Timing Effects on Fragmentation by Blasting
by
Omid Omidi
A thesis submitted to the Department of Mining
In conformity with the requirements for
the degree of Masters of Applied Science
Queen’s University
Kingston, Ontario, Canada
(September, 2015)
Copyright © Omid Omidi, 2015
ii
Abstract
Rock fragmentation has always been an indicator for the efficiency of blasts in mines. Several
suggestions have been made by blast operators and specialists to improve the rock fracturing
mechanisms in order to obtain smaller fragments. The order of blast hole initiations together with the
timing interval between holes has been observed to affect the blast results. In this study, a series of
small-scale tests, simulating bench blasting have been made to establish the effect of delays in the
sequence of blast initiation. The blasts were performed in high strength grout blocks, which were cast to
provide a similar to rock condition excluding the possible structural weaknesses of the rock material.
Homogeneity of the grout also helped to create a proper testing environment, ensuring the
comparability of the blast results from different specimens. The grout used in the experiments had a
strength of 50 MPa, density of 2.2 g/m3, and P-wave velocity of 4000 m/s. Unwanted reflections of blast
generated stress waves were eliminated by confining the blocks using a yoke. The tests were made with
a range of inter hole delays from 0 to 2000 µs. The fragments achieved after each blast were collected
and screened to analyze fragmentation from different delays. In general, coarse fragmentation was
obtained from short delays while back break was minimal. Relatively longer delays resulted in better
fragmentation with more damage to the back of the blocks. The work continued to investigate the effect
of blast gas on fragmentation by conducting similar tests in blocks but by placing copper pipes in the
blast holes to control the gas propagation through the blast zone. Although gas penetration did not
seem to be fully inhibited by the copper pipes, the new design yielded different results in the delay
range which had produced optimum fragmentation. The current study is considered to be a start point
for more investigations in the field of efficient blasting with regard to the requirements for the mine to
mill process.
iii
Acknowledgements
This research was accomplished with the financial support of the Centre for Excellence in Mining
Innovation (CEMI).
I would like to sincerely thank my supervisor, Dr. P.D. Katsabanis, for the guidance he has provided over
the past few years. I am very grateful for his kindness, encouraging comments, and patience throughout
the course of this project.
I would also like to thank Mr. Perry Ross, Mr. Oscar Rielo, and Mr. Larry Steele for assisting me with my
experiments and sharing their valuable views during this research.
Finally, I would like to express my gratitude to my parents for understanding and extraordinary sacrifices
made this thesis possible.
iv
Table of Contents
Abstract ............................................................................................................................................ ii
Acknowledgements ......................................................................................................................... iii
List of Figures .................................................................................................................................. vi
List of Tables ................................................................................................................................... vi
List of Abbreviations ........................................................................................................................ x
Chapter 1 Introduction .................................................................................................................... 1
Chapter 2 Literature Review ............................................................................................................ 4
Chapter 3 Material Properties ....................................................................................................... 36
3.1. .............................................................................................................................................. 36
3.2. Physical and Mechanical Properties of the Selected Material ............................................. 37
3.2.1. UCS ............................................................................................................................. 37
3.2.2. P-wave Velocity .......................................................................................................... 38
3.3. Determination of Shock wave Pressure and Duration ........................................................ 42
Chapter 4 Fragmentation Test Set-up............................................................................................ 49
4.1. Testing Blocks ....................................................................................................................... 49
4.2. Charging, Initiation, and Test Environment ......................................................................... 51
4.3. Analysis of the Blasted Material ........................................................................................... 55
Chapter 5 Fragmentation Results from Powder Factor of 1.2 kg/m3 ............................................ 57
5.1. Experimental Work ............................................................................................................... 57
5.2. Initial Results ........................................................................................................................ 58
