 175 200 225 251 270 300 311 350 381
Burden'B'inm
Diameter in mm
A=5, X80=30 A=13, X80=30
A=5, X80=80 A=13, X80=80

77. 54
densities of 0.9 and 1.2 g/cm3 for ANFO and emulsion respectively. The results have
been plotted in the following graph as Figure 4-11, which show the effect of explosives’
density on burden.
Figure 4-11 Effect of explosive density on burden.
In reality one would expect an even stronger difference as ANFO’s performance
depends on the charge diameter a lot more than the performance of the emulsion.
However Kuz Ram and similar models only consider the total energy of the explosive
and their density, so these results are expected.
2
3
4
5
6
7
8
50 100 150 200 250 300 350
BurdenBinm
Diameter mm
X80=30cm ANFO
X80=30cm Emulsion
X80=80cm ANFO
X80=80cm Emulsion

78. 55
4.7. Conclusion
The Kuz Ram model was used to predict the 80% blast fragmentation size as a function
of blasting parameters when drillhole diameter changes. The most appropriate
descriptions of stemming length and subdrilling were selected and the applicability of
the model in different conditions was demonstrated.

79. 56
Chapter 5
Drilling Considerations
5.1. Introduction
The previous chapter demonstrated the effect of fragmentation specification on blasting
parameters. Important considerations in the practical implementation of a blast design
are drilling parameters, the implementation of which is discussed in the present
chapter.
5.2. Drilling production
Gross Penetration Rate is the drilling rate obtained with the first rod and is expressed in
ft/min or m/min. The average drilling rate or net production rate of a drill rig as used in
the industry is the multiplication of the gross penetration rate with mechanical
availability and utilization which are dependent on the efficiency of the organization,
blasthole depth and manoeuvring time. The utilization is actually affected by moving a
machine from one blasthole to another, positioning and collaring, changing and
extracting rods, and cleaning and jamming of the blastholes.
(a) The mechanical availability is the percentage of time during which a machine is
operating or able to operate. In terms of probability it is expressed that a machine is
available for operation at any instant in time and a mathematical equation is formed as
follows:

80. 57
Theoretical availability= Mean uptime/(Mean uptime + Mean downtime)
All manufacturers generally provide mechanical availability of their drill machines.
However, mechanical availability varies from manufacturer to manufacturer and cannot
be compared as such. The manufacturers have their own criteria with which to decide
the factors affecting availability. In the current scenario of large and sophisticated
technological construction of machines, the operator has to depend on the reliability of
the machines rather than the provided directions of the manufacturers. New machine
models may not have historical data and may have to depend on speculations or
manufacturers’ simulations, which may not be accurate. For the calculation of
mechanical availability the down time is generally considered as time spent on
maintenance of the machine, while repair is another important factor to be considered.
In actuality the repairs are considered to be unwarranted maintenance, which occurs
due to failure of a part or process of a machine. The machines’ history, which show high
down time are due to repair considerations, partly or fully. It is the idle time for the
actual production of the machine, when all other related activities are not carried out to
continue production except repairs. Under the circumstances, repairs added to
maintenance further reduce utilization of the machine and the efficiency of the total
amount of work done.
(b) The utilization of a machine is usually dependent on its design configurations and
site situations which include geological factors and drilling design parameters. The

81. 58
effective utilization is defined as a ratio of operating hours divided by the scheduled
hours. The penetration rate of a drill is expressed as the length of hole drilled per
minute while the net production rate is expressed in terms of length of hole drilled per
hour. Utilization is actually the penetration rate multiplied by the effective utilization of
the machine and expressed in net production of drilling length per hour.
5.2.1. Extrapolation of data for penetration calculation when diameter is
changed
When the penetration rate is known for a given diameter, penetration rates at other
diameters can be estimated for the same rig using available equations. The equation
provided by Jimeno et al. (1995) rearanged in the following form was used in the
present work:
5.1
2
1
12 






d
d
VV dd ---------------------------------- Equation 5-1
where 1dV is an observed penetration rate at a drilled hole diameter d1 and 2dV is an
unobserved penetration rate at a drillhole 2d to be drilled.
5.2.2. Calculation for rotary-percussive and rotary drilling penetration
According to Jimeno et al. (1995) the penetration rate dV is inversely proportional to
the uniaxial compressive strength cU of the rock. Provided that all other factors remain
the same, the dV should increase if drilling is to be carried out in a softer rock. If the

82. 59
penetration rate and the uniaxial compressive strength for a certain rock are given, then
the penetration rate for a new rock can be calculated on the basis of its uniaxial
strength and several assumptions, outlined in the following.
When the same machine has to be moved from one location to another to drill the same
diameter of drillhole, using the same hammer and the same hammer pressure, the
required rate of penetration can be calculated according to the following empirical
equation, suggested by Jimeno et al (1995):
)(
1
5.3
)(
1
5.3
)(
)( *
)(
)(
gd
U
cc
U
gc
cd V
U
U
V
cc
gc



















--------------------------- Equation 5-2
where )(gdV is the given penetration rate and )(gcU is the uniaxial compressive strength
for the given rock, where the drilling has been carried out. )(cdV and )(ccU are the
penetration rate and uniaxial compressive strength for the rock to be calculated.
In the case of rotary rigs, the penetration rate is also inversely proportional to the
uniaxial compressive strength of the rock. If the value of any of the factors, like the
diameter of the tricone bit, its rotary speed and the pulldown force change, then
penetration rate changes as well.
The following empirical equation, with the same symbols of Equation 5-2, has been
obtained for rotary drills: