The Effect of Fragmentation Specification on Blasting · PDF fileDrilling and blasting are...
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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
Transcript of The Effect of Fragmentation Specification on Blasting · PDF fileDrilling and blasting are...
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
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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.
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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
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diameter also allows the examination of the suitability of the drill machine under the given
geological and operational conditions of the drilling site.
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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.
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
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
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
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.
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.
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.
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
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.
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:
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)
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 ( BH b / ) is larger
than 3. If BH b / = 1, the fragments will be large, with overbreak/backbreak around
holes and toe problems. With BH b / = 2, these problems are attenuated and are
completely eliminated when BH b / >3.
The condition BH b / >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.
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.
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.
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.
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.
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
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
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)]
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
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.
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
23
optimization of blasting and costing of fragmentation require quantifying these
parameters.
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
xy
--------------------------------------------------------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:
25
nbxey 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
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
eavE
QqAx
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
Bn
2
11*1142.2
b
cbbt
H
l
CLBL
CLBLm
B
D
d
Bn
1.05.0
1.0*2
11142.2
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
1302 3.0 nC
H
l
B
Dm
d
Bnn
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 ss
Rn
----------------------------- Equation 3-8
where sR is the scatter ratio and is expressed as:
x
ts
TR
6 ------------------------------------------------- Equation 3-9
with t being the standard deviation of the initiation system and xT the desired delay
time between holes.
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
30
the fines, or on the basis of the Swebrec function (Ouchterlony, 2005), which is a new
function describing fragmented rock.
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.
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.
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)
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
xxP
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:
nx
xb
50
maxln2ln2 --------------------
Equation 3-13
The model has been called the Kuznetsov – Cunningham – Ouchterlony (KCO) model.
(Ouchterlony, 2005)
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.
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
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
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.
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:
nxx
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
cbbE
ldmHABx
------ Equation 4-3
where is the density of explosive.
eQ
30
19
6
1
8.0
0
0
50
115)(
ANFO
eE
VAx
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
bbbE
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
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
bbbbE
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 ( BH b ) .
(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
IH
lmF
2
)1(1 ------------------------------- Equation 4-12
b
cbbt
H
lm
B
D
d
Bn
2
111142.2
I
t FB
D
d
Bn *1142.2
42
Combining the two equations 4-1 and 4-5, the following equation is obtained:
80
16.1 *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
6.11
xBFF
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.
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
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
Bu
rde
n in
m
Diameter in mm
Stemming=25d Stemming=30d Stemming=B
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
Bu
rden
in
m
Diameter in mm
Stemming=25d Stemming=30d Stemming=B
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
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
Un
ifo
rmit
y I
nd
ex
Diameter in mm
SUB=0.2B, X80=30cm SUB=8d,X80=30cm SUB=0.2B, X80=80cm SUB=8d, X80=80cm
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
Bu
rde
n in
m
Diameter in mm
X80=30cm, SUB=8d X80=30cm, SUB=0.2BX80=80cm, SUB=8d X80=80cm, SUBB=0.2B
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
Un
ifo
rmit
y I
nd
ex
'n'
Diameter in mm X80=30cm
Stemming=25d Stemming =30dStemming =B
0.1
0.3
0.5
0.7
0.9
1.1
1.3
50 100 150 200 250 300 350U
nif
orm
ity
In
de
x 'n
'
Diameter in mm X80=80 cm
Stemming=25d Stemming=30dStemming=B
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
Po
wd
er
fact
or
(k
g/
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
Po
wd
er
fact
or
(k
g/
m^
3)
Diameter in mm Stemming=ls in m X80=80 cm
ls=25d ls=30d ls=B
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
Av
era
ge
fra
gm
en
t si
ze
in c
m
Diameter in mm
Stemming=25d Stemming=30d Stemming=B
X80=80cm
X80=30cm
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
Un
ifo
rmit
y I
nd
ex
'n'
Diameter in mm
Deviation= 0.01 Deviation= 0.02 Deviation= 0.03
X80=30cm
X80=80cm
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
Bu
rde
n 'B
' in
m
Diameter in mm
A=5, X80=30 A=13, X80=30A=5, X80=80 A=13, X80=80
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
Bu
rde
n B
in m
Diameter mm
X80=30cm ANFO
X80=30cm Emulsion
X80=80cm ANFO
X80=80cm Emulsion
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.
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:
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
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
112
d
dVV 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
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
)(
15.3
)(
)( *
)(
)(
gd
U
cc
U
gc
cd V
U
UV
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:
60
)(
2
)(
)(
)( * gd
cc
gc
cd VU
UV
------------------------------------Equation 5-3
It is assumed that the drillhole diameter and the tricone bit diameter are the same. The
pulldown force and the number of revolutions change when rock of different UCS is
being drilled. The pulldown force and the rotary speed are usually left to the judgement
of the driller. When the actual observed values are not available, the multiplication of
the pulldown force by rotary speed has been assumed to be the same in both the cases.
In the absence of data, this formula can be useful to extrapolate the penetration rate of a
machine after observing its performance in a particular type of rock.
5.2.3. Data from drilling machines selected for this study
Drillhole diameters up to 127 mm and in special cases to 150 mm are drilled by top-
hammer drill machines, which are usually hydraulic machines. Rotary percussive
machines usually drill boreholes up to 216 mm (8 ½ inches) in diameter and in special
cases to 241 mm (9 ½ in). Large drillholes having diameters from 150 to 460 mm (6 to
18 in) diameter are drilled by rotary drill rigs.
To investigate the role of diameter on drilling and blasting costs once a fragmentation
target has been specified, a range of diameters from 75mm to 350mm was considered.
Drill penetration rates were collected from different manufacturers and users, and data
for the following drill machines were obtained:
61
(i) John Henry Tophammer, a hydraulic machine mounted on a crawler.
(ii) Atlas Copco DM 45 900 and 1070 machines, typical examples of In The
Hole (ITH) drill machines.
(iii) Driltech D75K, typical of the big rotary rigs.
(iv) Driltech D90K, Bucyrus BC 51R, and P&H 120 A, each unit represents a
large rotary rig used on large production mines.
Penetration rates obtained from these machines are given in Appendix B Tables B-5 and
B-9. A summary in terms of drilling production is presented in the following Table 5-1.
62
Table 5-1 Drilling net production rates of different machines.
Drill JH Tophammar DM45 900 D75K D90K BC 51 R
P&H 120A
Dia (mm)
63.5 89 127 140 155 165 175 200 251 270 311 350
Given UCS
172 MPa 126 MPa 118 MPa
121 MPa
110 MPa
124 MPa
Given
dV 96 64 32 39 40 36 32 24 30 31 38 36
Ref. UCS
126 MPa
Cal.
dV 128 85 43 39 40 36 32 24 29 29 28 34
dV = Penetration in m/hr, Ref.= Reference/base, Cal.= Calculated
5.3. Drilling penetration rates and comparison in given and calculated
UCS rock
The data collected are all from different manufacturers, users and environment.
However to be able to compare costs and associate them to blasting, a common base is
needed. In the case of the Atlas Copco DM 45 900 drill the rock for the drilling
production observation, in limestone, has a UCS of 126 MPa (18,000 psi) which is the
strength of a medium to hard rock. This was chosen as the reference and a base to
recalculate the penetration rates for all drill machines.
The penetration rate in Appendix B, Table B-1 is an actual observation of the company
staff for a DM 45, Atlas Copco Down The Hole Hammer drill (Edmunds, 2005). The
machine can drill a range of diameters from 127 to 200 mm; however the company
63
mostly encourages its use for 165 mm (6 ½ in) holes. On request, Atlas Copco provided
further information from 140 mm (5 ½ in) to 200 mm (7 7/8 in) holes, for the drill. In
the absence of data for the diameter of 127 mm (5 in), the value for the penetration rate
has been calculated and reported in Appendix B Table B-1. The penetration rates for
various diameters in limestone/medium hard rock are shown in the following Table 5-2
on the basis of rock with UCS of 126 MPa.
Table 5-2 Drilling production rates of different machines.
Diameter (mm) 140 155 165 175 200 Net Production Rate m/hr (1070) 39 43 39 34 26 Net Production Rate m/hr (900) 39 40 36 32 24
The John Henry Top hammer drill fits the first part of the drillhole diameter range (75
to 350 mm) for which the data has been observed in Barre Granite having UCS 174 MPa.
The graph chart plotted in Appendix D Figure D-1 shows curves based on actual UCS
174 MPa and the calculated penetration rates of drillhole diameters from 63.5 to 125
mm for limestone having UCS 126 MPa using equation 5.2. The calculations allow the
comparison of penetration rates in the same rock. Comparisons become more difficult
when multiple machines are used at different locations with varied speeds of the drill
and pull down pressure on the drill bit. In the case of soft rock, the penetration rate
increases as compared to hard rock when the pull down force and speed are kept
constant. Similarly, the penetration rate increases when the pull down/speed of the
drill increases in the same type of rock.
64
Table 5-3 shows calculated and observed data of a Driltech D75K rotary rig. The larger
diameter drill holes with diameters from 250 mm to 381 mm were drilled in a
limestone of UCS 140 Mpa. Penetration rates for diameters 251 and 311 mm were
available from the drill operator. To be within the adopted range of drillhole diameters
from 75 to 350 mm, the penetration rate for a diameter 350 mm has been calculated
using equation 5.1 (see Appendix B Table B-6). Values have also been produced using
equation 5-2 for limestone having UCS 126 MPa. The observed and calculated values of
the penetration rate have been plotted as graph curves in Appendix D Figure D-2. The
two curves show a visible difference of penetration rates; these heights are very useful
to compare the performance of a machine at drillhole diameters and different hardness
of rocks.
Table 5-3 Net production by D75K in limestone of UCS 140 and 126 MPa
Diameter (mm) 251 311 350
Net Production Rate (UCS 140MPa) m/h 22 12 10
Net Production Rate (UCS126MPa) m/h 28 15 13
Additional data were received for the following drills: Driltech D75K and D90K, Bucyrus
BC 51R, and P&H 120 A. All machines drilled in limestone having different hardness and
UCS. Similar to the previous, their penetration rates were recalculated for a limestone
rock of UCS 126 MPa. The results have been plotted in Figure 5-1.
65
Figure 5-1 Net production of various drill machines in different and similar
UCS rock.
The drill machines used underground are different than the machines used at the
surface. The major differences in the case of underground machines are that:
The mast height is smaller than in the case of the surface drill machines
A booster compressor is used
There are higher safety and environment protection requirements under
regulations
Penetration rates for diameters from 100 to 150 mm, provided by the drill operator for
a CUBEX Aries drill machine, were obtained for underground drilling in hard rock
having UCS of 176 MPa (Mauro, 2005). The calculated drilling net production rates are
shown in the Appendix B Table B-3 and plotted in Appendix D Figure D-4.
0
20
40
60
80
100
120
140
63.5 89 127 140 155 165 175 200 251 270 311 350
172 MPa 126 MPa 118 MPa
121 MPa
110 MPa
124 MPa
JH Tophammar DM45 900 D75K D90K BC 51 R
P&H 120A
Ne
t p
rod
uct
ion
m/
hr
Diameter in mm
Vd for given UCS
Vd for 126 MPa UCS
66
The hammer used for the 100 mm and 125 mm holes is the same and moves at the
same revolutions per minute. The hammer used to drill a 150 mm diameter drillhole
has a larger diameter and rotates the bit faster. The value of penetration rate for the
150 mm diameter hole is higher than for 100 and 125 mm diameter holes, because the
larger size hammer consumes/transfers more energy to the bit-rock interface.
5.4. Effect of bailing velocity on penetration rate
Air flushing gives maximum penetration rates and longer cutter life, depending upon
whether adequate velocity and volume of air is provided for drilling. According to
Morrell, air flushing gives maximum penetration rates and good cutter life. Air of
adequate velocity and quantity is required to achieve best results (Morrell et al. 1973).
The quantity of air supplied is directly proportional to the velocity of air, if drillhole and
string diameters are kept the same. The air of the hammer, after running the hammer,
exhausts through the holes in the drill bit and flushing is also carried out with this
exhausted air. Atlas Copco provides the machine (DM 45) with two compressor
configurations, 900 CFM (25.5m3/min) and 1070 CFM (30.3 m3/min) at the same
pressure 350 psi (2.41 MPa). The field observations show that the penetration rates
improved after using this higher capacity compressor (see Appendix B Table B-1, and
Appendix D Figure D-4 for details). The increased penetration rates resulted with the
higher capacity compressor and change of hammer which causes change in the
67
delivered price and fuel consumption of the machine. This case demonstrates the effect
of the change of compressor to increase the blowing impact, which ultimately changes
the bailing effect to clear the formed chips by the same machine.
5.5. Effect of mechanical availability and utilization of drill machines
All data of drill performance are either provided by the operators or the drill machine
manufacturers. These machines are actually used with these availability and utilization
factors. Currently emphasis is placed on improving the reliability and getting maximum
utilization out of a machine. Thus an investigation of how these factors affect drilling
operations and therefore drilling and blasting costs is useful.
The penetration rates for Top-hammer JH, have been observed in a hard rock (Barre
Granite) with UCS 172 MPa, and the availability for the drill was reported to be 80%.
The utilization was 67% and the product of availability and utilization is 0.54.
In the rest of the data, the least given value of availability was 82% for D75K drill and
the highest was 92% for the DM 45, BC 51R, and P&H drills. The smallest utilization was
63%, for the DM 45 drill and seems to be most realistic in the current situations.
Utilization of 76% was the highest value. The product of availability and utilization
ranges from 0.47 to 0.7 and the selected range from 0.5 to 0.55 seems to be very
realistic and achievable. (Rao, 1996; Daneshmend, 2004)
68
In the following paragraphs it is appropriate to examine what effect the change in the
availability and the utilization have on the net production and finally on the cost of
production. For these purposes the availability ‘a’ and utilization ‘u’ are given two
values each, a high and a low. The lowest value for availability was assumed equal to
0.75 and the highest equal to 0.92 while the values for utilization were 0.63 and 0.76
respectively.
Figure 5-2 provides penetration rates for all the machines under discussion. The trends
are nearly the same, exponentially declining from 63 to 200 mm diameter boreholes
and then becoming almost horizontal. In the case of machine data obtained from sites of
different geological and structural properties, the curve, as expected, is undulating.
Clearly the machines used to drill smaller diameter drillholes have higher rates of net
production than the machines drilling larger diameter holes and can be benefited more
by increases in availability and utilisation.
69
Figure 5-2 Net production rates of various drilling machines with different
availability and utilization.
5.6. Conclusions
Drill penetration data have been obtained to establish a relationship between
penetration rate and diameter. The penetration rate of a drill machine is affected by
the UCS of rock, bailing velocity of air, and mechanical availability and utilization.
0
20
40
60
80
100
120
140
160
50 100 150 200 250 300 350
Pe
ne
tra
tio
n i
n m
/h
r
Diamete in mm
aXu given Calculated UCS a0.75Xu0.63 a0.92Xu0.76
70
Chapter 6
Cost Calculations
6.1. Introduction
Costs are associated with all types of organizations and mining is no exception. To
create more value at lower cost is the philosophy and an important objective of most
modern organizations. Costs are generated by a variety of activities/processes. These
activities that cause costs have to be identified and estimated for further planning,
decision making and setting of standards. The discussion in this case is limited to
drilling and blasting, the two processes being considered for cost calculations in this
study.
A discussion on the various types of costs and methodology adopted to calculate the
drilling and blasting costs appears in the following paragraphs and sub-chapters. To
examine the profitability of a machine, costs are calculated and the productivity must be
at a cost allowing profitable production. Ownership costs are made up of investment
and depreciation values and are charged against the productivity of the machine on an
hourly basis. This theoretical definition provides a reserve of capital with which a drill
can be replaced when it is no longer economically serviceable. (Wagner, 1987)
The simple cost behaviour pattern is the breakdown of costs into fixed and variable
components. The cost estimation method adopted here is the one commonly used in
71
practice for engineering calculations. For the sake of simplicity a straight line method is
proposed instead of more sophisticated methods, which change from company to
company and country to country.