Chapter 6 Fragmentation Results from Powder Factor of 2.4 kg/m3 ............................................ 62
6.1. Experimental Work ............................................................................................................... 62
6.2. Results .................................................................................................................................. 63
Chapter 7 Fragmentation Results from Copper-lined Blast-holes ................................................. 67
7.1. Effect of Gas on Fragmentation ........................................................................................... 67
7.2. Experimental Work ............................................................................................................... 69
7.3. Results .................................................................................................................................. 69
Chapter 8 Fragmentation Results from a Medium-scale Granite Bench ....................................... 73
8.1. Experimental Work ............................................................................................................... 73
8.2. Results .................................................................................................................................. 74
v
Chapter 9 Analysis of Results and Discussion ................................................................................ 77
9.1. Blasting and Fragmentation ................................................................................................. 77
9.2. New Approach toward Optimization of Fragmentation ...................................................... 79
9.2.1. Effect of Timing on Fragmentation ............................................................................ 79
9.2.2 Uniformity and Delay .................................................................................................. 83
9.2.3. Effect of Stress Wave on Creating Fragmentation ..................................................... 87
9.2.4. Effect of Gas Pressure on Fragmentation of x10, x50, and x80 Under Lined
and Unlined Conditions .............................................................................................. 90
9.2.5. Fragmentation Distribution Curves Under Lined and Unlined Conditions ................ 91
9.3. Back-break ............................................................................................................................ 94
9.4. Analysis of the Granite Bench Experiments ......................................................................... 96
Chapter 10 Conclusion ................................................................................................................. 100
References ................................................................................................................................... 103
Appendices ................................................................................................................................... 113
Appendix A: P-wave Velocities ..................................................................................................... 113
Appendix B: Shock wave Records ................................................................................................ 117
Appendix C: Fragmentation Distribution Curves, Powder Factor = 1.2 kg/m3 ............................ 130
Appendix D: Fragmentation Distribution Curves, Powder Factor = 2.4 kg/m3 ............................ 142
Appendix E: Fragmentation Distribution Curves, Copper lined Blast holes ................................ 182
Appendix F: Fragmentation Distribution Curves, Granite Bench ................................................. 198
vi
List of Figures
Figure 1.1 Structure of the Thesis .................................................................................................... 3
Figure 2.1 Effect of Degree of Fragmentation on Different Operating Costs and Overall
Mining Costs (after Mackenzie, 1967)…………………………………………………………………………………………6
Figure 2.2 Overall Mining Costs for Various Powder Factors (Eloranta, 1997)……………………………..7
Figure 2.3 Effect of Delay on Fragmentation – Reduced Scale Tests (USBM Data) ....................... 15
Figure 2.4 Effect of Delay on Fragmentation – Full Scale Tests (USBM) ........................................ 16
Figure 2.5 Effect of Delay on Fragmentation (Katsabanis and Liu, 1996) ...................................... 16
Figure 2.6 Lagrange Diagram Representing the One Dimensional Propagation of
Longitudinal (P) Wave, Shear (S) Wave, and a Crack (C), Rossmanith (2002) .............. 17
Figure 2.7 Representation of a One Dimensional Stress wave /Pulse in the Space and
Time Domain, Rossmanith (2002)................................................................................. 18
Figure 2.8 Representation of Fronts and Ends of a P-wave (PF, PE) and an S-wave (SF, SE)
for a Short Pulse; After Rossmanith (2002)…………..………………………………………………….19
Figure 2.9 Lagrange Diagram of the Interaction Patterns of the Waves from Two Simultaneously-Initiated Blastholes; After Rossmanith (2002)…………….......................20 Figure 2.10 Sequence of Events from Two Detonating Blast Holes (McKinstry, 2004)……………….23 Figure 2.11 Desired Case for Overlap of Tensile (Negative) Pulses (Modified from
Vanbrabant and Espinosa, Johansson, 2011) ............................................................................... 24
Figure 2.12 Average Fragmentation as a Function of Delay in Granodiorite Blocks
