Rajpot Muhammad a 200903 MScEng

7/29/2019 Rajpot Muhammad a 200903 MScEng

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The Effect of Fragmentation Specification onBlasting Cost

by

Muhammad Arshad Rajpot

A thesis submitted to the Department of Mining Engineering in conformitywith 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 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

Queens 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

Gr ap h ch art s an d fi gu re s _____________________________________________________________ 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 todrillhole 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 byvarious 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 X 80=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 oraccessories 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 byupdating 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 size80k

Ammonium Nitrate with fuel oil (explosive) ANFO/Anfo

Availability a

Bench heightbH m

Bulk modulus K Pa

Burden B m

Charge lengthcl

Charge length above gradecbl

Charge mass Q kg

DepreciationdC

Depth/length of blasthole/drillholel

d m

Diameter of blasthole d m or mm

Drillhole inclinationid cm or m

Drilling deviationdD m

Elastic modulus E Pa

Explosive densitye kg/m

3

Mean fragment size50k


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Owning and operating costOO

Particle size x cm

Penetration ratedV m/min

Powder factor q kg/m3

Rock factor A

Shear modulus G Pa

Spacing S m

Spacing to burden ration bm

Stemming lengthsl m

Subgrade drilling length SUB m

Total drilling costtdC

Total quantity of explosive Q kg

Total volume of rock 0V

Trinitrotoluene (explosive) TNT

Uniaxial compressive strengthcU

Uniformity coefficient or index n

Utilization u

Velocity of detonation VOD

Weight strength of explosive related to AnfoANFOE


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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.


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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


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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. Bonds 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


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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 ofDrill to Mill fragmentation flow sheet


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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 modelThis 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 fragmentationThe 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 requirementsThe 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 certainfragmentation

A costing model must be designed to calculate the cost of drilling and blasting once

fragmentation targets are provided.


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1.2.5.Effect of diameter on costFinally 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.


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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.


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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


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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 rockA 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.


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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 factorAn attempt to quantify the effect of rock parameters on fragmentation was made by

Cunningham (1987), who used Lillys (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

Cunninghams publication (Cunningham, 1987).

2.3.Controllable factors

For the purposes of blast design, the controllable parameters are classified in the

following groups:


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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)


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2.3.1.Height of benchUsually the working specifications of loading equipment determine the height of the

bench. The bench height limits the size of the charge diameter and the burden. (Ash

1968), states that when the bench height to burden ratio is large, it is easy to displace

and deform rock, especially at the bench centre. The optimum ratio ( BHb / ) is larger

than 3. If BHb / = 1, the fragments will be large, with overbreak/backbreak around

holes and toe problems. With BHb / = 2, these problems are attenuated and are

completely eliminated when BHb / >3.

The condition BHb / >3, is usually found in quarries and coal strip mining operations.

In metal mining the bench height is conditioned by the reach of the loading machine

and the dilution of the mineral as well.

When bH is small, any variation in the burden B or spacing S has a great influence on

the blasting results. When bH increases, with B kept constant, spacing can increase to

maximum value without affecting fragmentation. If the bench height is very large, there

can be problems of blasthole deviation, which will not only affect rock fragmentation

but will also increase risk of generating strong vibrations, flyrock, and overbreak

because the drilling pattern and subsequently the explosives consumption will not

remain constant in the different levels of the blasthole.


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2.3.2.Blasthole inclinationAccording 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.


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(v) Problems in charging the explosive, especially in blastholes with

water. (Jimeno et al., 1995)

2.3.3.StemmingIf 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.


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(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.SubdrillingIf 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.


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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 spacingThe 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.


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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 patternsIn 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


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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 deviationAssociated 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


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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 companys 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)]


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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 boreholesDue 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 boreholesThe costs of drilling, priming and initiation are high.

Charging and stemming of drillholes, and connecting them in a blasting circuit is time

consuming.


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2.4.3.Advantages associated with larger diameter boreholesLarge 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 diameterIf 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


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optimization of blasting and costing of fragmentation require quantifying these

parameters.


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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:


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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 ofthe quantity of explosive per blasthole, eQ and the relative to

ANFO weight strength of explosives, ANFOE and the powder factor, q = Q/Vo. Kuznetsovs

equation is typically written as:

cx


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------------------------- Equation 3-4

This is the most useful format, especially when absolute weight strengths are not given

by manufacturers. (Clark, 1987)

Kuznetsovs 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 RosinRammler equation with an

empirically calculated uniformity index. Several forms of this uniformity index can be

found in the literature suggesting the difficulty in encapsulating the effect of all blasting

parameters in the blast by a single constant. The following parameters are related to

muckpile uniformity.

(i) Distribution of explosive in the blast (burden, spacing to burden ratio,

borehole diameter, collar, subgrade, bench height)

(ii) Firing accuracy of detonators used

(iii) Timing of detonators used

30

19

6

1

8.0 115)(

ANFO

eav

E

QqAx


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(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


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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)

41(206.0 ssR

n ----------------------------- 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.


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3.3.Kuz-Ram model

If one uses Kunetsovs 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


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the fines, or on the basis of the Swebrec function (Ouchterlony, 2005), which is a new

function describing fragmented rock.


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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.


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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 fragmentationTo 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.


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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)


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3.4.2.Swebrec functionAnother 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)


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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.


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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 Mackenzies (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


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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 Lafarges Exshaw

cement operation. This study was aimed at replacing the 1372 mm (54-inch) primary

gyratory crusher. Exshaws 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


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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.


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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 Kuznetsovs 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

QQ

VAx


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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:

ddHlbc

308 ----------------------Equation 4-4

Substituting cl in Kuznetsovs 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

Ifstemming 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


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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 ( BHb ) .

(Cunningham, 1983)

The value of drilling deviation tD varies from 1% to 5% of bH and can be modified

according to the requirements. It is defined according to the type of machine in use, the

location and the training of the crew. In the present case, the deviation is taken as 2%

plus one drillhole diameter of bH . Let us rewrite the equation in the following format:

----------------------- Equation 4-11

where IF is equal to:

b

cbb

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


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Combining the two equations 4-1 and 4-5, the following equation is obtained:

801

6.1 *4306.0* xBF nb ------------------------------------ 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.


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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 burdenStemming 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


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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 a

Rajpot Muhammad a 200903 MScEng

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