The cost of drilling has to be calculated on the basis of $ per length drilled, in order to
be useful in this work. The cost components include direct labour costs of operating
equipment, repair and maintenance, and direct material costs of supplies, which include
consumables and energy. The sum of all the indirect costs is called the operating cost.
Indirect costs include ownership costs and henceforth will be termed owning costs. The
owning costs include investment and depreciation of the drilling equipment. The
investment costs include interest, insurance rates and taxes (I.I. & T). The depreciation
is calculated by the straight line method. The total of the two gives the ‘Operating and
Owning Costs’ (Oo).
The blasting cost has to be classified on the basis of ‘Volume of Production’. It contains
variable costs such as the quantity of explosives used and charged as dollars per
kilogram, detonators used and charged as the number of detonators used per hole
multiplied by the total number of blast holes. In blasting operations, a semi-variable
cost is incurred on direct labour when labour is contracted out for a fixed quantity of
explosive and more than that quantity, if used, is charged per kilogram.
The blasting operation also has step costs. Such cost includes the transportation of
explosives from supplier to the blasting site, which depends on the size of the truck
72
used. It is fixed from one kilogram of explosive to the maximum capacity of the truck
and then changes for the next bulk load. The loading of blastholes is mostly charged per
day or per bulk load with a blaster’s fee. Charging may be carried out by labour or by
bulk loading trucks.
Fixed costs of blasting may have to be considered. Such costs may include magazine
depreciation, insurance and security.
6.2. Drilling costs
The drilling cost expressed per meter drilled ($/m) is actually the sum of a number of
direct and indirect costs, and presented by Jimeno (1995) as follows:
Total Drilling Cost TDC : Adding all the direct and indirect cost factors, the cost per
meter ($/m) is obtained by the following equation:
r
BLEOMIATD
P
CCCCCCCC
------------------------ Equation 6-1
where )( AC is depreciation ($/h), IC is the interest rate and insurance ($/h), (indirect
costs), MC is maintenance and repair ($/h), OC labour ($/h), EC fuel or energy, LC oil,
grease and filters ($/h) BC bits, rods, sleeve and shanks ($/h) (direct costs) and Pr is
the drilling productivity in (m/h). (Jimeno et al., 1995)
73
Ingmarsson presented the following model which has been adapted here into the metric
system for the Total Drilling Cost;
mlifeBit
priceBit
mlifeHammer
iceHammer
hrmtyproductiviNet
hrtslaborD
mC R
TD
$$Pr$cos$
where RD is the drill rig cost ($/hr). (Ingmarsson, 1998)
Jimeno’s model is more general and was adopted as a reference for this thesis. To
calculate the total cost of drilling, the direct and indirect costs are discussed in the
following sections.
(a) Indirect costs
The “Owning Costs”, which are indirect costs and composed of annual investments and
annual depreciation, are calculated on the basis of local tax regulations.
I., I. & T percentages: A model given by Jimeno, explains that interest rates and
insurance ( IC ) , can be calculated as:
h
np
IW
TIIPN
N
C
)%(2
1
-------------------------------------- Equation 6-2
where N = Number of years of service life. PP Purchase price I = interest
nI Insurance T = Taxes hW Work hours per year (Jimeno et al., 1995)
74
To calculate interest rate and insurance costs (I., I. & T), the number of hours per year
(hrs/yr) is determined as: hrs./day X days/week X weeks/year, and the hourly
investment is calculated by the following equation:
Hourly investment cost = [Total delivered price X AaF X (I.I.&T.)] / (hrs/yr)],
(Wagner, 1987)
where the AaF factor can be calculated using N
N
2
1factor of Equation 6-2.
Total useful hours of the machine are estimated to be equal to 20,000. Interest charges
are taken equal to those, which would have been earned by investing the money to earn
interest and usually range from 8% to 10%. Insurance is typically 3% to 4% of the cost
of the machine to protect the machine from damage or loss due to accident, fire etc.
Taxes are applied to ongoing use, property, etc. and depend upon time, place and
situations. Adding all these together a value of 14% can be used for estimating
purposes.
Depreciation: It can be calculated by the following equation:
AC (Purchase price – residual value)/hours of life---------- Equation 6-3
(Jimeno et al., 1995)
75
Deterioration produced by use and due to aging and loss of value is the basis of
depreciation )( AC . Garrison explains that historically, depreciation has been closely tied
to the useful life of an asset, with year-by-year depreciation deductions typically
computed by a variety of methods. Also in computing some cases, companies have
generally given recognition to an asset’s expected salvage value by deducting the
salvage value from the asset’s cost and depreciating only the remainder.
(Garrison, 1991)
According to Wagner the drill depreciation is calculated as follows:
Hourly depreciation cost = Total delivered price / Total useful hours --------------------------------------------------------------------------------Equation 6-4
This equation calculates depreciation without making allowance for resale or salvage
value. Hence: Total hourly owning cost = IC + Hourly depreciation cost or
Total hourly owning cost = Hourly investment cost + Hourly depreciation cost ------------------------------------------------------- Equation 6-5
(Wagner, 1987) All these equations are useful in formulating a drilling cost model to calculate the cost of
drilling per length.
(b) Direct Costs
Maintenance Cost: It is actually based on two factors:
76
Preventive maintenance cost: This is estimated as 15% – 20% of power costs,
depending upon the machine type and the manufacturer’s instructions.
(Jimeno et al., 1995)
This maintenance cost is the total cost of lubricating oil plus grease, filters and labour to
accomplish maintenance or it is based on the past experience and record of the
machine. The cost is expressed in terms of “Mechanical Availability”, which is equal to
operating hours divided by the total of operating hours plus the maintenance hours,
(Daneshmend, 2004). When translated in terms of cost, the cost of direct labour plus
the cost of parts is added to the cost of time lost; however, in this thesis, for the sake of
simplicity, only the cost of direct labour and that of parts are taken into consideration.
Repair cost: It is actually based on the past experience of the machines to formulate an
interpolation factor for future calculations. It is given as a percentage of the delivered
price of the machine and it is usually up to 75%. To calculate the repair cost the
delivered price is multiplied by the interpolated factor and divided by the useful life of
the machine. (Wagner, 1987)
Jimeno explains that when maintenance costs include the costs of preventive
maintenance and breakdowns, it is also calculated as a combined factor as:
MC [(Purchase price) / 1000] XrF (%) ($/hr)---------------- Equation 6-6
where rF is a reparation factor (available from manufacturers). It should include the
cost of spares plus the maintenance labour.
77
When the repair factor does not include labour charges, then labour charges have to be
included by multiplying the prevailing rate with the down time of the machine. The
method has been adopted in the following calculations of a drill by Atlas Copco. For the
sake of simplicity the maintenance cost in this study is compiled as:
Cost of spares $/hr + (labour charges per hour X percentage of downtime of the
machine)
Operating Cost: These are also called labour charges, and include the wages of driller
and helper (where necessary), and their fringe benefits in total. (Jimeno et al., 1995)
Fuel or Energy Cost ( EC ): The specifications of the diesel engines or electric motors,
can be used to calculate this cost of drilling according to the following equations:
EC Power hp * (Litres/hp) * $/l ----------------------------------Equation 6-7
EC Power kWh * $/kWh ------------------------------------------- Equation 6-8
(Jimeno et al., 1995)
The fuel cost is calculated taking the average diesel consumption, as indicated by Atlas
Copco, in US gallons/ hr X 3.8 (conversion factor litres/ gallon) X cost ($/l) or $/kWh in
case of electricity consumption as in the case of the CUBEX drill.
Cost of Consumables: The hardness of the rock has high influence on the cost of
consumables such as bits, rods, sleeves and shanks/ pipes, hammers, etc. As the
consumption of these items depend upon the hardness of the rock, their costs can run
up to 15 - 40% of the total drilling costs.
78
The cost of bit and hammer is calculated as total cost/ useful life of the consumable, but
the cost of pipe is calculated differently. Jimeno has given an equation to calculate the
‘rod meters’ as:
p
pl
lml
lddl
2* ---------------------------------------------- Equation 6-9
where ml is rod meters or tube meters, ld is length of blasthole and pl length of each
extension rod/ pipe in ‘m’ (Jimeno et al., 1995).
Taking into consideration total drilling length or rod meters is important to decide the
maximum length and service life of the pipe, but it is also important to consider the
total number of pipes required to calculate the cost per meter or per hour. To simplify
the calculation, the number of pipes placed in series in a blasthole column is used to
find the cost of the pipe. This total cost is divided by the life of the pipe, for cost per
meter or per hour. In the present case, when the bench height is 12 m and the maximum
length of a pipe accommodated by the drill machine mast (e.g., Atlas Copco DM 45) is 6
m (usually manufactured as 6.1 m), rounding up gives two pipes in a 12 m column to
complete a blasthole length. Hence 3 pieces of pipe will be needed to complete the
drilling of the hole. Thus:
Cost of drill rod (pipe) /m or hour drilling = (2+1)*(Cost $/pipe)/ life of pipe in meters
or hours.
79
In the case of a rotary drill machine, either the life of the tricone bit is given or
calculated by the following equation:
d
r
d VN
EdmLife 3
**14.28)(
67.155.1
-------------------- Equation 6-10
where d= Diameter (inches) Ed = Pulldown force on the bit (thousands of pounds)
Nr = Rotary speed (r/min) dV = Penetration rate (m/h) (Jimeno et al., 1995)
6.3. Cost estimates for surface mining drilling operations
Surface mining deals with large volumes of rock, employing large drills
6.3.1. Introduction
It must be stressed that no machine can drill the entire range of drillhole diameters
from 75 to 350 mm which have been considered in this project.
To drill a different drillhole diameter either the whole drill machine or the drilling
accessories such as the hammer, drill pipe/string, shank, couplings and in some cases
the compressor must be changed. The accessories increase/decrease costs and the
penetration rate of the machine.
Cost estimates have been thoroughly discussed in the following sections of this chapter
based on actual drilling operations mostly from surface mines using the most common
80
machines. For the smallest diameter, data for a tophammer machine was for the year
1998, which was updated to 2005 using Table 6-1. An example of an underground
operation has also been included in the present chapter.
To calculate the costs of drilling, data were collected from Atlas Copco drilling
(Edmunds, 2005). The estimates provided by them have been incorporated in Table 6-
3. This format is designed to determine the cost of drilling per hour and per meter cube
of rock. The figures taken were from a quote in 2005. Using MS EXCEL, all previously
discussed costs have been calculated. The format for drilling cost calculations presented
in Table 6-3 is the same throughout this thesis.
6.3.2. Cost estimate for surface drilling by top hammer (diameter smaller
than 127mm)
To drill a hole less than 125 mm in diameter, top hammers are considered more
suitable than ITH rigs. To be able to examine the cost of drilling as a function of
diameter observed costs from a construction site from 1998 (see Appendix B Table B-
11) using a John Henry Tophammer Rockdrill (JHTR) have been used (McLaughlin,
2005). The costs were converted to current dollar values using Marshall and Swift
Equipment quarterly cost indices (see Appendix C Table C -4). Abstracts of Chemical
Engineering from September 1998 to January 2006 for detail), Table 6-1 is constituted
for recent cost calculations.
81
Table 6-1 Cost Index, an abstract from: Marshall & Swift Equipment quarterly cost indices (see Appendix Table C-4 for detail).
Year 1st Q 2nd Q 3rd Q 4th Q 1998 1097.1 1098.2 1097.7 1096.6 2005 1304.8 1326.5 1331 1341.2 Q=Quarter, Adopted 4th Q of each year, for calculations
Based on the index figures of the 4th quarters of years 1998 and 2005, cost figures were
calculated for 2005 using the cost to index equation.
The results of the detailed calculations are plotted in Figure 6-1.
Figure 6-1 Cost per meter length of drilling and the cost trends with respect to
drillhole diameter for JH Tophammer.
6.3.3. Drilling cost estimates for diameters between 127mm and 250mm
The Atlas Copco DM45 is a drill suitable for drillhole diameters between 127 and
228mm. Details of the drill can be found on their web page [Atlas Copco (1) and (2)]. A
cost model based on the Atlas Copco DM 45 900 drill accounting figures is given in
$2
$3
$4
$5
$6
$7
60 80 100 120
Dri
llin
g C
ost
$/m
Drillhole Diameter in mm
Drilling Cost
82
Table 6-2. A detail table for this cost model is available as Appendix B Tables B-1 and B-
2.
83
Table 6-2 Atlas Copco - DM45 900 drilling cost estimate
Diameter 165 mm/6.5 in
Production Information Figures Units
Rock Strength 127.00 MPaBench Height 12.00 mAvailability 0.92Utilization 0.63Gross Penetration Rate 62.80 m/hrNet Production Rate 36.40 m/hr
Fuel Cost
Fuel Consumption 27.00 US Gal/hrFuel Cost 0.92 $/lFuel Cost per Hour 94.39 $/hrFuel Cost per Meter 2.59 $/m
Operation Costs
Operator Cost per Hour 50.00 $/hr
Helper Cost per Hour 0.00 $/hrOperator Cost per Meter 1.37 $/m
Maintenance Costs
Hourly Labour Cost 50.00 $/hrParts Cost per Hour 60.00 $/hrTotal Maintenance Cost Per Hour 64.00 $/hrMaintenance Cost per Meter 1.76 $/m
Consumable Cost
Estimated Bit Life 2439.00 mEstimated Drill Pipe Life 18290.00 mNumber of Drill Pipe Used 2Estimated Hammer Life 12200.00 mBit Cost 840.00 $/unitDrill Pipe Cost 1300.00 $/unitHammer Cost 6500.00 $/unitBit Cost per Meter 0.34 $/mPipe Cost per Meter 0.21 $/mHammer Cost per Meter 0.53 $/mTotal Consumable Cost Per Meter 1.09 $/m
Adopted for thesis as Table 6.3, on Feb10,08
84
Atlas Copco - DM45 900 Drilling Cost Estimate Table 6.2 continued
Owning Costs
Suggested Factory List PriceFrieght Duties, Fees, Etc, To Land On Site
Total Delivered Price
Hours per Day
Days per Week
Weeks per Year
Hours per Year
Useful Life of The Machine Hrs
Years To Depreciate (Rounded To Next Year)
Hourly Investment Cost (Taking I. I. & T. 0.14)
Hourly Depreciation Cost
Hourly Owning Cost
Owning Cost per Meter
Summary of costs $/m Figures Units
Fuel Cost per Meter 2.59 $/m
Operator Cost per Meter 1.37 $/mMaintenance Cost per Meter 1.76 $/mConsumable Cost per Meter 1.09 $/mTotal Operating Costs per Meter 6.82 $/mTotal Owning Cost per Meter 1.38 $/m
Total Operating and Owning Costs 8.19 $/m
$660,419$25,000
$685,419
14
$34.27
$50.17
$1.38
5
50
3,500
20,000
6
$15.90
Adopted for thesis as power point presentation, on Feb10,08
85
(i) Explanation of the model used in the cost calculations
The penetration rate in Table 6-2 is an actual observation by company staff and the cost
calculation model is based on the 165 mm or 6 ½ in. bit/drillhole diameter, using a
“Down The Hole” hammer (the hammer size is always smaller than the bit diameter).
The instruction manual of the machine indicates a range from 127 to 200 mm diameter
drilling capacity, but the company encourages users to use it at 6 ½ in. (165 mm). On
request, Atlas Copco provided further information from 5 ½ in (140 mm) to 7 7/8 in.