(Katsabanis et al. 2006) ............................................................................................... 26
Figure 2.13 Average Fragmentation from Short Delay Experiments (Katsabanis et al. 2006) ...... 26
Figure 2.14 Fragmentation Data from Johansson (2012) and Petropoulos (2013) ....................... 29
Figure 2.15 Geometry of the Two Blast Hole Model ..................................................................... 30
Figure 2.16 Non Reflecting Boundaries and Free Surfaces ............................................................ 31
Figure 2.17 Vertical Cuts used in the Results Presentation ........................................................... 32
Figure 2.18 The Overall Crack Pattern Resulted from Finite Element Simulation (Delay = 0 ms) . 33
Figure 3.1 Cylindrical Samples Before and After Strength Testing ................................................ 37
Figure 3.2 A General Representation of the Stress waves Travelling through Rock
(Richards, 2009) ............................................................................................................................. 39
vii
Figure 3.3 Experimental Set-up used to Measure P-wave Velocity ............................................... 40
Figure 3.4 Picking the Arrival Time of P-wave ............................................................................... 41
Figure 3.5 A Plan View of the Grout Block Specimens Used for P-wave
Velocity Measurements ................................................................................................................. 41
Figure 3.6 Locations of the Carbon Resistor Gauges ..................................................................... 43
Figure 3.7 Typical Record for a Pressure-Time Pulse (Ghorbani, 1997) ........................................ 45
Figure 3.8 Pressure as a Function of Distance ............................................................................... 46
Figure 3.9 Pulse Duration as a Function of Distance ..................................................................... 47
Figure 3.10 Lagrangian Diagram to Show the Interaction of Stress Waves ................................... 48
Figure 4.1 Dimensions of the Grout Blocks (main design) ............................................................. 50
Figure 4.2 Dimensions of the Yoke ................................................................................................ 50
Figure 4.3 Lagrangian Diagram to Show Interaction of a Shock Wave with an Arrested
Crack from a Previously Detonated Hole ....................................................................... 52
Figure 4.4 The Components of the Electronic Initiation System ................................................... 54
Figure 4.5 Set-up for a Block Placed in the Yoke ........................................................................... 55
Figure 5.1 Block #1 after Successive Blasts .................................................................................... 59
Figure 5.2 An Example of Two Distribution Curves ....................................................................... 60
Figure 6.1 Distribution Curves from the 10 µs Test ....................................................................... 64
Figure 6.2 Distribution Curves from 40 µs Test ............................................................................. 64
Figure 6.3 Average Fragment Size as a Function of Delay ............................................................. 65
Figure 6.4 Effect of Powder Factor on Fragmentation .................................................................. 66
Figure 7.1 A Schematic of Crushed Zone, Fracture Zone, and Fragment Formation Zone ............ 68
Figure 7.2 Average Fragmentation, Lined and Unlined Conditions ............................................... 70
Figure 8.1 The Granite Bench......................................................................................................... 73
Figure 8.2 Results from Granite Bench .......................................................................................... 75
Figure 8.3 Fragmentation Districbution Curves from Bench Blasting ........................................... 75
Figure 8.4 Granite Bench, Before and After Blasts ........................................................................ 76
Fig 9.1 The Variation of Different Fragment Sizes with Time ........................................................ 82
Figure 9.2 Fines Below 1 mm ......................................................................................................... 83
Figure 9.3 Slope at x50 .................................................................................................................... 84
Figure 9.4 Slope through x80 and x20 ................................................................................................. 85
Figure 9.5 Slope through x60 and x40 ................................................................................................. 85
viii
Figure 9.6 Rosin-Rammler Uniformity Index vs. Delay .................................................................. 86
Figure 9.7 Uniformity Expressed as x60/x10 vs. Delay ..................................................................... 87
Figure 9.8 Interaction of Tensile Waves ........................................................................................ 88
Figure 9.9 Lagrangian Diagrams to Create Zones of Maximum Tension
(Katsabanis et al., 2014) ................................................................................................................. 89
Figure 9.10 Effect of Copper lining on x10, x50, and x80 ................................................................... 91
Figure 9.11 Effect of Copper lining on Distribution Curves, Delay = 100 µs .................................. 92
Figure 9.12 Effect of Copper lining on Distribution Curves, Delay = 200 µs .................................. 92
Figure 9.13 Effect of Copper lining on Distribution Curves, Delay = 700 µs .................................. 93
Figure 9.14 Effect of Copper lining on Distribution Curves, Delay = 800 µs .................................. 93
Figure 9.15 Block Condition After a Simultaneous Initiation Shot................................................. 94
Figure 9.16 Block Condition After 40 µs and 1000 µs Shots .......................................................... 95
Figure 9.17 Block Condition After 200 µs Shots, Lined and Unlined ............................................. 96
Figure 9.18 Two Frames from Granite Bench 6 ms and 30 ms After Initiation, Delay= 0 ms ........ 97
Figure 9.19 Two Frames from Granite Bench 0 ms and 8 ms After Initiation, Delay= 500 ms ...... 98
Figure 9.20 Six Frames from Granite Bench, Delay = 2 ms ............................................................ 99
ix
List of Tables
Table 2.1 Description of Simulations ............................................................................................. 32
Table 3.1 Some Physical and Mechanical Properties of the Grout Samples ................................. 38
Table 3.2 Pressure Results ............................................................................................................. 45
Table 5.1 Initial Blasts .................................................................................................................... 57
Table 5.2 Swebrec Parameters from First Block ............................................................................ 58
Table 5.3 Swebrec Parameters from Second Block ....................................................................... 60
Table 6.1 Swebrec Results for Main Design Tests.......................................................................... 63
Table 7.1 Swebrec Results for Copper-lined Blasts ........................................................................ 70
Table 8.1 Swebrec Parameters for the Granite Bench .................................................................. 74
x
List of Abbreviations, Symbols, and Definitions
A…………………………………………………….Rock mass factor
B…………………………………………………….Burden (m)
b…………………………………………………….Undulation parameter
Cp …………………………………………………..P-wave velocity (m/s)
PETN………………………………………………Pentaerythritol tetranitrate
n…………………………………………………….Rosin-Rammler uniformity index
Rosin-Rammler……………………………..Particle size distribution function (Rosin et al.)
Swebrec function ………………………….Curve fitting function (after Ouchterlony)
UCS ……………………………………………….Uniaxial Compressive Strength (kg/m3)
VOD ………………………………………………Velocity of detonation (m/s)
x50 …………………………………………………Average fragment size (mm)
x80 …………………………………………………80% fragment size (mm)
xmax ……………………………………………….Maximum fragment size (mm)
1
Chapter 1
Introduction
Any mining operation consists of different processes from blasting, loading, hauling, and mineral
recovery. Although these phases seem to be independent from each other, in a comprehensive
mine design plan they all relate to each other from the cost reduction viewpoint. Since any
phase provides the next with the required feed, outcome of each unit directly affects the
subsequent operation as well as the overall efficiency. Blasting, for example, is designed to
reduce the size of material to a degree that it can be transported to the mineral processing
plant. Several studies show that any attempt to modify blasting results, mainly fragmentation,
could benefit the overall mining operation in terms of haulage requirements and reducing
energy consumption in the mill.
Researchers at the Julius Kruttschnitt Mineral Research Centre (JKMRC) have identified the
following as the parameters influencing the blast fragmentation (Scott, 1996).
- Strength parameters: the static compressive, tensile, and shear strength of the rock
mass
- Mechanical parameters: Young’s Modulus and Poisson’s ratio of the rock
- Structural parameters: intactness of the rock, natural discontinuities including joint
spacing and joint orientation
2
- Absorption parameters: the ability of the rock to absorb or transmit the energy liberated
by the blast which influences the type of explosives required as well as its quantity, and
firing sequence of the charges and timing.
Monitoring several surface blasts in mines and small-scale tests, Singh et al., (2012) presented a
number of factors to design blasts in order to optimize fragmentation. These factors included
the spacing to burden ratio, burden to hole diameter ratio, explosives quantity, stemming
length, the ratio between the total weight of explosives and the amount of rock broken (powder
factor), and the ratio of bench height and burden (stiffness). Fragmentation improvement
recommendations made based on these factors are typically limited to using smaller burdens in
the blast design, higher quantity of explosives, shorter stemming (in hard rocks with fewer
discontinuities), and choosing larger powder factors. To implement these recommendations,
one could assume that higher amounts of explosives would be required implying larger powder
factors. Although large powder factors could deliver better fragmentation results, they could be
associated with some disadvantages such as increased blasting costs, excessive and undesired
damage to the surrounding rock, higher vibration levels, larger risk of fly-rock, etc. Research on
another effective factor on fragmentation, timing, has been conducted since the 1980’s.