(200 mm) drillholes, for a DM45 drill. In the absence of data for 5 in (127 mm), the
value of the penetration rate has been calculated according to the method presented in
the previous chapter. With the addition of all these diameter sizes a complete picture of
the drilling performance of this machine appears. The costs have been calculated in an
identical manner as in Table 6-4 for machines with two different compressors of 900
CFM (25.5 m3/min) and 1070 CFM (30.3 m3/min). A detailed table for each machine is
attached as Appendix B Table B-1 and B-2 and a summary Table 6-3 from these two
tables is presented here for consultation.
Table 6-3 Net production rate and costs at a range of drillhole diameter
Diameter (mm) 127 140 155 165 175 200
Net Production Rate m/hr (1070) 34 39 43 39 34 26
Net Production Rate m/hr (900) 34 39 40 36 32 24
Cost $/m DM 45 1070 9.18 8.16 8.10 8.66 9.62 12.98
Cost $/m DM 45 900 8.71 7.67 7.58 8.19 9.16 12.50
86
6.3.4. Drilling cost estimates for diameters above 250mm
Peterson (2005) provided data using various drill machines to drill holes from 250 to
381 mm diameter. As already indicated, each diameter size warranted either changes in
the machine accessories or the replacement of the drill machine itself. After completing
a small range of drillhole diameter sizes another model and make of machine is
required.
Thus several drills, each drilling a specific range of hole diameters, are considered.
Often mining companies contract their drilling and blasting work to an external
contractor who takes care of these operations. The contractors calculate the owning
cost for their machines and are always ready to quote. They keep on updating
operational and consumable costs according to the market conditions and keep these
figures for ready reference. An example of a contract work is included here. Peterson
(2005) provided data in the form of owning cost per hour (capital cost), and operating
cost per hour, for different machines used in large diameter drilling operations. All
received information was used to calculate drilling cost per hour according to the
details of Appendix B Table B-5. The final cost figures have been plotted in Figure 6-2.
87
Figure 6-2 Cost per meter length of drilling by different machines for limestone
at different locations.
The cost has fluctuations due to the use of different machines employed in various
locations with varying lithology.
6.4. Comparative cost results from small to large size diameter ranges
of drillholes (surface mining)
The available data for a range of drillhole diameters from 63mm to 350 mm, can be
divided into three sub ranges: a small diameter range of 63 to 127 mm, drilled by a drill
similar to the John Henry Tophammer Rockdrill, a medium diameter range of 140 to
200 mm, drilled by a drill similar to the Atlas Copco DM 45 900 drill and a large
diameter range of 250 to 350 mm, drilled by drills such as the D75K, D90K, BC 51R,
P&H 120A models. To examine the changes in cost per meter from small to large
$11.47
$12.40
$9.91
$10.99
$8
$10
$12
$14
251 270 311 350
118 MPa 121 MPa 110 MPa 124 MPa
D75K D90K BC 51 R P&H 120A
Co
st o
f d
rill
ing
$/
m
Diameter in mm, UCS and name of drill machines
Drilling Cost for different machines
88
diameter, all these three different ranges of drillhole diameters have been plotted as a
column chart in Figure6-3.
Figure 6-3 Cost per meter length of drilling by different machines for
limestone of different UCS at different locations.
Values of drilling costs per meter length of drill hole, plotted in the above column chart
are based on site observations. All data have been tabulated in Appendix B Tables B-1,
B-5, and B-7. It is understood that a relationship between cost and diameter cannot be
proposed yet. The data come from different sources and are obtained from drilling in
different conditions. All three ranges have different locations of varied hardness of rock
with different UCS and holes were drilled with different types of machines.
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
63.5 89.0 127.0 140 155 165 175 200 251 270 311 350
172 MPa 126 MPa 118 MPa
121 MPa
110 MPa
124 MPa
John Henry Top Hammer Rockdrill
DM 45 900 D75K D90K BC 51 R
P&H 120A
Dri
llin
g c
ost
$
/m
Drillhole diameter in mm, name of drill machines and UCS
Drilling Cost $/m
89
6.4.1. Influence of different rock UCS on drilling rate and cost of
production
McLaughlin, 2005, provided cost figures for calculation of three drillholes at diameters
251, 311 and 381 mm. The figures of penetration rates for diameters 251 and 311 mm
were available from the drill operator, while the rate of penetration for the third
diameter at 381 mm had to be extrapolated; calculations have been carried out and are
presented in Appendix B Table B-6.
This is attributed to the difference in penetration rate due to the different strengths of
limestone. Cost differences will also result due to different locations and lithology.
Using data from different sources it is possible to show the effect of the compressive
strength of the rock on the cost of drilling. This is shown in Figure 6-4. The graph gives
a good comparison of the costs per meter when the holes are drilled in the same type of
rock with different UCS at different locations.
90
Figure 6-4 Cost per meter length of drilling by Driltech D75K in limestone at
different locations with different UCS.
Clearly it costs more to drill a harder rock with the same model and type of machine.
Similarly, in previous Section 4.3.1., the cost of drilling per meter in the case of larger
diameters holes is less than for a D75K drill when drilled in soft rock with larger
machines and at different locations.
6.4.2. Effect of bailing velocity on the cost of drilling
Air flushing gives a higher penetration rate and a longer cutter life due to adequate
velocity bearing cooling and timely removal of cuttings from the drillhole. According to
Morrell et al. (1973), the quantity of air supplied is directly proportional to the velocity
of air, if drillhole and string diameters are kept the same. The air of the hammer, after
running the hammer, exhausts through holes in the drill bit, and flushes the hole.
$15.14
$14.00
$11.47
$10
$14
251 251 251
142 MPa 140 MPa 118 MPa
Dri
llin
g c
ost
$
/m
Diameter in mm and Unidirectional Compressive Strength (UCS) of Rock
Drilling Cost by D75K for different UCS
91
In the case of middle range diameter holes the machine was used with a 900 CFM (25.5
m3/min) at 350 psi (2,413 kPa) compressor and the drilling machine is named a DM 45
900 after this compressor. To take advantage of the quantity of air on bailing velocity,
Atlas Copco provides machine DM 45 1070 which has a large compressor generating a
higher quantity of air (1070 CFM or 30.3 m3/min at the same pressure 350 psi or 2.41
MPa).
A change of the compressor affects drilling as well as the delivered price and fuel
consumption of the machine. Higher capacity compressors cost more than the lower
capacity ones and the same applies to the hammer. Based on the cost calculation
results, the cost curves plotted in Figure 6-5 show higher costs per meter of drilling for
the 1070 CFM (30.3 m3/min) compressor. In this case, the change to a higher capacity
compressor increased operating and owning costs per meter of drilling.
Figure 6-5 Cost per meter length of drilling in limestone using different
pressure compressors.
$7
$8
$9
$10
$11
$12
$13
125 150 175 200
Co
st $
/m
Drillhole diameter in mm
Drilling Cost of AtlasCopco DM 45 1070Drilling Cost of Atlas Copco DM 45 900
92
The increased penetration rate ultimately helps to increase the production rate per
annum from the same machine at a somewhat higher cost of production (see Appendix
B Table B-1 and B-2).
6.5. Drilling operation for underground mining
Drilling cost estimates were calculated based on an Aries ITH drill which is commonly
used underground. The estimates are presented in Table 6-4. The description of the
drill can be found on the web page of CUBEX. (Mauro, 2005)
93
Table 6-4 CUBEX- ARIES-(ITH) drilling cost estimate for u/g production information
Production Information
100 Diameter in mm Rock Strength MPa 175.8 Bench Height m 12 Availability 0.85 Utilization 0.7 Gross Penetration Rate m/min 0.3 Net Production Rate m/hr 10.71
Fuel Cost Energy Consumption kWh 94.00 Energy Cost $/kWh 0.10 Energy Cost per Hour $/hr 9.11 Energy Cost per Meter $/m 0.85
Operation Costs
Operator Cost per Hour $/hr 50.00 Helper Cost per Hour 0.00 Operator Cost per Meter $/m 4.67
Maintenance Costs Hourly Labour Cost $/hr 50.00 Parts (Repair)/ Hour 30 Parts (Maint.)/ Hour (20% Energy Cost) 1.82 Total Maintenance Cost Per Hour 39.32 Maintenance Cost per Meter 3.67
Consumable Cost Estimated Bit Life m 550 Estimated Drill Pipe Life m 1530 Number of Drill Pipe Used 7 Estimated Hammer Life m 5490 Bit Cost 500 Drill Pipe Cost 350 Hammer Cost 3000 Bit Cost per meter $/m 0.91 Pipe Cost per meter $/m 6.41 Hammer Cost per meter $/m 0.55 Total Consumable Cost Per Meter $/m 7.86
94
CUBEX- ARIES-(ITH) drilling cost estimate (for u/g) Table 6.5 cont.... Owning Costs ($) Suggested Factory List Price 800000 Frieght Duties, Fees, Etc, To Land On Site
25000
Total Delivered Price 825000 Hours per Day 20 Days per Week 6 Weeks per Year 50 Hours per Year 6000 Useful Life of the Machine Hr 20000
Years to Depreciate (Rounded To Next Year) 4 Hourly Investment Cost (Taking I. I. & T 0.14.) 12.13 Hourly Depreciation Cost 41.25 Hourly Owning Cost 53.38 Owning Cost per Meter 4.98
Summary of costs $/m
Fuel Cost per Meter 0.85 Operator Cost per Meter 4.67 Maintenance Cost per Meter 3.67 Consumable Cost per Meter 7.86 Total Operating Costs $/m 17.05 Total Owning Cost per Meter 4.98 Total Operating and Owning Costs 22.04
6.5.1. Cost calculations for underground drilling operation
The procedure adopted to calculate cost per meter of drilling length is the same as the
one used for surface drilling. The drill machines used underground are different than
the machines used on surface. The major differences are:
The mast height is smaller than in the case of the surface drill machines
A booster compressor is used for operation
95
There are higher safety and environment protection requirements under
regulations. (Ontario Ministry of Labour, 2003)
The cost calculations, shown in Table 6-5, include all the sub-headings adopted in the
case of surface drilling operations by the Atlas Copco DM45 drill. Data provided by the
operator were for three diameters of drillholes ranging from 100 to 150 mm. The
manufacturer provided machine life as 20,000 hours and its annual use was based on
20 hours per day, 6 days a week and 50 weeks per annum. All cost calculations are
based on these assumptions, and the results have been tabulated in Appendix B Table
B-3. A summary of the results is presented in Table 6-5.
Table 6-5 CUBEX -ARIES-ITH drilling for drillhole length of 12 m
Dia (mm) 100 125 150 Cost $/m 22.04 22.23 20.52 Net Production Rate m/hr 10.71 10.71 12.50
The penetration rates for diameters from 100 to 150 mm, provided by the drill operator
for the CUBEX Aries drill machine, were observed for underground drilling carried out
in hard rock having UCS of 175 MPa (25000 psi). The calculated drilling net production
rates are shown in Table 6-5 and cost in terms of $/m in Appendix D Figure D-5.
The hammer used for the 100 mm and 125 mm holes is the same and moves at the
same number of revolutions per minute. The hammer used for the larger 150mm
diameter hole has a larger diameter and rotates the bit faster. The value of penetration
96
rate for the 150 mm diameter is higher than the penetration rate in the case of the 100
and 125 mm diameter holes because of the larger size hammer which
consumes/transfers more energy to the bit-rock interface.
As already mentioned and for the sake of simplicity, the drillhole length is 12 m, which
can be considered representative for underground mining methods such as room and
pillar, and long hole stoping. It is understood that a typical long hole stope would have
larger heights. Whatever the height of the stope, the height of the development levels
restricts the height of the drill machine mast, which ultimately restricts the length of a
drill pipe. In the case of the Aries drill, the length of pipe had to be 1.8 m. If the height of
a drillhole in a stope is reduced, it affects the cost of drilling. Similarly, the use of a
machine per day and/or per week affects the annual use of the drill machine, which
finally changes the cost.
6.6. Blasting costs
To calculate the blasting cost, a summary of the costs for labour charges and accessories
has been tabulated in Table 6-6, which were obtained from two explosives
manufacturers (see Appendix C Table C-1 ORICA CANADA; Table C-2 ETI – Canada
Inc.). Both quotations have been included as Appendix Tables C-1 and C-2 respectively.
It is worth noting that for actual purchasing, usually the lowest quotes are negotiated.
97
For budgeting purposes, keeping in view the trends of increasing market prices, higher
prices instead of the lowest ones are adopted.
Summary Table 6-6 is based on these two quotations for estimation purposes. A strict
rule of minimum cost selection or budget estimation has not been followed in this case
of cost estimation because the quotations either address unit cost or unit cost for a bulk
supply. Some explanations/clarifications are provided in the following paragraphs:
(i) Delivery charges: These are the step costs, which include freight and
handling charges of delivery vehicles to the test/blasting site. The charges
remain fixed for a certain limit of explosive quantity but add up to the next step
with the same quantity limit of explosive. Both suppliers quoted their prices in
different ways which explains the market trend and practice (see Appendix C
Tables C-1and C-2 for details).
For the sake of simplicity of calculations, freight is taken at $0.50 per kg and delivery
vehicle handling at site, drillhole charging etc. at $50 per hole. Larger quantities of
explosive shipments include delivery vehicle handling charges in the transportation
cost. Currently in the market there are very efficient delivery systems which transport
explosive and load drillholes by pumping. Blastholes can be loaded at a rate as high as
1.5 kg/s (200 lb/min) by the smallest system.
If the manufacturing companies send their own blaster they charge per contract or
according to prevailing rates (see Appendix C Table C-2 for details). A charge of $75 per
98
hole has been included for this purpose in Table 6-6, which includes the charges of
blaster and helper, blast monitoring and dewatering holes according to the location.
(ii) Explosives and Accessories: These are variable costs and vary with the
quantity of explosive used. The explosive is sold per bag or in bulk load carried
by special trucks (see Appendix C Tables C-1 and C-2 for details).
For consultation purposes the cost for a kilogram of explosive has been calculated and
tabulated in Table 6-6, and a price of $1.12/kg has been adopted for further calculation
of total explosive charges per hole in this study. Detonator costs calculated per unit
depending on the leg wire size is taken in addition to the delivery charges. The cost of
detonators has been totalled according to the length of wires required in each hole.
Minor accessories used in blasting are connectors (tape, delays), cable etc., which have
not been included here in this table but are required in the case of large operations.
These small accessories, even if they are included, make a negligible difference.
(iii) Compilation of blasting charges: This study is aimed to calculate costs
based on a single blasthole and hence compilations have been carried out
accordingly. Transport and labour charges have been distributed per kg of
explosive and per detonator.
In the case of each drill hole, for example, this unit price is multiplied by the total
quantity of explosive used plus the cost of detonator(s). The drillhole is supposed to be
blasted by two detonators, one at the bottom and the other at the top of the column, to
99
avoid misfires. The cost of each detonator varies with the length of the leg wires. The
length of the leg wires of a detonator for the top of each hole is calculated equal to the
sum of the distance to the point of initiation plus the spacing (approximately two
spacing lengths), and for the bottom is equal to the spacing plus the drillhole length.
With these minimum required lengths, the next manufactured length of detonator leg
wires is selected. The handling and drillhole charging is included at $50 per drillhole.
Bulk prices lower the blasting cost. An average workable figure has been inserted in
Table 6-6 for simplification reasons and to keep the costs closer to the actual mining
operations.
100
Table 6-6 Cost of explosives and blasting accessories
Delivery charges (Freight) to test site Item and Unit Max.