Distinguished researchers have published their results in many papers. Examples of some
studies can be found in the literature (Stagg, M.S. and Nutting, M.J., 1987; Otterness et al., 1991,
Katsabanis et al., 2006). A large variety of suggestions on the application of delay timing have
been made; however, many unanswered questions have remained regarding the selection of
appropriate timing in order to maximize fragmentation while negative outcomes of blasts (fly-
rock, vibration, etc) are controlled.
3
With the uncertainties over finding a proper timing to increase fragmentation, this study
presents a series of results from experimental tests using high strength grout blocks which were
blasted using a vast range of delays from 0 to 2000 µs. The results from small-scale blocks are
also compared with a few data points obtained from a medium-scale granite bench. The findings
of this investigation are presented to address some of the main issues regarding blast
fragmentation such as: the role of short and long delays in producing fragmentation, the effect
of fracturing mechanisms (gas and stress waves) in different ranges of delay, the influence of
timing on uniformity of the fragments, and the role of the delay on the formation of back break.
The structure of the thesis is shown in Figure 1.1.
Figure 1.1 Structure of the Thesis
• Chapter 1: Introduction
• Chapter 2: Literature Review
• Chapter 3: Material Properties
• Chapter 4: Fragmentation Test Set-up
• Chapter 5: Fragmentation Results from Powder Factor of 1.2 kg/m3
• Chapter 6: Fragmentation Results from Powder Factor of 2.4 kg/m3
• Chapter 7: Fragmentaion Results from Copper-lined Blast-holes
• Chapter 8: Fragmentation Results from a Medium-scale Granite Bench
• Chapter 9: Analysis of Results and Discussion
• Chapter 10: Conclusion
4
Chapter 2
Literature Review
Historically, in the mining industry, blasts are designed to break in-situ rock and prepare it for
excavation and transport. In the cycle of mining, blast fragmentation is usually considered good
enough when it is in agreement with instructions for proper digging, loading, transportation,
and also mill requirements. These requirements are based on the capacity of the loading and
transportation equipment and the maximum fragment size that can be fed to the rock crushers.
Each division in mining is responsible for enhancing its productivity in order to lower the costs
associated with their operation. In some cases, this has led to lack of a comprehensive view on
the overall mine cost and profit planning. As an example, the mine processing plant may work
with close to optimal efficiency when it is provided with a certain size and quality of the raw
material as its feed, while other parts such as the mining department may decide to keep their
costs down by lowering the powder factor or using traditional blast initiation systems. This
attitude is typically due to the fairly high price of newer initiation systems while their
advantages in increasing fragmentation are ignored. This decision will unwantedly affect the
subsequent processes that need to be done on the broken rock. This is one common issue with
many of the mines around the world. In recent years, progressive mines have begun considering
plant productivity as one of the major requirements for cost and profit estimations. Due to this,
a revision on the use of low powder factor and traditional blast initiation systems has been put
in place to ensure that proper feed is provided to the mill (Rorke, 2012).
The Mine-to-Mill concept was introduced to the mining industry first by the Julius Kruttschnitt
Mineral Research Centre (JKMRC) in the recent years (Grundstorm et.al, 2001). The goal of such
5
studies is to find the parameters involved in reducing the overall mining costs, while the
increased mill throughput is accounted for. A long list of parameters has been investigated in
the Mine-to-Mill (M2M) studies. Among all, blasting and fragmentation play an important role
as the initial phase of comminution. In this literature review, some of the attempts made to
show the importance of a good fragmentation in the entire mining operation will be discussed,
as well as some of the findings on optimization of fragmentation using theories of shockwaves
and gas pressurization.
2.1. Blasting, First Phase of Rock Comminution
Blasting is the first phase in fragmenting rock. Fragmentation is usually defined as breaking rock
into suitable sizes in accordance with mill requirements such as feed size and grindability.
Influence of blasting on the fragmented rock size and the rock resistance to crushing has been
observed in several mine plants. Examples of such cases will be reviewed with focus on
reductions in overall mining costs.
Benefits of proper fragmentation are energy savings due to decreasing feed size of the primary
crusher and productivity improvements in the subsequent breakage operations. The largest
potential for energy savings in the mill occurs as the amount of undersize that bypasses the
crushing stage increases (Ouchterlony, 2003). Also, some mine-to-mill studies suggest that
remarkable grinding improvements can be achieved through optimization of fragmentation
(Kim, 2010). The latter improvement depends on the micro-fractures that can survive in the
primary crushing stage; however, such fractures emerge as they are influential in weakening the
rock when it is processed in the grinding phase. Since mechanical crushing and grinding are
expensive operations at a mine plant, any possible energy saving and cost reduction is
6
recommended in those operations. This goal seems to be reachable through good
fragmentation despite of higher costs associated with blasting (Katsabanis, et al., 2004).
Another saving in the costs is achieved in operations such as excavation of the broken rock,
loading, and hauling. The chance of increasing mill throughput and subsequent higher revenues
should also be considered as a result of improved fragmentation (Ouchterlony, 2003).
In 1967, Mackenzie proposed simple graphs to show the importance of improved blasting and
fragmentation in the overall mining costs (Mackenzie, 1967). His model was based on the effect
of variation of the mean fragment size on different operating costs. Figure 2.1 illustrates how
costs associated with loading, hauling, drilling, and crushing are decreasing with increasing
fragmentation while drilling and blasting costs are increasing in this model.
Figure 2.1 Effect of Degree of Fragmentation on Different Operating Costs and Overall Mining Costs (after
Mackenzie, 1967)
7
Although Mackenzie’s model was a primitive attempt to explain the reduction of costs by
improving fragmentation, one could assume that by combining all the costs from individual
mining units an optimum range of fragmentation size can be achieved with minimum
fragmentation cost, and thus minimum overall mining costs. Mackenzie’s studies concentrated
on the direct mining costs. In order to further quantify processing costs with optimization of
fragmentation, Eloranta (1997) conducted a research project with focus on cost information
from the Minntac iron mine in Minnesota. Optimization of fragmentation was achieved through
increase in powder factor in the blasts. As shown in Figure 2.2, processing costs have a declining
trend steeper than the rise in blasting costs as the powder factor is increased. This means that
total costs of mining can be reduced using improvements in fragmentation. Clearly, as shown by
Mackenzie, a range of optimum fragmentation and cost reduction can be found in Eloranta’s
work.
Figure 2.2 Overall Mining Costs for Various Powder Factors (Eloranta, 1997)
8
Many other people investigated the effect of blast optimization on downstream processes.
Grundstrom et al. (2001) made an attempt to find the possibility of increasing mill throughput
using high powder factors in the blasting operation at the Porgera Gold Mine. This research
which was conducted with cooperation of the Porgera joint venture and Dyno Nobel, showed a
25% increase in mill throughput from 673 tph (standard blast design with powder factor of 0.24
kg/t) to 840 tph (modified blast design with powder factor of 0.31 kg/t).
In the attempts mentioned so far, benefits of improved fragmentation were studied from
increase in powder factor viewpoint. Powder factor is calculated based on the amount of
explosive required to break the rock and the pattern of the blast holes including burden,
spacing, and the length of the blast holes.
Another parameter used to design a blast is the sequence of firing of the blast holes. This
sequence is normally achieved through pre-determined timing delays between charges.
Initiating explosives are designed to safely activate larger explosive charges according to the
pre-determined sequence. Initiating explosives can generally be classified into electric and non-
electric types. In electric systems, a device that can generate or store electrical energy transmits
the energy to the initiating explosives via a circuit of insulated conductors. Blast sequences can
be controlled by means of electric timing systems but delay timing is usually achieved through
pyrotechnic delay elements incorporated inside detonators. Non-electric initiating systems use
reactive chemicals to store and transmit energy by controlled burning, detonation, or shock
waves (ICI1, 1997). Detonators are compact devices that are designed to safely initiate and
control the performance of larger explosive charges. In recent years, electronic detonators have
1 Imperial Chemical Industries
9
been widely used in mines to initiate the charges in accordance with their defined timing
sequence at high precisions.