Kg/trip $/trip $/kg Delivery
$/unit Cost $/unit or kg
1 - 20 cases/trip* 500 250 0.50 0.50 0.50 Up to 270 cases/trip*
6,750 300 0.04 0.04 0.04
Labour at site Labour charges Charges $ Handling delivery vehicle at site 50 50.00
Drillhole Charging 75 75.00 Explosives Item Unit Kg/unit $/unit $/ kg Amex Bag 25 21.67 0.87 0.87 Apex Gold Bulk 100 115.00 1.15 1.15 Detonators Item Units/box $/box $/unit 3.5m Electric ms #0 25 119.00 4.76 0.50 5.26 4.5m Electric ms #1 to 20
25 133.00 5.32 0.50 5.82
8m Electric ms 15 126.75 8.45 0.83 9.28 12m Electric ms 10 113.50 11.35 1.25 12.60 18m Electric ms 8 116.40 14.55 1.56 16.11 25m Electric ms 6 111.96 18.66 2.08 20.74 Max.= Maximum, * Each case has 25kg and number of cases per trip depend on the capacity of the vehicle,
(iv) Cost per blasthole
Based on the previous discussion, the cost per blasthole for specific 80% passing sizes
(X80) is calculated. Two different case studies, one with 80% passing size of 30cm and
the other with 80% passing fragment size of 80cm are presented. These sizes represent
conditions of coarse and fine fragmentation respectively as it has been explained
101
earlier. Figure 6-6 shows the cost per blasthole using an emulsion and ANFO to show
the trends in each case of fragment sizes.
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.
The cost per drillhole for fragment size 30 and 80 cm increases exponentially from
smaller to larger diameter. The two curves are very close from 75 mm to 125 mm
diameter, but the difference increases with the diameter size. In the case of X80=30cm,
the curve is sharper than for X80=80 cm. Comparing two different strengths of
explosives in terms of cost per blasthole, it appears that the use of emulsion is more
expensive than ANFO. However it is expected that the cost of drilling will be less in the
case of the emulsion, since the emulsion bulk strength is higher than the bulk strength
of ANFO. The total cost will be examined in the following sections.
0
200
400
600
800
1000
75 100 125 150 175 200 225 250 270 300 325 350
Co
st $
/B
last
ho
le
Drillhole diameter in mm
$/Blastlhole for X80=30cm ANFO
$/Blastlhole for X80=80cm ANFO
$/Blastlhole for X80=30cm Emulsion
$/Blastlhole for X80=80cm Emulsion
102
6.7. Drilling cost per unit volume of rock blasted
The cost per meter cube of rock is calculated using the following Equation 6-11:
Drilling cost/m3 of rock blasted
0
2.0*
V
BHO bo ----- Equation 6-11
where oO is the total operating and owning cost per meter length, in $/m, bH is the
bench height and B is the burden in ‘m’, while 0V is the total volume of rock in m3.
Burden and spacing are calculated according to the equations presented in Chapter 4.
Using the values of these parameters and the drilling costs which are analytically shown
in Appendix B Table B-9, the drilling net production rates and costs per meter cube of
rock blasted have been calculated and tabulated as Appendix B Table B-10.
6.8. Drilling blasting costs per unit volume of rock blasted with ANFO
The total drilling and blasting costs per drillhole, which were calculated in previous
sections, have been added and divided by the total volume of the rock blasted per total
length of the respective diameter drillhole to calculate the cost per unit volume of rock.
The trends of the drilling and blasting costs per meter cube of rock with respect to a
drillhole diameter for generating 80% passing fragment size of 30cm have been plotted
in Figure 6.7.
103
Figure 6-7 Drilling and blasting cost per cubic meter of rock with different UCS
and X80=30 cm.
The trends projected in the case of drilling cost show a small variation of costs over a
diameter range from 50 to 350 mm. However the cost of blasting is affected by the
diameter. Initially the increase of diameter has a favourable effect due to the reduction
of accessories needed; later, due to the necessary increase of the powder factor, to keep
fragmentation according to the specifications, costs seems to climb. Figure 6-8 has been
plotted based on the actual field data provided by the drill operators from different
sites having different geological situations. In the case of 80% passing size at 80 cm the
cost trends projected are nearly the same and do not show much variation, except the
cost is lower than in the case of finer fragmentation. Figure 6-8 shows costs for this
case.
0.00.51.01.52.02.53.03.54.04.55.0
63.5 89 127 140 155 165 175 200 251 270 311 350
172 MPa 126 MPa 118 MPa
121 MPa
110 MPa
124 MPa
John Henry Top Hammer Rockdrill
Atlas Copco DM 45 900 D75K D90K BC 51 R
P&H 120A
Co
st i
n $
/m
^3
Diameter in mm, UCS in MPa, and name of drill machines
Drilling Cost $/m^3 Blasting cost$/m^3 Drill+Blast Cost $/m^3
104
Figure 6-8 Drilling and blasting cost per cubic meter of rock with
different UCS and X80=80 cm.
6.9. Drilling blasting costs per unit volume of rock blasted with
emulsion
Explosives density and energy output affect blasting results. In the case of most
commercial products higher densities are typically associated with higher energy yields
per unit volume. As a result larger pattern dimensions result from the use of high
density explosives, such as emulsions and blends of emulsions with ANFO. On the other
hand explosive costs and cost trends per blasthole are much higher in the case of
emulsions than ANFO. Figure 6-9 shows the costs of drilling for ANFO and a typical
emulsion. It appears that the cost of drilling is higher for ANFO than emulsion.
0.00.20.40.60.81.01.21.41.6
63.5 89 127 140 155 165 175 200 251 270 311 350
172 MPa 126 MPa 118 MPa
121 MPa
110 MPa
124 MPa
John Henry Top Hammer Rockdrill
Atlas Copco DM 45 900 D75K D90K BC 51 R P&H 120A
Co
st i
n $
/m
^3
Diameter in mm, UCS in MPa, and name of drill machines
Drilling cost $/m^3 Blasting cost$/m^3 Drill+Blast cost $/m^3
105
Figure 6-9 Drilling (D) cost per cubic meter of limestone by using emulsion
(Emul) orANFO for different UCS and X80=30 and 80 cm.
Figure 6-10 shows the total cost of drilling and blasting per volume of blasted rock.
ANFO appears to be the most economic explosive in large diameter applications while
emulsion appears to be more economic in smaller diameters in this particular case.
0.00.10.20.30.40.50.60.70.80.9
63.5 89 127 140 155 165 175 200 251 270 311 350
172 MPa 126 MPa 118 MPa
121 MPa
110 MPa
124 MPa
John Henry Top Hammer Rockdrill
Atlas Copco DM 45 900 D75K D90K BC 51 R
P&H 120A
Co
st $
/m
^3
Diameter in mm, UCS in MPa and name of drill machine
D. Cost Emul X80=30cm D.Cost ANFO X80=30cmD.Cost Emul X80=80cm D.Cost ANFO X80=80cm
106
Figure 6-10 Drilling and blasting cost per cubic meter of limestone by using
emulsion or ANFO for different UCS and X80=30 and 80 cm.
6.10. Conclusions
The derived engineering model can be used to calculate the drilling and blasting costs
for the required fragmentation.
There is no drill machine available which can drill a large range of diameters, from 75 to
350 mm. Every make and model of drill machine is good only for a particular diameter
size or a small range of diameters with few variations.
For a range of drillhole diameters, more than one machine is required to drill holes.
With the change of a drill machine, investment cost and operational costs change. Cost
per meter cube of blasted rock shows a small variation with drillhole diameter. The
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
63.5 89 127 140 155 165 175 200 251 270 311 350
172 MPa 126 MPa 118 MPa
121 MPa
110 MPa
124 MPa
John Henry Top Hammer Rockdrill
Atlas Copco DM 45 900 D75K D90K BC 51 R
P&H 120A
Co
st $
/m
^3
Diameter in mm, UCS in MPa and name of drill machine
D+Blast Cost Emul X80=80cm D+Blast Cost ANFO X80=80cm
D+Blast Cost Emul X80=30cm D+Blast Cost ANFO X80=30cm
107
only advantage to using a larger size drillhole seems to be to drilling fewer holes to
meet large production targets.
108
Chapter 7
Cost Comparisons and Optimization
7.1. Introduction
After discussing engineering, fragmentation and cost models, the cost of drilling was
discussed based on available data from different machines. These machines were
deployed in different rocks.
To compare the cost of drilling by multiple machines and to optimize the cost of drilling,
the calculations should be based on similar conditions. Among them, geological
conditions are important and difficult to predict because they change frequently within
the same vicinity or in the same type of rock from one location to another. Similarly,
machine variables such as availability, utilization and type of machine also influence the
drillability and ultimately the cost of drilling per meter length or per cubic meter of
rock.
The penetration rate of a machine is a very important factor in controlling cost. The
penetration rate and the factors which have a significant effect on it have been
discussed previously. According to the empirical equations discussed, the penetration
rate increases if drilling is to be carried out in a softer rock or air pressure in the
hammer is increased. The prices of fuel, consumables, spare parts and even the labour
wages change, which ultimately affect the unit cost. The total production depends on
109
the rock parameters, actual penetration rate, mechanical availability of the machine and
utilization. The rock parameters (in this case UCS and hardness of the rock) are
controlled by nature and they are essentially uncontrollable factors.
The owning cost is dependent on the delivered price of the machine and it occurs once
and has to be considered for the total life of the machine. The only two factors left are
the mechanical availability and the utilization.
7.2. Optimization of drilling costs
The drill production rates have been presented with drillhole diameter, mechanical
availability and utilization of the machines in Appendix B (see Tables B-1 to B-5 for
details). The trends of drilling costs are given in the following.
7.2.1. Assumptions for operating costs
The fuel cost calculated from the engine and compressor specifications remain
the same in each case of observed or calculated penetration rates. Similarly the
operator, mechanic and helper’s wages per hour remain the same and are usually
related to the machine type; however the variation in the penetration rate changes the
cost per meter.
The changes in rock type, abrasiveness and drilling methods affect the service life of the
drilling accessories, which affect the ultimate costs. When the penetration rate is based
110
on the UCS of the rock, the abrasiveness is assumed to remain the same for all
calculations presented here. The consumables depend on site conditions and vary from
one location to another and from one type of machine to another. For the sake of
simplicity, consumables stay the same and the change in cost per meter is a result of the
penetration rate only, which varies due to the heterogeneity of the rock.
7.2.2. Assumptions for owning costs
In the given examples of the drill machines in this study, the utilization hours vary
customarily from one machine to another, from one location to another, and according
to the field of application. According to the manufacturers, Atlas Copco and Driltech,
(Edmunds, 2005; McLaughlin, 2005) machines are given 20,000 hours total useful life
while John Henry Rockdrill machines have useful lives of 10,000 hours (see Appendix B
Table B-7 for details). The machine mechanical availability increases if down time is
reduced. With the introduction of new research and development in the design and
maintenance of the machines, the availability and utilization are improving.
The total number of useful hours of a machine’s life, before it goes for a major repair, is
provided by the manufacturer. The total life of a machine is determined on the basis of
its active use per year. In the given examples the utility of the machines from one type
to another is different. For example a source is using a DM 45, a Driltech 75 for 14 hours
and John Henry for 8 hours at 250 days per annum, while another source is using
Driltech, Bucyrus and P& H machines for 21 hours per day at 351 days per annum (see
111
Appendix B Table B-9 for details). Hence the life of a machine in terms of years would
be different. To make the accounting procedure simple, the total useful life and the
active use per year in number of hours have been used to calculate the machine life in
years. It is already explained in Chapter 6 that the drilling operation cost is converted
into operating and owning cost per hour by adding the investment and straight line
depreciation cost in hours. Here, in the case of a drilling operation, the penetration rate
or net production comes into play and this hourly cost is divided by the net production
per hour of a machine to get the cost of drilling per meter length of drilling. To compare
the owning cost per meter length of drilling for a multiple number of drill machines,
there should exist parity of operations at all drillhole diameters. For this study to create
equality and to examine the efficiency of a machine with respect to the other, standard
accounting practices have been taken into consideration and adopted. The cost per
meter length of drilling for all drill machines individually, is calculated with the
following assumptions:
Useful Machine Life hours
Total useful life of a machine 20,000 hours
Daily utilization 14 hours per day
Days per week 5 Weeks per year 50
112
7.3. Discussion
a) Cost comparison for small diameter holes drilled in rocks of different UCS
Using the observed data for the John Henry Tophammer drill, penetration rates in rocks
with various uniaxial compressive strengths were calculated and drilling costs were
estimated. The results are shown in Figure 7-1. A curve for Barre Granite having UCS
172 MPa shows, as expected, higher costs at each drillhole diameter than the assumed
limestone having UCS 126 MPa.
The graph shows that the drilling cost per meter length by this machine is the lowest at
the smallest diameter. The rising upward trend in the hard rock drilling trend is
sharper than for drilling in the softer rock. Hence soft rock drilling has an advantage of
higher production over the hard rock case when drilling from small to large diameter
(see Appendix B Table B-7 for detail).
113
Figure 7-1 Comparative cost per meter length of drilling in rocks of different UCS
by John Henry Tophammer Rockdrill.
b) Costs comparison for a range of large drillhole diameters drilled by D75K,
in rocks of different UCS
Similarly, drilling costs are calculated for larger diameter holes and rocks with different
compressive strength on the basis of performance data for the D75K drill provided by
McLaughlin, 2005 (see Appendix B Table B-6). The curves in Figure 7-2 show a
significant decrease in cost per meter of drilling length as the UCS decreases.
The lowest drilling cost is observed for the smallest diameter. The cost of drilling in
hard rock is rising steeper than in soft rock when drilling changes from small to large
diameter holes.
$1
$2
$3
$4
$5
$6
50 75 100 125
Dri
llin
g c
ost
$/
m
Drillhole diameter in mm
Drilling Costs (Rock UCS 126MPa)
Drilling Cost (Rock UCS 172MPa)
114
Figure 7-2 Comparative cost per meter length of drilling in rocks of different
UCS by Driltech D75K.
c) Cost comparison for a range of large drillhole diameters drilled by multiple
drill machines
In practice the range of drillholes between 250 to 350 mm diameters would be drilled
by a variety of different machines. Using identical rock strength conditions and the data
provided for known conditions and a variety of drills, the cost of drilling can be
calculated at different diameters (see Figure 7-3 and Appendix B Table B-5 for details).
$10
$15
$20
$25
$30
250 275 300 325 350
Dri
llin
g c
ost
$
/m
Drillhole diameter in mm
D75K Drilling Costs UCS 140 MPaD75K Drilling Costs UCS 126 MPa
115
Figure 7-3 Comparative cost per meter length of drilling in rocks of different
UCS by various machines.
d) Cost comparison for a long range of drillhole diameters drilled at each
drillhole by a different drill machine
To examine the final trends of the cost of drilling as a function of drillhole diameter the
given examples were combined. The drilling costs for all these machines have been
summarized in Figure 7-4.
The observed cost values under various conditions show an undulating trend. When the
variables of the drill machine, cost components and rock UCS are assumed to be the
same for each machine with respect to the range of drillhole diameters drilled, the trend
becomes uniform rising up from borehole at 63 to 311 mm diameter and then
decreasing. This trend may be somewhat different when machines different than the
$11.47$12.40
$9.91
$10.99$11.66
$12.61 $12.63
$11.41
$8
$10
$12
$14
251 270 311 350
126MPa 126MPa 126MPa 126MPa
118 MPa 121 MPa 110 MPa 124 MPa
D75K D90K BC 51 R P&H 120A
Co
st o
f d
rill
ing
$/
m
Diameter in mm, rock UCS (observed and extrapolated) and name of drill machines
Drilling Cost for different machines and rock UCS
Drilling Costs for diff. machines and same rock UCS 126 MPa
116
ones selected, are used. The rising trends mean that the cost per meter length to drill
larger diameter drillholes is higher than the small diameters; however the quantity of
the rock blasted at each drillhole determines the drilling cost per cubic meter of rock.