The idea of using electronic detonators was raised in 1973 at the Kentucky Blasters Conference
(Miller et al., 2007); however, the new technology was first used in Australia in the mid 1980’s
(Miller et al., 2007). Paul Worsey presented a paper on the commercial use of electronic
initiation at the ISEE1 meeting in 1983 (Cunningham, 2005). Subsequently, in 1987, the ICI Group
introduced a pre-programmed electronic detonator system with 64 delays available. The system
was used to determine the potential of precise timing as well as the ability to identify changes in
blast results under controlled timing condition (Beattie et al., 1989). In 1990, Expert Explosives
(ExEx) and Altech Technologies independently began to develop programmable electronic
detonators for the mining industry2. Finally, as the demand for this technology grew in many
countries including South Africa and Australia, Orica Mining Services began manufacturing the
electronic detonators in large-scale productions in 1999 (Miller et al., 2007).
During 1980’s and 1990’s, mine managers did not welcome the use of electronic detonators.
One reason was that the cost ratio of these detonators to traditional blasting caps was initially
10 to 1 in favor of the old systems (McKinstry, 2004). This attitude gradually changed as the
advantages of the new initiation system were understood in price reduction of the overall
mining activities and safety enhancements in mines around the world. Miller et al., (2007)
presented examples of his observations at quarries in the north, south, and west of Australia
1 International Society of Explosives Engineers 2 History of Programmable Electronic Detonators, available on DetNet Website: http://www.detnet.com/index.php?option=com_content&view=article&id=19&Itemid=63
10
regarding the use of electronic detonators. He concluded that the following was achieved as a
result of using electronic detonators:
- 23% increase in loading and hauling rates
- 18% increase in crusher throughput
- An overall 13% decrease in operational costs despite the increased blasting costs
In 2001, an evaluation was performed at the Betze Post open pit mine in Nevada aiming to
assess the potential benefits of precise timing delays to the downstream processes (McKinstry
et al., 2004). Precision in delays between holes was obtained by using electronic detonators.
Two types of tests were made to study the effect of the electronic delayed blasts on
fragmentation, excavator productivity, and mill throughput. In the first test, the pyrotechnic
blast method was used whereas in the second test electronic detonators initiated the charges.
In both tests 40 blast holes were drilled in the same geology and ore type. Results from the two
tests showed an 11% increase in excavator productivity in the electronic trial which fully
compensated for the additional costs of the new initiation system. Estimates showed a 6.5%
increase in excavator productivity would offset these additional costs. Mill throughput increased
from 152 to 167 St/hr while the plant operating work index experienced a 1 kWh/St decrease,
which meant less energy was required to process the same amount of rock. Image analysis of
the muck pile from both tests also showed a 44% improvement in fragmentation in the
electronic blast. Additional evaluations were also conducted in 2002 (McKinstry et al., 2004)
with focus on mill throughput benefits using electronic detonators in blasting. The outcome of
the new evaluations also confirmed the results from the initial evaluation. The studies
altogether convinced the management of the mine to adopt the new technology, electronic
detonators, as their initiation system. In 2003, the net value added to mill throughput by the
new technology at the Betze Post open pit was in excess of 2 million dollars.
11
2.2. Evaluation of Fragmentation
Fragmentation of a blast is usually evaluated through analysis of the fragmentation distribution
curves. Such curves are constructed using sieved broken fragments. The broken fragments form
a wide range of fragment sizes from fine to coarse which is graphed to obtain some
characteristics of the blasted material. Average fragment size (x50), eighty percent fragment size
(x80), and maximum fragment size (xmax) are some the typical indicators of fragmentation. These
indictors can also be obtained using image analysis of a blast muck pile. Image analysis is usually
recommended for large scale tests in mines or quarries due to high costs and difficulties
associated with muck pile screening in such cases.
Many attempts have been made to describe blast-induced fragmentation by introducing
prediction models. Among these, the Kuz-Ram model (Kuznetsov-Rammler) is considered to be a
popular tool for such predictions.