Figure 7-4 Comparative cost per meter length of drilling for the range of
drilhole diameters in rocks of different UCS by various machines.
e) Effect of mechanical availability and utilization on the cost of drilling
Figure 7-5 has been plotted to examine cost of drilling as a function of diameter for a
range of drillholes. Four columns have been developed. One is based on the cost
calculated on the basis of data provided by the manufacturer or the operator, the
second presents cost data on the basis of drilling in the same rock having assumed
values of UCS and the same availability and utilization, a third one is based on assumed
02468
101214
63.5 89 127 140 155 165 175 200 251 270 311 350
172 MPa 126MPa 118 MPa
121 MPa
110 MPa
124 MPa
John Henry Tophammer
Rockdrill
Atlas Copco DM 45 900 D75K D90K BC 51 R
P&H 120A
126MPa 126MPa 126MPa
Dri
llin
g c
ost
$/
m
Drillhole diameter in mm, UCS of rock in MPa and name of drill machine
Costs/m drilling length for rock having different UCS
Costs/m drilling length for rocks having UCS 126 MPa
117
minimum values of availability and utilization of the particular machine under
discussion, and the fourth is based on the maximum values of availability and
utilization. The curves allow a continuous definition of cost as a function of diameter.
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).
The two column charges having assumed UCS with minimum and maximum of
availability and utilization behave similarly and the difference in cost value per meter
length of drilling increases from smaller diameter to the larger. Hence any
improvement in availability and utilization brings a visible cost difference. To achieve
better results, changes in the design parameters, improved training of the operator and
condition monitoring to increase uptime and reduce downtime of the machine have to
be adopted. The column with the given values shows an irregular increase in length at
larger diameter, resulting from observations under different conditions.
$0$2$4$6$8
$10$12$14$16$18
63.5 89 127 140 155 165 175 200 251 270 311 350
John Henry Top Hammer Rockdrill
DM45 900 D75K D90K BC 51 R
P&H 120A
Co
st $
/m
Diamter in mm
aXu UCS given UCS 126 MPa a0.75Xu0.63 a0.92Xu0.76
118
7.4. Optimization and comparison of drilling cost per unit volume of
rock
To examine the cost trends under similar conditions of rock mechanical behaviour, the
costs of drilling per volume of rock to produce a specified fragmentation upon blasting
were calculated using rock with a common uniaxial compressive strength of 126 MPa.
The cost values per unit volume of fragmented rock for the two fragmentation
specifications are shown in Figure 7-6. The drilling cost per cubic meter of rock for 30
cm fragments is two and a half times the cost per cubic meter of 80 cm fragment sizes.
All three ranges of drill machines have been joined together and the curves obtained
show undulating curves. The crests are the junction points of machine ranges, with one
ending and the other starting. Each machine needs a different application for each
diameter smaller or larger than that suggested by the manufacturer. It is clear from the
calculation that the drilling cost is smaller at a suggested diameter and increases with
an increase or decrease of diameter. The same applies to each range of the drill
machine.
119
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.
Figure 7-7 examines cost behaviour under conditions of maximum and minimum
availability and utilization costs at variable conditions and when drilling in rock of the
same UCS are also presented for comparison. The comparison of drilling production
costs in the previous Sections 7.3. (d) and (e), has been done using column charts. To
use curves was not appropriate when given values of UCS were different in each case of
diameter in Figures 7-4 and 7.5. In Figure 7-6 the values of UCS are similar and hence
represented by curves. In the following Figure 7-7, before optimizing the model it has to
be seen how the curves look in case of given values and in case the UCS is assumed and
values of availability and utilization are different in each case as compared to the
assumed values of UCS, availability and utilization.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
50 100 150 200 250 300 350
Co
st $
/m
^3
Drillhole diameter in mm
Drilling Cost $/m^3 X80=30
Drilling Cost $/m^3 X80=80
120
Figure 7-7 Drilling cost per cubic meter of limestone under given and assumed
conditions of UCS, availability (a) and utilization (u).
All these cost curves are based on the cost of drilling per cubic meter of rock
fragmented for the 80% passing size of 30cm, representing fine fragmentation.
In this case the assumed values of maximum and minimum availability and utilization
showed nearly the same trends as in Figure 7-5, but without much difference between
the two extreme ends. The cost curves based on the given values of data and common
value of UCS show undulation and they are neither smooth nor parallel to each other.
This is also due to the small range of each drill machine and a suggested drillhole
diameter which is considered to be the most economical. For example, in the case of the
ITH drill machines the most economical points are between 150 to 175 mm. A drillhole
diameter size smaller than 140 mm requires a change to a number of accessories
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
50 100 150 200 250 300 350
Co
st $
/m
Drillhole diameter in mm
Given
UCS 126 MPa
a0.75Xu0.63
a0.92Xu0.76
121
including the drill hammer, pipes and compressor, which may bring a reduction in the
cost but not necessarily an increase in the net production of the machine. Similarly,
drilling with a diameter larger than 175 mm, according to the manufacturer, is possible
but with options of new compressors and drill hammers, which may not be very
economical. Under the circumstances the operators prefer to deploy rotary drill rigs for
200 mm and larger size drill holes.
To further refine and reach a visible solution of cost trends as a function of drillhole
diameter, the crest points of each range were left out. Thus, to avoid the impact of the
uneconomic limits of the range of each drill, values of cost at the limits of each range
have been deleted.
After removing two points at 140 and 200 mm diameters, the two cost curves, one with
the lowest values of availability and utilization and the other with the highest values of
availability and utilization, were drawn in Figure7-8.
122
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.
These two values of availability and utilization have been plotted to present two
extreme levels. A drill machine having any value of utilization and availability can be
placed in between the two extremities to estimate the cost of drilling. These two curves
successfully accommodate the economical and most economical values of the cost of
drilling and provide a comparison from one diameter to the other. This exercise
clarifies that the cost per cubic meter does not increase linearly with the drillhole
diameter. The cost varies from one drillhole diameter to another in the shape of a curve
that may be a trough or a crest. It is easy to select a required diameter which may be
economical in the small range of the machine diameters, and to compare the same
machine to another machine.
123
The of cost of drilling per cubic meter trend for an 80% passing fragment size of 80 cm,
can also be calculable in a similar manner.
7.5. Optimization and comparison of blasting costs
To calculate the cost of blasting with respect to a drillhole diameter, explosive and
accessory costs provided in supplier quotations have been used. The blast design
parameters calculated according to the discussion in the previous chapters provide the
total quantity of explosives to produce a given 80% passing particle size. This total
quantity of explosive and the required accessories multiplied by the respective costs
give the total cost of blasting per blasthole. The most suitable subdrilling and stemming
lengths, already explained in the previous chapters, have been adopted to reach a sound
solution. In the following sub-sections, the effects of the rock type, explosive type and
fragmentation on the cost are discussed.
7.5.1. Effect of rock factor ‘A’ on cost of blasting
As discussed in the previous chapter factor ‘A’ in the Kuz Ram model represents the
resistance of rock to blasting. Cunningham (1983) initially assumed that ‘A’ is equal to 5
for very soft rock, 9 for medium and 13 for very hard rock, but later he presented a
model to calculate the rock factor. To examine the impact of A on the cost of blasting per
cubic meter three case scenarios for ‘A’ representing soft, medium and hard rocks have
been presented in Figure 7-9 .
124
Figure 7-9 Blasting cost per cubic meter of rock with different rock factor (A)
and fragment size of X80=30 cm.
The trends in the above graph show that the cost of blasting for a soft rock does not
change significantly in the range of diameters between 125 to 250 mm; however, it
changes sharply in the small to smaller diameters. Similar trends are observed in the
cases of the rocks with higher values of A. Results similar to the previous case are
obtained for the larger fragment size specification.
7.5.2. Effect of type of explosive on the cost per cubic meter of rock
blasting
Manufacturers of explosives usually recommend emulsions for all sizes of drillholes.
Because of their small critical diameter emulsion explosives are often used in smaller
drillholes. Figure 7-10 shows the cost of blasting using emulsions and ANFO. Clearly
emulsions result in a higher cost; however, explosive performance in the Kuz Ram
1
2
3
4
5
6
7
50 100 150 200 250 300 350 400
Co
st $
/m
^3
Diameter in mm
Blast.Cost A=13 Blast. Cost A=9 Blast. Cost A=5
125
model is reduced to a simple energy factor and energy partition is ignored. The graph
shows that blasting costs rise in small and large diameter applications. This is due to the
cost of accessories in the small diameters, and the required increase of the powder
factor to maintain a fragmentation target in the large diameters. Thus, in every case of
explosive selection or fragmentation specification, a minimum cost of blasting results at
a certain diameter.
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.
7.5.3. Effect of fragment size on cost
It is clear from the previous sections that the cost is affected by the fragmentation
specification. The two different specified sizes for the fragmentation have significantly
different costs covering a substantial range of what may be required by blasting and
essentially providing limits of blasting costs at the various diameters of application.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
50 100 150 200 250 300 350
Co
st $
/m
^3
Drillhole diameter in mm
X80=30 cm ANFO x80=30 cm Emul x80=80 cm ANFO x80=80 cm Emul
126
7.6. Optimization and comparison of drilling-blasting cost
The cost of drilling and blasting per cubic meter of rock has been discussed in the
previous chapter for a variety of drill machines operating under different conditions. All
drills were brought under identical conditions to examine the effect of diameter on
drilling cost enabling the calculation of the cost of drilling and blasting which is
presented in Figure 7-11.
The cost of blasting is four to five times higher than the cost of drilling; hence the sum of
the two shows the same trends as that of blasting.
Figure 7-11 Drilling and/or blasting cost per cubic meter of rock having UCS
126 MPa, fragment size of X80=30 cm.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
50 100 150 200 250 300 350
Co
st $
/m
^3
Drillhole diameter in mm
Drilling Cost $/m^3 X80=30 Blasting Cost $/m^3 X80=30
Drilling+Blasting Cost X80=30
127
Apparently the cost is minimum in the middle range of drillholes diameters (127-
250mm) with a sharp rise in the small drillhole diameters. In the large hole diameter
range the cost increase is rather small.
7.6.1. Drilling-blasting costs under assumed conditions
It is clear from the discussions of this study that it is not possible today or in the near
future to drill a large range of drillhole diameters with one drill machine. After
discussing all possible aspects of drilling, blasting and their costs, it is appropriate to
discuss a hypothesized case, where a range of drillhole diameters from 63 to 350 mm
have similar conditions of rock formation, geology and drill machines. To calculate the
cost of drilling-blasting under similar conditions let us assume the following
parameters:
Type of explosive to be used ------------------------- ANFO
UCS of rock -------------------------------------------- 126 MPa
Mechanical availability of the drill machine ------- 88%
Machine Utilization ------------------------------------ 63%
Ignoring all other factors including type of machine, bit, hammer etc., the costs of
drilling, blasting, and drilling-blasting were re-calculated. The final outcome of cost of
drilling-blasting for 80% passing fragment size for 30 and 80 cm have been plotted as
graphs in Figure7-12.
128
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.
These outcomes give a clear trend of the cost of drilling-blasting. It appears that the cost
of drilling-blasting for 80% passing fragment size of 30cm is minimal for drillhole
diameters ranging from 125 to 175 mm while for fragment size at 80 cm, it is minimum
for the range from 100 mm to 175 mm. Thus smaller diameter boreholes are more cost
efficient in producing small fragment sizes such that a primary crusher may be avoided.
7.6.2. Drilling-blasting cost under realistic assumptions, a final discussion
Figure 7-13 is a graph of the drilling and blasting costs using a smoothened drilling cost
obtained from different drills and excluding high costs at diameters considered to be
uneconomical. Thus the costs at diameters of 140 and 155 mm were eliminated.
129
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.
Again, a minimum cost is observed for diameters between 100 to 250 mm with cost
increase for smaller and larger diameters, preceding and exceeding this range
respectively. In the smaller diameters the cost of blasting accessories drives the cost
higher, while, in the larger diameters, blasting is not as efficient, requiring an increase
of powder factor to maintain a desirable fragment size.
7.7. Conclusion
It was shown that drilling and blasting costs depend on drillhole diameter. While this is
well known, the effect of the drillhole diameter on the cost, when fragmentation is
specified, defies some of the practical thinking. It appears that cost savings, using large
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
50 100 150 200 250 300 350
Co
st $
/m
^3
Drillhole diameter in mm
Drilling+Blasting Cost X80=30
Drilling+Blasting Cost X80=80
130
diameter boreholes, are minimal when a fragmentation target has been established and
small fragment sizes need to be produced. Intermediate diameter boreholes are well
suited in balancing explosive and accessories cost with the powder factor and explosive
distribution required to produce a certain fragmentation target, while in the case of
small diameter boreholes the cost of blasting accessories increases the total cost
sharply.
131
Chapter 8
Cost Component Sensitivities
8.1. Introduction
In cases of high uncertainty it becomes difficult for decision makers to reach a strong
conclusion. In this thesis engineering models provided blast design parameters based
on fragmentation specifications and a certain geometrical configuration of the blast and
the drilling and blasting cost was calculated for a variety of possible drillhole diameters.
The drilling cost component is controlled by the production rate which depends on the
penetration rate of the machine together with its availability and utilization. The above
factors lead to uncertainties, which have to be considered when defining alternatives.
Sensitivity analysis is widely used by decision makers in such cases. Sensitivity analysis
involves repeated computations with different analysis factors to compare results
obtained from these substitutions with results from the original data. Several formats
are suitable for sensitivity studies. More-or less-favourable estimates can bracket the
original estimates to obtain a range of values for an estimate’s worth. (Riggs et al., 1986;
Norman et al., 1978)
For the sensitivity analysis of the present study, the value of critical components has
been changed by 50% to examine the effect on the total cost outcome of drilling and
blasting.
132
8.2. Assumptions made in this study
In the previous chapters it has been discussed that the drilling and blasting operations
have a number of variables, parameters and components. Some of them are controllable
and few are uncontrollable. The assumptions made in this study are the following:
The rock factor, quantifying uncontrollable and geological factors was set equal
to 7, representing medium rocks. For a certain rock the factor will stay constant.
The same geometry was used in all calculations. Bench height used was 12 m
and blasthole deviation was one diameter plus 2% of the bench height.
For the base case scenario the rock strength was standardized to 126 MPa,
representing the strength of the rock for which performance parameters were
available.
The same availability and utilization figures have been used, which were
provided by the manufacturer or the operator for the related machine.
For most of the drillhole diameter sizes, data of drill machines (penetration rate,
availability, utilization) available from the manufacturers or operators (Atlas
Copco (1) and (2); Edmund, 2005; Peterson, 2005; McLaughlin, 2005) have been
used. Where observations were not available, empirical equations were used
according to the discussion in Chapter 5, Sections 5.1.1. and 5.1.2.
133
For explosive cost, quotations provided by the suppliers were collected.
Fuel/energy costs used in the drilling operation were adopted from average
costs of diesel for 2005 and Canadian Hydro (see Table C-3 Average retail prices
for fuel (diesel) by city in 2005, and Table C-4 Canadian Hydro).
Total useful life of a drill machine was 20,000 hours, and daily utilization 14
hours per day.
8.3. Sensitivity analysis for drilling and blasting cost by changing the
component costs
The drilling and blasting component costs which really influence the total outcome for a
given type of rock and geometrical configuration are the explosives and accessories
costs as well as drilling production rates influenced by availability and utilization
factors. The influence of the variability of these factors is discussed in the following
paragraphs.
8.3.1. Sensitivity of the blasting cost components
Two principal components of the blasting cost were analysed, cost of explosive and cost
of accessories.
134
1- Cost of explosive: This component of blasting cost is a major contributor to the
total cost (Figure 8-1). Of interest is the great variation of the total cost in the
case of the large diameters. As diameter increases, stemming length increases
affecting the uniformity of the muckpile. To compensate for the loss of
uniformity, in order to satisfy fragmentation size requirements, explosives
consumption increases, making the price of the explosive a critical component in
the total cost.
2- Cost of blasting accessories: The detonators are the chief component of these
accessories, while connectors and cables contribute little to this cost. The
sensitivity of the blasting cost to this component was examined by increasing
and decreasing the cost by 50%. The results obtained for 80% passing size of 30
cm have been plotted in Figure 8-1, where the effect of explosive cost and
accessories cost is presented. It is evident that the cost of fragmentation in small
diameter applications is sensitive to the price of accessories while the cost of
fragmentation in large diameter applications is sensitive to the price of the
explosive.
135
Figure 8-1 Cost trends of the total blasting cost, when cost of explosives or accessories changed by 50%.
The 50% change in the cost of accessories showed almost insignificant change in the
total cost of blasting at larger diameters, but the change at the smaller drillholes is
significant. Apparently, switching to more expensive accessories, such as electronic
detonators, in larger diameter applications is easier from an economic point of view.
The cost of explosive is important in every case. Thus parameters affecting it, such as
fuel prices and AN availability, play a major role in blasting costs.
Trends of cost for various drillhole diameters and a larger eighty percent passing size of
80 cm are given in Appendix D Figure D-6 with similar results. The following two spider
diagrams provide the sensitivities of the explosive and accessory costs in the case of a
136
small diameter drillhole (Figure 8-2) and in the case of a large diameter drillhole
(Figure 8-3).
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.
-20.0%
-10.0%
0.0%
10.0%
20.0%
-50.0% -30.0% -10.0% 10.0% 30.0% 50.0%
Pe
rce
nta
ge
ch
an
ge
in
to
tal
cost
of
dri
llin
g
an
d b
last
ing
Percentage change in explosive cost components d 89 mm
Expl.inc/dec.50%, X80=30 cm Acc.inc/dec.50%, X80=30 cm
Expl.inc/dec.50%, X80=80 Acc.inc/dec.50%, X80=80 cm
137
Figure 8-3 Change in total cost of drilling blasting when the cost of explosive
or accessories changes by 50% at adrillhole diameter of 350 mm.
8.3.2. Sensitivity of drilling operation cost components to the cost of
drilling and blasting.
The operating and owning cost components, mechanical availability and utilization are
the important factors of any drilling operation. The sensitivity effect of these
components on the total cost of drilling blasting is discussed in the following
paragraphs.
-40.0%
-30.0%
-20.0%
-10.0%
0.0%
10.0%
20.0%
30.0%
40.0%
-50.0% -30.0% -10.0% 10.0% 30.0% 50.0%
Pe
rce
nta
ge
ch
an
ge
in
to
tal
cost
of
dri
llin
g a
nd
bla
stin
g
Percentage change in explosive cost components d 350 mm
Expl.inc/dec.50%, X80=30 Acc.inc/dec.50%, X80=30 cm
Expl.inc/dec.50%, X80=80 cm Acc.inc/dec.50%, X80=80 cm
138
A- The effect of changes in mechanical availability and utilization of the
drill machines to the cost of drilling blasting.
The range taken for availability is 60% to 90%, while utilization is considered to range
from 40% to 80%. In normal mining production activity the drill machine operation
usually stays between these limits. The results obtained have been plotted as a column
chart in Figure 8-4.
Figure 8-4 Cost of drilling production $/m length by several machines with
different availability and utilization.
From Figure 8-4, it appears that the assumption of higher availability and utilization
(a0.9Xu0.8) provides costs closer to the actual obtained results. On the other hand
when the lower limits of availability and utilization are selected a significant change in
the cost of drilling production at each drillhole diameter is observed.
139
Availability and utilization are related to the efficiency of the drilling machines. Due to
the effect of the large drills on production any change in efficiency causes a drastic
change in the cost. Sensitivity analysis was performed by selecting 89 mm as the
smallest and 350 mm as the largest diameter drillholes for the fragmentation targets
adopted in this thesis (30cm and 80cm).
The results of the sensitivity analysis are summarized in Figures 8-5 and 8-6.
B- Sensitivity analysis of capital and operating cost of drill machine
The effect of capital cost of the drill machine on the total cost of drilling and blasting is
small compared to other costs. The results of the sensitivity analysis have been plotted
in Figure 8-5. Similarly the basic constituents of the operational cost of the drill were
examined. It was found that at a drillhole diameter of 89 mm a change in fuel cost of
50% results in an overall cost change of 1%, while at 350 mm drillhole diameter the
change is 4.5%. Similarly the maintenance cost at this diameter does not show
significant change. The results for 80% passing size of 80 cm are nearly the same; they
are shown in Figure 8-5, for ready reference.
140
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 operation cost of drill machines increases or decreases by 50%.
8.4. Sensitivity analysis for drilling and blasting cost by changing
design parameters
In the previous section the sensitivity analysis was carried out by changing the
component costs and machine efficiencies to examine the overall effect on the total cost
-8.0%
-6.0%
-4.0%
-2.0%
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
14.0%
16.0%
18.0%
20.0%
-50% -40% -30% -20% -10% 0% 10% 20% 30% 40% 50%
Pe
rch
tag
e c
ha
ng
e i
n t
ota
l co
st o
f d
rill
ing
an
d b
last
ing
Percentage change in drilling component cost d 350 mm
Drill. capital cost inc/dec. 50%, X80=30 cm Drill capital cost inc/dec by 50%, X80=80 cm
Operating cost inc/dec by 50%, X80=30 cm Operating cost inc/dec by 50%, X80=80 cm
X80=30 cm a0.6Xu0.45 X80=80 cm a0.6Xu0.45
141
of drilling and blasting. This section examines the effects of design parameters, such as
bench height and fragment size specification. Bench height affects uniformity and
therefore powder factor (drilling and explosives consumption), so its selection is of
critical importance. It is always suggested that there must be compatibility between
bench height and borehole diameter. Fragmentation size is also important since
blasting may be considered as an alternative to crushing effort.
8.4.1. Sensitivity analysis of drilling and blasting cost by changing
selected bench height
Practically, in the case of surface mining, the selection of bench height depends, in
addition to diameter, on the boom height of the loading and scaling equipment. In the
case of underground workings the stope height is determined by geotechnical studies.
The selection of bench height of 12 m was considered to be economical and practical
with all the drillhole sizes in the selected range from 75 to 350 mm. A bench height 50%
shorter than the 12m column is a drastic change and is considered non practical,
particularly for the larger sizes of drillholes. Collar lengths become large to avoid
flyrock and the distribution of explosive in the bench suffers. As a result, blasting, to
achieve satisfactory fragmentation, becomes highly uneconomical and usually
impractical; hence a design with short bench height is not adopted by blasting
engineers. The short bench height has been selected to examine the sensitivity of the
142
total cost of drilling blasting on bench height. The 50% increased size would be 18m
and is very suitable for the large size of drillhole diameters. In both cases of 80%
passing sizes of 30 and 80 cm, the change in the cost trends are similar. The results for
the larger (350mm) and smaller (89mm) diameter applications have been plotted in
Figures 8.6 and 8.7.
Figure 8-6 Sensitivity analysis when the bench height changes by 50% at a
drillhole diameter of 350 mm.
-20.0%
0.0%
20.0%
40.0%
60.0%
80.0%
100.0%
120.0%
140.0%
160.0%
180.0%
-50% -30% -10% 10% 30% 50%
Pe
rce
nta
ge
ch
an
ge
in
to
tal
cost
of
dri
llin
g a
nd
b
last
ing
Percentage change in value of component
X80=30cm, H=6m (dec.50%) d 350 mm X80=30cm, H=18m (inc.50%) d 350 mm
X80=80cm, H=6m (dec.50%) d 350 mm X80=15 cm d 350 mm
143
Figure 8-7 Sensitivity analysis when the bench height changes by 50% at a
drillhole diameter of 89mm.
A detailed presentation of the costs at various bench heights as a function of diameter is
given in Figure 8-8 and Appendix D Figure D-7.
-40.%
-20.%
0.%
20.%
40.%
60.%
80.%
100.%
120.%
140.%
-50% -30% -10% 10% 30% 50%
Pe
rce
nta
ge
ch
an
ge
in
to
tal
cost
of
dri
llin
g
an
d b
last
ing
Percentage change in value of component
X80=30cm, H=6m (dec.50%) d 89 mm X80=30cm, H=18m (inc.50%) d 89 mmX80=80cm, H=6m (dec.50%) d 89 mm X80=80cm, H=18m (inc.50%) d 89 mmX80=15 cm d 89 mm
144
Figure 8-8 Cost of blasting when height of bench enlarged from 12 to 18 m or
reduced to 6 m.
It can be observed that the shortest bench height has the highest cost. The change in
reduction in cost starting from 6m to 18m is exponential. This is evident from the
change of slope in the final sensitivity analysis graph (Appendix D FigureD-7). The
shorter height bench has very steep lines compared to the longer or increased height
benches and shows a drastic change in the total cost of drilling and blasting.
145
8.4.2. Sensitivity analysis of the effect of fragmentation specification on
the drilling and blasting cost
It was evident in the previous chapters that the cost of blasting to produce 80% passing
fragment size of 30 cm is two to two and a half times higher the cost to produce 80%
passing size of 80 cm. Obviously fragmentation specification has an impact on cost. This
is shown in Figure 8-9. It appears that in all cases, intermediate borehole diameters are
more cost effective. Apparently small diameters are not cost effective and they seem to
become worse as the fragment size is reduced. .
Figure 8-9 Drilling-blasting cost curves when 80% passing size reduced to 20,
15 or 10 cm.
146
This may appear strange as smaller diameters result in better charge distribution,
however at an increased cost. The total cost is actually the end result of the cost
contribution of all items required for blasting. As fragmentation specification becomes
finer and the diameter is decreased, explosives consumption, drilling costs and costs of
accessories are modified. These changes may not be in the same direction. Thus the
competition between cost increases and decreases may result in counter intuitive
results. This is why the present model, calculating all cost contributions, is useful.
The effect of rock hardness on the cost of blasting has been examined in Section 7.5.1. of
Chapter 7, choosing three values of A to examine the variation in the cost. The rock
factor A encapsulates the effect of geological and rock mechanics properties. Hard rock
having a rock factor equal to 13 showed very high cost per cubic meter of rock blasted,
the next lower cost was with a rock factor of 9 and the next lowest was soft rock having
a rock factor equal to 5. These results showed that the change in rock and mechanical
properties change the cost e.g., the higher the UCS value of rock results in a higher cost
of blasting and vice versa.
8.5. Final spider diagram and conclusion
From the previous analysis it can be suggested that, although there is uncertainty in the
data collected, price structures and market predictions, the model exhibits robust
behaviour. To examine the comparative sensitivity of the components of drilling
147
blasting and design parameters, a spider diagram was generated, combining all
components to obtain the one which exhibits the steepest curve. Two diameters have
been selected for discussion and the results are plotted in Figure 8.10, for the 350mm
diameter and Appendix D Figure D-7 for the 89mm diameter. From the graph, the most
important parameter is the bench height.
The rest of the components have a lower impact on cost as evident from the slopes in
the spider diagram. A careful study reveals a few interesting and important factors:
- When the price of explosive drops, large diameters gain a further advantage.
- The accessories cost is not a significant component in the case of large diameter
applications. This makes a switch to electronic detonators easy in large
diameters drillholes.
- Fragment size reduction causes an increase in cost with an exponential rise. The
elimination of a primary crusher is possible (see discussion in Chapter 4 Section
4.1.) but to eliminate a secondary crusher needs a very careful comparative
study of fragmentation by explosive or mechanical crushing.
- The bench height is the most important factor to optimize a blast design. If the
height can be controlled (technically within the reach of the equipment, geo-
technically and within mine plan specifications), then larger bench heights are
most cost effective.
148
Figure 8-10 Spider diagram for the sensitivity analysis at drillhole diameter
350 mm .
-50.0%
0.0%
50.0%
100.0%
150.0%
200.0%
-50% -30% -10% 10% 30% 50%
Pe
rce
nta
ge
ch
an
ge
in
to
tal
cost
of
dri
llin
g a
nd
bla
stin
g
Percentage change in cost omponent or design parameter
X80=30cm, H=6m (dec.50%) d 350 mm X80=30cm, H=18m (inc.50%) d 350 mm
X80=80cm, H=6m (dec.50%) d 350 mm X80=15 cm d 350 mm
Expl.inc/dec.50%, X80=30 cm d 350 Acc.inc/dec.50%, X80=30 cm d 350
Expl.inc/dec.50%, X80=80 cm d 350 Acc.inc/dec.50%, X80=80 cm d 350
X80=30 cm a0.6Xu0.45 d 350 mm X80=80 cm a0.6Xu0.45 d 350 mm
149
Chapter 9
Summary, Conclusions and Recommendations
9.1. Summary
The Kuz-Ram model has been used to calculate blast fragmentation and the effect of
blasthole diameter on fragmentation. The model was used to calculate the cost of drill
and blast operations once the fragmentation targets were specified. For the purpose of
calculating cost, the blasthole diameter was allowed to vary significantly from a small
value (75mm) to a large value (350mm).
The cost was divided into the cost of drilling, consisting of the capital and operational
cost of the drill machine, and the cost of blasting, consisting of the cost of the explosive
and accessories of the blast. The range of drillhole diameters from 75 to 350 mm is
large and cannot be drilled by one drilling machine. For this range of diameters, several
and different machines are needed. Every make and model of a machine is good for a
particular diameter and a small range of diameters close to it. In this study the change
of a drill machine was represented as a change in investment and operational cost.
It is also noticeable that, even for drilling a small range of drillhole diameters, for which
the machine was manufactured, a change of drill bit, string/pipe, drill hammer and in
some cases the size of compressor are required from one size of drillhole to another.
Similarly, mechanical characteristics in each machine are different. The pull down and
150
thrust on the bit is distinctive in various makes and models with different machine
utilization and mechanical availability for each drill machine. All these characteristics
taken together result in unequal penetration rates in each case, affecting the drilling
cost.
The drilling cost, expressed in terms of dollars per cubic meter of blasted rock, shows
an uneven trough-shaped curve, for the range of drillhole diameters used. On the other
hand, the blasting cost is high in small diameter applications and lower as diameter
increases, reflecting the use of smaller quantities of accessories. Due to the effect of the
diameter on the selection of stemming lengths, as diameter increases and subsequent
stemming lengths increase, the use of the borehole is less efficient. As a result both
drilling and blasting costs increase. Apparently an optimum diameter can be selected
that optimizes total cost and the current approach is a step in this direction.
A sensitivity study showed that the total cost of drilling and blasting is sensitive to the
bench height, reflecting the importance of having or selecting appropriate bench
heights. Furthermore, fragment size specification, explosive cost, and availability and
utilization of the drill machine affect the cost and the selection of the optimum
diameter. In the case of smaller diameters, the cost of blasting accessories is the most
important cost component.
151
9.2. Conclusions
To complete this study a mathematical model was formulated using the existing Kuz-
Ram engineering model to calculate the most suitable drilling and blasting design
parameters, and for producing a required 80% passing size of fragmented rock after
blasting using a given drillhole diameter size.
The derived mathematical model made it possible to calculate changes in the design
parameters, total quantity of rock to be fragmented after a blast, explosive required and
powder factor, when the drillhole diameter is changed keeping the required fragment
size the same.
The model acts as a tool to select an optimum diameter for the given fragment size and
drill machine.
To calculate cost, a costing model was prepared to calculate drilling and blasting costs
of the required rock fragmentation based on the blast design parameters provided by
the previous models.
All calculated blasting costs presented in this study have been used to compare the
blasting costs for the range of drillhole diameters from 75 to 350 mm. It appears that
the cost is driven by the blasting cost, which is much higher than the drilling cost.
Intermediate diameters of this range are the most economical, while large diameters
are not as cost efficient due to the poor distribution of the explosive charges in the blast,
152
which results in high explosive consumption. At a small diameter the explosive
consumption is lower but the cost of blasting accessories becomes higher.
9.3. Recommendations for further work
The 80% passing size is common as the requirement for run of mine fragmentation.
However, a diameter change affects the amount of fines produced. Fines are required or
discarded by a mine depending on the nature of processing and/or utilization. If fines
are considered to be detrimental to the operation, a specification for fines is necessary
and may be considered a cost. If production of fines is beneficial to increase throughput,
then fines may be considered as a benefit.
Once a certain cost is specified or benefit from association with fines produced by the
blast, the costing model developed here will be of assistance. However, since it is known
that the Rammler equation is not appropriate for the estimation of fines, it is prudent to
develop a cost model on the basis of a model using a more reliable distribution, i.e. the
Swebrec or the TCM model described in the text.
153
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162
Appendix A
Blasting Costs, Summary
List of Tables Page No Table A-1 Blasting cost per cubic meter of rock with different stemming length and explosives, and rock factor=7 (summary)
163
163
Table A - 1, Blasting cost per cubic meter of rock with different stemming length and explosives, and rock factor=7 (summary)
Emulsion Emulsion
Diameter C=25D C=30D C=B C=B C=25D C=30D C=B C=B
mm $/m3 $/m3 $/m3 $/m3 $/m3 $/m3 $/m3 $/m3
75 2.59 2.75 2.60 2.66 0.83 0.87 0.96 0.97
100 2.29 2.50 2.23 2.32 0.70 0.76 0.81 0.85
125 2.18 2.47 2.06 2.21 0.68 0.74 0.76 0.82
150 2.20 2.60 1.99 2.18 0.67 0.78 0.74 0.83
175 2.31 2.89 1.99 2.21 0.69 0.85 0.75 0.84
200 2.49 3.39 2.01 2.26 0.73 0.96 0.76 0.87
225 2.76 4.24 2.05 2.33 0.79 1.16 0.79 0.90
250 3.17 5.90 2.10 2.41 0.89 1.48 0.81 0.94
270 3.65 8.98 2.15 2.48 0.99 1.99 0.84 0.98
300 4.92 10.23 2.23 2.60 1.25 4.23 0.88 1.03
325 7.30 10.70 2.31 2.70 1.65 10.08 0.91 1.08
350 7.06 10.96 2.39 2.79 2.50 10.96 0.95 1.14
SUB=0.2B 80% Passing Size = 30cm 80% Passing Size = 80cm
ANFO ANFO
164
Appendix B
Cost calculations using Table 6-2 as costing model
List of Tables Page o
Table B-1 Atlas Copco - DM45 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 dirillhole diameter 172
Table B-6 Drilling cost estimate for top drive hydraulic rotary, Driltech D75k (track mounted)
174
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 capital 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
165
Table B-1 Atlas Copco - DM45 900 drilling cost estimate
--------Continued on the next page.
Dia inches 5..5 6.13 6.50 6.95 8.00 Dia mm 140 155 165 175 200
Rock Strength MPa 127 127 127 127 127 Bench Height m 12 12 12 12 12 Availability % 92% 92% 92% 92% 92% Utilization % 63% 63% 63% 63% 63% Gross Penetration Rate m/hr 67.07 69.82 62.80 54.88 41.46 Net Production Rate m/hr 39 40 36 32 24
Fuel Consumption US Gal/hr 27 27 27 27 27 Fuel Cost $/l 0.92 0.92 0.92 0.92 0.92 Fuel Cost per Hour $/hr 94.39 94.39 94.39 94.39 94.39 Fuel Cost per Meter $/m 2.43 2.33 2.59 2.97 3.93
Operation Costs Operator Cost per Hour $/hr 50.00 50.00 50.00 50.00 50.00 Helper Cost per Hour $/hr 0.00 0.00 0.00 0.00 0.00 Operator Cost per Meter $/m 1.29 1.24 1.37 1.57 2.08
Maintenance Costs Hourly Labour Cost $/hr 50.00 50.00 50.00 50.00 50.00 Parts Cost per Hour $/hr 60.00 60.00 60.00 60.00 60.00 Total Maintenance Cost Per Hour $/hr 64.00 64.00 64.00 64.00 64.00 Maintenance Cost per Meter $/m 1.65 1.58 1.76 2.01 2.66
Consumable Cost Estimated Bit Life m 2,622 2,713 2,439 2,147 1,622 Estimated Drill Pipe Life m 16,770 10,060 18,290 39,600 91,500 Number of Drill Pipe Used 2 2 2 2 2 Estimated Hammer Life m 12,200 12,200 12,200 12,200 12,200 Bit Cost $ 700.00 730.00 840.00 860.00 1,890.00 Drill Pipe Cost $ 1,200.00 1,300.00 1,300.00 1,300.00 1,300.00 Hammer Cost $ 6,500.00 6,500.00 6,500.00 6,500.00 6,500.00 Bit Cost per Meter $/m $0.27 $0.27 $0.34 $0.40 $1.17 Pipe Cost per Meter $/m $0.21 $0.39 $0.21 $0.10 $0.04 Hammer Cost per Meter $/m $0.53 $0.53 $0.53 $0.53 $0.53 Total Consumable Cost Per Meter $/m $1.01 $1.19 $1.09 $1.03 $1.74
Production Information
Fuel Cost
166
Atlas Copco - DM45 900 Drilling Cost Estimate Table B-1 continued
167
Table B-2 Atlas Copco - DM45 1070 drilling cost estimate
--------Continued on the next page.
Dia inches 5.50 6.13 6.50 6.95 8.00 Dia mm 140 155 165 175 200
Rock Strength MPa 127 127 127 127 127 Bench Height m 12 12 12 12 12 Availability % 92% 92% 92% 92% 92% Utilization % 63% 63% 63% 63% 63% Gross Penetration Rate m/hr 67.1 74.7 67.1 58.5 44.2 Net Production Rate m/hr 39 43 39 34 26
Fuel Consumption US Gal/hr 27 31 31 31 31 Fuel Cost $/l 0.92 0.92 0.92 0.92 0.92 Fuel Cost per Hour $/hr 94.39 108.38 108.38 108.38 108.38 Fuel Cost per Meter $/m 2.43 2.50 2.79 3.20 4.23
Operator Cost per Hour $/hr 50.00 50.00 50.00 50.00 50.00 Helper Cost per Hour $/hr 0.00 0.00 0.00 0.00 0.00 Operator Cost per meter $/m 1.29 1.16 1.29 1.47 1.95
Hourly Labour Cost $/hr 50.00 50.00 50.00 50.00 50.00 Parts Cost per Hour $/hr 70.00 70.00 70.00 70.00 70.00 Total Maintenance Cost Per Hour $/hr 74.00 74.00 74.00 74.00 74.00 Maintenance Cost per Meter $/m 1.90 1.71 1.90 2.18 2.89
Estimated Bit Life m 2620 2900 2440 2260 1720 Estimated Drill Pipe Life m 16760 7010 14170 28040 76200 Number of Drill Pipe Used 2 2 2 2 2 Estimated Hammer Life m 9140 9140 9140 9140 9140 Bit Cost $ 700 730 840 860 1890 Drill Pipe Cost $ 1200 1300 1300 1300 1300 Hammer Cost $ 6500 6500 6500 6500 6500 Bit Cost per meter $/m 0.27 0.25 0.34 0.38 1.10 Pipe Cost per meter $/m 0.21 0.56 0.28 0.14 0.05 Hammer Cost per meter $/m 0.71 0.71 0.71 0.71 0.71 Total Consumable Cost Per Meter $/m 1.19 1.52 1.33 1.23 1.86
Production Information
Fuel Cost
Operation Costs
Maintenance Costs
Consumable Cost
168
Atlas Copco - DM45 1070 Drilling Cost Estimate Table B-2 continued
$1.35 $1.21 $1.35 $1.54 $2.04
Fuel Cost per Meter $2.43 $2.50 $2.79 $3.20 $4.23
Operator Cost per Meter $1.29 $1.16 $1.29 $1.47 $1.95
Maintenance Cost per Meter $1.90 $1.71 $1.90 $2.18 $2.89
Consumable Cost Per Meter $1.19 $1.52 $1.33 $1.23 $1.86
Total Operating Costs per Meter $6.81 $6.89 $7.31 $8.08 $10.93
Total Owning Cost per Meter $1.35 $1.21 $1.35 $1.54 $2.04
Total Operating and Owning Costs per Meter $8.16 $8.10 $8.66 $9.62 $12.98
$16.58
$35.74
$52.32
$689,778.00
$25,000.00
$714,778.00
14.00
5.00
50.00
Hourly depreciation cost
Hourly owning cost
Owning Cost per meter
3,500.00
20,000.00
6.00Years to depreciate (rounded to next year)
Useful life of the machine Hrs
Suggested factory list price
Frieght duties, fees, etc, to land on site
Total delivered price
Hours per day
Hourly investment cost (taking I. I. & T. 0.14)
Summary of costs $/m
Owning Costs
Days per week
Weeks per year
Hours per year
169
Table B-3 CUBEX- ARIES-(ITH) drilling cost estimate (for u/g)
--------Continued on the next page.
Production Information Dia inches 3.9 4.9 5 7/8
Dia mm 100 125 150
Rock Strength MPa 176 176 176
Bench Height m 12 12 12
Availability 85% 85% 85%
Utilization 70% 70% 70%
Gross Penetration Rate m/min 0.30 0.30 0.35
Net Production Rate m/hr 11 11 12
Fuel CostEnergy Consumption kWh 94 112 149
Energy Cost $/kWh $0.097 $0.097 $0.097
Energy Cost per Hour $/hr $9.11 $10.85 $14.44
Energy Cost per Meter $/m $0.85 $1.01 $1.16
Operation CostsOperator Cost per Hour $/hr $50.00 $50.00 $50.00
Helper Cost per Hour $0.00 $0.00 $0.00
Operator Cost per Meter $/m $4.67 $4.67 $4.00
Maintenance CostsHourly Labour Cost $/hr $50.00 $50.00 $50.00
Parts (Repair)/ Hour $30.00 $30.00 $30.00
Parts (Maint.)/ Hour (20% Energy Cost) $1.82 $2.17 $2.89
Total Maintenance Cost Per Hour $39.32 $39.67 $40.39
Maintenance Cost per Meter $3.67 $3.70 $3.23
Consumable CostEstimated Bit Life m 550 550 550
Estimated Drill Pipe Life m 1,530 1,530 1,530
Number of Drill Pipe Used 7 7 7
Estimated Hammer Life m 5,490 5,490 5,490
Bit Cost $500.00 $500.00 $500.00
Drill Pipe Cost $350.00 $350.00 $350.00
Hammer Cost $3,000.00 $3,000.00 $3,000.00
Bit Cost per Meter $/m $0.91 $0.91 $0.91
Pipe Cost per Meter $/m $6.41 $6.41 $6.41
Hammer Cost per Meter $/m $0.55 $0.55 $0.55
Total Consumable Cost Per Meter $/m $7.86 $7.86 $7.86
Diameter inches
Diameter mm
Extrapolated Penetration with Diameters
Parts cost taken 20%
Adopted for thesis
170
CUBEX- ARIES-(ITH) Drilling Cost Estimate (for u/g) Table B-3 continues
Owning Costs
Suggested Factory List Price $800,000 $800,000 $800,000
Frieght Duties, Fees, Etc, to Land On Site $25,000 $25,000 $25,000
Total Delivered Price $825,000 $825,000 $825,000
Hours per Day 20 20 20
Days per Week 6 6 6
Weeks per Year 50 50 50
Hours per Year 6000 6000 6000
Useful Life of The Machine Hrs 20000 20000 20000
Years to Depreciate (Rounded to Next Year) 4 4 4
Hourly Investment Cost (Taking I. I. & T. 0.14) $12.13 $12.13 $12.13
Hourly Depreciation Cost $41.25 $41.25 $41.25
Hourly Owning Cost $53.38 $53.38 $53.38Owning Cost per Meter $4.98 $4.98 $4.27
Summary of costs $/m
Fuel Cost per Meter $0.85 $1.01 $1.16
Operator Cost per Meter $4.67 $4.67 $4.00
Maintenance Cost per Meter $3.67 $3.70 $3.23
Consumable Cost per Meter $7.86 $7.86 $7.86
Total Operating Costs $/m $17.05 $17.25 $16.25
Total Owning Cost per Meter $4.98 $4.98 $4.27
Total Operating and Owning Costs $22.04 $22.23 $20.52
For power point
171
Table B-4 CUBEX- ARIES-(ITH) drilling cost estimate (for u/g)
--------Continue on the next page.
Production Information Dia inches 3.9 4.9 5 7/8 Dia mm 100 125 150
Rock Strength MPa 176 176 176 Bench Height m 5 5 5 Availability 85% 85% 85% Utilization 70% 70% 70% Gross Penetration Rate m/min 0.30 0.30 0.35 Net Production Rate m/hr 11 11 12
Fuel Cost Energy Consumption KWh 94 112 149 Energy Cost $/kWh $0.097 $0.097 $0.097 Energy Cost per Hour $/hr $9.11 $10.85 $14.44 Energy Cost per Meter $/m $0.85 $1.01 $1.16
Operation Costs Operator Cost per Hour $/hr $50.00 $50.00 $50.00 Helper Cost per Hour $0.00 $0.00 $0.00 Operator Cost per Meter $/m $4.67 $4.67 $4.00
Maintenance Costs Hourly Labour Cost $/hr $50.00 $50.00 $50.00 Parts (Repair)/ Hour $30.00 $30.00 $30.00 Parts (Maint.)/ Hour (20% Energy Cost) $1.82 $2.17 $2.89 Total Maintenance Cost Per Hour $39.32 $39.67 $40.39 Maintenance Cost per Meter $3.67 $3.70 $3.23
Consumable Cost Estimated Bit Life m 550 550 550 Estimated Drill Pipe Life m 1,530 1,530 1,530 Number of Drill Pipe Used 3 3 3 Estimated Hammer Life m 5,490 5,490 5,490 Bit Cost $500.00 $500.00 $500.00 Drill Pipe Cost $350.00 $350.00 $350.00 Hammer Cost $3,000.00 $3,000.00 $3,000.00 Bit Cost per Meter $/m $0.91 $0.91 $0.91 Pipe Cost per Meter $/m $1.37 $1.37 $1.37 Hammer Cost per Meter $/m $0.55 $0.55 $0.55 Total Consumable Cost Per Meter $/m $2.83 $2.83 $2.83
172
CUBEX- ARIES-(ITH) Drilling Cost Estimate Table B-4 continues
173
Table B-5 Cost estimate to drill larger dirillhole diameter
DT75K DT90K BC51R P&H 120A Dia inches 9 7/8 10 5/8 12 1/4 13 3 3/4
Dia mm 251 270 311 350 Rock Strength MPa 118 121 110 124 Bench Height m 12 12 12 12 Availability % 82% 86% 92% 92% Utilization % 76% 76% 76% 76% Gross Penetration Rate m/min 0.80 0.80 0.90 0.85 Net Production Rate m/hr 30 31 38 36
Operating Cost per Hour US$/hr $105.00 $125.00 $145.00 $160.00 Operating Cost per Hour US$=1.2C$ CD$/hr $126.00 $150.00 $174.00 $192.00 per Meter $/m $4.21 $4.78 $4.61 $5.38
Estimated Bit Life m 1,100 1,200 3,500 5,200 Estimated Drill Pipe Life m 26,000 31,000 45,000 51,000 Number of Drill Pipe Used 2 2 2 2 Bit Cost $ 2,900.00 3,450.00 4,150.00 6,400.00 Drill Pipe Cost $ 9,000.00 13,000.00 16,000.00 19,500.00 Bit Cost per Meter $/m 2.64 2.88 1.19 1.23 Pipe Cost per Meter $/m 1.04 1.26 1.07 1.15 Total Consumable Cost Per Meter $/m 3.67 4.13 2.25 2.38
Hours per Day 21 21 21 21 Days per Year 351 351 351 351 Hourly Owning Costs in US $ 100.00 105.00 110.00 110.00
Hourly Owning Costs CD $ (US$*1.2) 120.00 126.00 132.00 132.00 Owning Cost per meter 4.01 4.02 3.50 3.70
Operation Cost per Meter $/m $4.21 $4.78 $4.61 $5.38 Consumable Cost Per Meter $/m $3.67 $4.13 $2.25 $2.38 Total Operating Costs $/ft $/m $7.89 $8.91 $6.86 $7.76 Total Owning Cost per Meter $/m $4.01 $4.02 $3.50 $3.70 Total Operating and Owning Costs $/m $11.90 $12.93 $10.36 $11.46
Operation Cost Fuel+Operator+Maintenance Costs
Consumable Cost
Production Information
Name of Drill machine
Owning Costs
Summary of costs $/m
174
Table B-6 Drilling cost estimate for top drive hydraulic rotary, Driltech D75K (track mounted)
--------Continue on the next page.
Production Information Dia mm 251 311 350 Rock Strength MPa 140 140 140 Bench Height m 12 12 12 Availability 75% 75% 75% Utilization 66% 66% 66% Gross Penetration Rate m/hr 45 25 21 Net Production Rate m/hr 22 12 10 Fuel Cost Fuel Cost per Hour $/hr $100.00 $100.00 $100.00 Fuel Cost per meter $/m $4.49 $8.08 $9.65 Operation Costs Operator Cost per Hour $/hr $50.00 $50.00 $50.00 Helper Cost per Hour $0.00 $0.00 $0.00 Operation Cost per Hour $/hr $50.00 $50.00 $50.00 Operation Cost per meter $/m $2.24 $4.04 $4.82 Maintenance Costs Hourly Labour Cost $/hr $50.00 $50.00 $50.00 Parts (Rapair)Cost ($100,000 in total) $/hr $5.00 $5.00 $5.00 Preventive maintenance cost $/hr $50.00 $50.00 $51.00 Total Maintenance Cost Per Hour $/hr $67.50 $67.50 $68.50 Maintenance Cost per meter $/m $3.03 $5.45 $6.61
Estimated Bit Life hr 4,000 4,000 4,000 Bit tooth life m 75 75 75 Estimated Drill Pipe Life hr 20,000 20,000 20,000 Number of Drill Pipe Used # 2 2 2 Bit Cost $ $750.00 $850.00 $1,000.00 Bit tooth Cost $ $64.00 $80.00 $112.00 Drill Pipe Cost (9m) $ $3,500.00 $3,500.00 $5,000.00 Bit Cost per hour $/hr $0.19 $0.21 $0.25 Bit tooth cost per hour $/hr $19.01 $13.20 $15.48 Pipe Cost per hour $/hr $0.53 $0.53 $0.75 Total Consumable Cost Per Hour $/hr $19.72 $13.94 $16.48 Total Consumable Cost Per meter $/m $0.89 $1.13 $1.59
Consumable Cost
175
Continued Table B-6 Drilling cost estimate Driltech D75K, from previous page
176
Table B-7 Hydraulic Tophammer, John Henry Rockdrill (mounted on excavator)
--------Continueon the next page.
Production Information Dia in 2.5 3.5 5.0
Dia mm 63.5 89 127
Rock Strength M Pa 24,500 24,500 24,500
Bench Height m 12 12 12
Availability 80% 80% 80%
Utilization 67% 67% 67%
Gross Penetration Rate m/min 3 2 1
Net Production Rate m/hr 96 64 32
Fuel CostFuel Cost per Hour $/hr $20.00 $20.00 $20.00
Fuel Cost per meter $/m $0.21 $0.31 $0.62
Operation CostsOperator Cost per Hour $/hr $50.00 $50.00 $50.00
Helper Cost per Hour $0.00 $0.00 $0.00
Operation Cost per Hour $/hr $50.00 $50.00 $50.00
Operation Cost per meter $/m $0.52 $0.78 $1.55
Maintenance CostsHourly Labour Cost $/hr $50.00 $50.00 $50.00
Parts (Rapair)Cost $/hr $50.00 $50.00 $50.00
Preventive maintenance cost $/hr $30.00 $30.00 $30.00
Total Maintenance Cost Per Hour $/hr $90.00 $90.00 $90.00
Maintenance Cost per meter $/m $0.93 $1.40 $2.80
Consumable CostEstimated Bit Life m 1,750 2,250 2,500
Coupling life m 2,000 2,000 2,000
Estimated Drill rod Life m 2,000 2,000 2,000
Shank life m 3,500 3,500 3,500
Hammer life m 2,400 2,400 2,400
Number of Drill rods Used # 3 3 4
Bit Cost $ $700.00 $700.00 $700.00
Coupling Cost $ $389.00 $389.00 $389.00
Estimated Drill rod Cost $ $320.00 $428.00 $479.00
Shank Cost $ $500.00 $500.00 $500.00
Hammer Cost $ $3,500.00 $3,500.00 $5,000.00
Bit Cost/ hr $/hr $0.40 $0.31 $0.28
Coupling Cost/ hr $/hr $0.19 $0.19 $0.19
Estimated Drill rod Cost/ hr $/hr $0.96 $1.28 $2.40
Shank Cost/ hr $/hr $0.14 $0.14 $0.14
Hammer Cost/hr $/hr $1.46 $1.46 $2.08
Total Consumable Cost Per Hour $/hr $3.16 $1.60 $2.23
Total Consumable Cost Per meter $/m $0.03 $0.02 $0.07
177
Continued Table B-7 Hydraulic Tophammer, John Henry Rockdrill from previous page
Owning Costs
Suggested factory list price
Frieght duties, fees, etc, to land on site
Total delivered price
Hours per day
Days per week
Weeks per year
Hours per year
Useful life of the machine Hrs
Years to depreciate (rounded to next year)
Hourly investment cost (taking I. I. & T. 0.14)
Hourly depreciation cost
Hourly owning cost
Owning Cost per meter $0.44 $0.66 $1.31Summary of costs $/m
Fuel Cost per Meter $0.21 $0.31 $0.62
Operator Cost per Meter $0.52 $0.78 $1.55
Maintenance Cost per Meter $0.93 $1.40 $2.80
Total Consumable Cost Per Meter $0.03 $0.02 $0.07
Total Operating Costs per meter $1.69 $2.51 $5.04
Owning Cost per meter $0.44 $0.66 $1.31
$2.13 $3.17 $6.36Total Owning and Operationg Cost per meter
275187
22626
297813
8
5
50
2,000
$42.29
10,000
5
$12.51
$29.78
178
Table B-8 Drilling cost/m of Hydraulic Tophammer, John Henry Rockdrill by updating cost
Production Information Dia in 2.5 3.5 5.0 2.5 3.5 5.0
Dia mm 63.5 89 127 63.5 89 127
Rock Strength M Pa 172 172 172 126 126 126
Bench Height m 12 12 12 12 12 12
Availability 80% 80% 80% 80% 80% 80%
Utilization 67% 67% 67% 67% 67% 67%
Gross Penetration Rate m/min 3 2 1 4.0 2.6 1.3
Net Production Rate m/hr 96 64 32 128 85 43
Fuel Cost per Meter $0.21 $0.31 $0.62 $0.16 $0.24 $0.47
Operator Cost per Meter $0.52 $0.78 $1.55 $0.39 $0.59 $1.18
Maintenance Cost per Meter $0.93 $1.40 $2.80 $0.71 $1.06 $2.12
Consumable Cost Per Meter $0.03 $0.02 $0.07 $0.02 $0.02 $0.05
Total Operating Costs per meter $1.69 $2.51 $5.04 $1.28 $1.90 $3.82
Total Owning Cost per meter $0.44 $0.66 $1.31 $0.33 $0.50 $0.99
$2.13 $3.17 $6.36 $1.61 $2.40 $4.81
Changed UCS
from 172 to 126 Mpa
Total Owning and Operationg Cost per meter
Costs from 1998 to 2005 Using Marshall & Swift quarter IV Cost
Index
Summary of costs $/m
179
Table B-9 Net production rates of various drill machine with different UCS, availability and utilization
Drill machines Diameter (mm) Given UCS, a, u UCS 126 Mpa a0.75Xu0.63 a0.92Xu0.76 63.5 96 128 113 168
89 64 85 75 112 127 32 43 38 56 140 39 39 32 47 155 40 40 33 49 165 36 36 30 44 175 32 32 26 38 200 24 24 20 29
D75K 251 30 29 20 29 D90K 270 31 29 21 31 BC 51 R 311 38 28 19 28 P&H 120A 350 36 34 23 34
Drill machines Diameter (mm) Given UCS, a, u UCS 126 Mpa a0.75Xu0.63 a0.92Xu0.76 63.5 $2.13 $1.61 $1.65 $1.06
89 $3.17 $2.40 $2.46 $1.59 127 $6.36 $4.81 $4.94 $3.19 140 $7.67 $7.67 $9.44 6.53 155 $7.58 $7.58 $9.29 6.49 165 $8.19 $8.19 $10.09 6.98 175 $9.16 $9.16 $11.33 7.77 200 $12.50 $12.50 $15.37 10.66
D75K 251 $11.90 $11.57 $15.74 $11.66 D90K 270 $12.93 $13.14 $16.98 $12.61 BC 51 R 311 $10.36 $12.51 $17.86 $12.63 P&H 120A 350 $11.46 $11.31 $16.02 $11.41
DM45 900
Cost per meter length by different machines ($/m)
John Henry Top Hammer
Rockdrill
DM45 900
John Henry Top Hammer
Rockdrill
180
Table B-10 Cost per meter cube of rock with different stemming length and explosive
X80=30cmDrll
machine UCS Dia (mm) $/m^3 UCS $/m^3
63.5 0.74 0.56
89 0.66 0.5
127 0.81 0.61
155 0.75 0.75
165 0.74 0.74
175 0.77 0.77
D75K 118 MPa 251 0.66 0.64
D90K 121 MPa 270 0.66 0.67
BC 51 R 110 MPa 311 0.46 0.55
P&H 120A 124 MPa 350 0.45 0.44126 MPa
Atlas
Copco
DM 45
126 MPa
Table B-10 Drilling Cost
126 MPa
126 MPa
John
Henry Top
Hammer
172 MPa
181
Appendix C
Price Quotations
List of Tables Page No 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
182
Table C-1 Orica Canada Inc.
ORICA CANADA INC. Price Quotation for Products and Services
Orica is pleased to offer the following updated prices for supply of explosives and related services to Queen’s University, Kingston On. Prices are effective from November 15, 2005 to March 31, 2006.
Packaged Explosives
Amex $27.99 / 25kg bag
Magnafrac Plus (HW) 50x400 $159.93 / 25kg case
Powerfrac 50x400 $244.59 / 25kg case
Bulk Explosives
Apex Gold 2171*** $115.01/ 100kg
Detonators
3.5m Electric ms #025 unit / box $4.76 / unit
4.5m Electric ms #1 to 20 25 unit / box $5.32 / unit
5m Handidet 25/50090 unit / case $5.21 / unit
6m Connectadet 17ms & 42ms $5.42 / unit
Excel Lead in Line – Bulk Shock Tube – 2 x 610m** $394.32 / case
6m I-kon (Electronic) $31.30 / unit
(Note -To use I-kon detonators a trained I-kon Blaster is required) *Technical Datasheets for the above products are available upon request* **Special Order – (see page 5: Terms and Conditions, item 6) ***Minimum order quantity of 3,000 kg’s
Delivery and Service Charges
Test Site – Oaks Flats 1 to 20 case 21 to 270 case
$250.00 / trip $300.00 / trip
All other deliveries 1 to 20 cs. 21 to 350 cs.
$ 1.10 / km return $ 1.30 / km return
Bulk Product Delivery $ 1.30 / km
Bulk Product on site, greater than 10,000 kg’s $50.00 / hr / truck
Bulk Product on site, 5,000 to 9,999 kg’s $75.00 / hr / truck
Bulk Product on site, 3,000 to 4,999 kg’s $100.00 / hr / truck
Bulk Product less than 3,000 kg’s Unavailable
Labour on Site (includes delivery vehicle) $ 50.00 / hour / man
I-kon Blaster $125 / hour, starting at Orica site
ORICA CANADA INC. Price Quotation for Products and Services, Table-6 continued
183
Table C-2 EIT Canada Inc.
184
Table C-3 Average retail prices for diesel in 2005
185
Table C- 4 Canadian hydro
186
Table C- 5 Marshal & Swift Equipment Cost Index
187
Appendix D
Graph charts and figures
List of Tables Page No
Figure D-1 Drilling net production of Tophammer at various drillhole diameters
188
Figure D-2 Drilling net production of D75K one machine at various drillhole diameters in limestone
188
Figure D-3 Drilling Net production of different machine at various 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
188
Figure D-1 Drilling Net production of Tophammer at various drillhole diameters
Figure D-2 Drilling Net production of D75K one machine at various drillhole diameters
in limestone.
25
50
75
100
125
50 75 100 125
Pen
etr
ati
on
m/h
r
Drillhole Diameter in mm, John Henry Tophammer Hydraualic Rockdrill
Penetration in Barre Granite UCS 174 MPa
Penetration in Limestone UCS 126 MPa (Calculated)
10
15
20
25
30
250 275 300 325 350
Pe
ne
tra
tio
n m
/h
r
Drillhole Diameter in mm
Drilling Penetration (Limestone UCS 140 MPa)
Drilling Penetration (Limestone UCS 126 MPa) Extrapolated
189
Figure D-3 Drilling Net production of different machine at various drillhole diameters in
limestone
Figure D-4 Drilling Net production of Atlas Copco Drill Machine DM 45 with different
capacity compressors.
20
25
30
35
40
251 270 311 350
126MPa 126MPa 126MPa 126MPa
118 MPa 121 MPa 110 MPa 124 MPa
D75K D90K BC 51 R P&H 120A
Dri
llin
g p
en
etr
ati
on
m/
hr
Diameter in mm, UCS in MPa, and name of drill machines
Penetration in varied UCS rocks Penetration in calculated UCS 126MPa
20
25
30
35
40
45
150 175 200
Ne
t p
rod
uct
ion
m/
hr
Diameter in mm
DM 45 1070 DM 45 900
190
Figure D-5 Drilling cost of production/m in underground mining by CUBEX-Aries
191
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).
0.5
1.0
1.5
2.0
50 100 150 200 250 300 350
Co
st i
n $
/m
3
Diameter in mm
X80=80 cm BASE CASE Expl.inc.50%, X80=80 cm Expl.dec.50%, X80=80 cm Acc.inc.50%, X80=80 cm Acc.dec.50%, X80=80 cm Expl+Acc.inc.50%, X80=80 cm Expl+Acc.dec.50%, X80=80 cm
192
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).
-50.0%
0.0%
50.0%
100.0%
150.0%
200.0%
-50% -30% -10% 10% 30% 50%
Pe
rce
nta
ge
ch
an
ge
in
to
tal
cost
of
dri
llin
g a
nd
bla
stin
g
Percentage change in cost component or design parameter
X80=30cm, H=6m (dec.50%) d 89 mm X80=30cm, H=18m (inc.50%) d 89 mm
X80=80cm, H=6m (dec.50%) d 89 mm X80=80cm, H=18m (inc.50%) d 89 mm
X80=15 cm d 89 mm Expl.inc/dec.50%, X80=30 cm d 89
Acc.inc/dec.50%, X80=30 cm d 89 Expl.inc/dec.50%, X80=80 cm d 89
Acc.inc/dec.50%, X80=80 cm d 89 X80=30 cm a0.6Xu0.45 d 89 mm
X80=30 cm a0.93Xu0.86 d 89 mm X80=80 cm a0.6Xu0.45 d 89 mm
X80=80 cm a0.93Xu0.86 d 89 mm