The Kuz-Ram model (Cunningham, 1987) is based on expression of fragmentation by
Kuznetsov’s average fragment size model (1973) and the Rosin-Ramler distribution (Rosin et al,
1933). In Kuznetsov’s model, the average fragment size is calculated through some parameters
that define the rock and blast characteristics (Equation 2.1).
𝑥50 = 𝐴. 𝑄1
6. (115
𝑆𝐴𝑁𝐹𝑂)19/30𝑞0.8 (Equation 2.1)
where,
A = rock mass factor
Q = mass of explosive per blast hole (kg)
SANFO = weight strength of explosive relative to ANFO
12
q = powder factor (kg/m3)
The Rosin-Ramler distribution utilizes the calculated average fragment size and uniformity index
(n) to predict fragmentation at any fragment size (Equation 2.2).
𝑃𝑅𝑅(𝑥) = 1 − 2−(
𝑥
𝑥50)𝑛
(Equation 2.2)
Cunningham (1987) presented an equation to calculate uniformity index based on geometry of
the blast (Equation 2.3).
𝑛 = (2.2 − 14𝐵
𝑑) (1 −
𝑊
𝐵) (1 +
𝑆
𝐵−1
2) (
𝐿
𝐻) (Equation 2.3)
Where,
B = burden
d = diameter of boreholes
W = standard deviation of drilling precision
S = spacing
L = length of borehole
H = height of bench
Ouchterlony (2005) presented a prediction model for fragmentation. His model uses the
Swebrec function (Equation 2.4), to describe the fragmentation distribution together with the
Kuznetsov’s model (Equation 2.1) to achieve the average fragment size. The Swebrec function
takes into account three major parameters including x50, xmax, and the undulation parameter (b).
13
𝑃(𝑥) =1
[1+[ln(
𝑥𝑚𝑎𝑥𝑥
)
ln(𝑥𝑚𝑎𝑥
𝑥50)]
𝑏
]
(Equation 2.4)
The Swebrec fragmentation function was introduced as a result of work conducted by the
Swedish Blasting Research Centre. The undulation parameter is a function of the average and
maximum fragment sizes (Equation 2.5)
𝑏~0.5. 𝑥500.25. ln [
𝑥𝑚𝑎𝑥
𝑥50] (Equation 2.5)
It can be derived from the proposed fragmentation prediction models that these models are
sensitive to the powder factor, geometry of the blast, the mass of explosive per borehole, and
the type of rock and explosives used. In none of the models, timing intervals between boreholes
and distribution of blast-generated energy are considered despite their role in creating
fragmentation (Chung and Katsabanis, 2001).
Chung et al. (2000) examined some of the experimental fragmentation data published by the
USBM. They applied non-linear regression analysis to the USBM data and suggested that the
Kuznetsov’s equation can be re-written as (Equation 2.6).
𝑥50 = 𝐴. 𝑄−1.176𝐵2.271(𝑆𝐵𝑅)1.165𝐻1.165𝑡−0.231 (Equation 2.6)
14
where, SBR is the spacing to burden ratio. Since very little effect of timing was observed from
the experimental data especially at short delays, it was decided to eliminate this factor from the
equation. Thus, the final average fragment size predictor was presented as (Equation 2.7).
𝑥50 = 𝐴. 𝑄−1.193𝐵2.461(𝑆𝐵𝑅)1.254𝐻1.266 (Equation 2.7)
As shown in the presented equations, none of the models considered timing as a contributing
factor to fragmentation. A simple explanation for this could be the large scatter existing in the
experimental results even when accurate timings were used. Since this made it difficult to draw
a certain conclusion on the effect of delay, researchers preferred to ignore this factor.
2.3. History of Attempts on Improving Fragmentation
Early attempts on improving fragmentation were made by Stagg and Nutting (1987) in 18 cm (45
inch) high limestone benches. Their work is known as “Reduced-scale Tests”. Stagg and Rholl
(1987) also conducted a series of “Full-scale Tests” in 6.6 m (22 ft) high benches of limestone. In
continuation of these attempts, Otterness et al., (1991) made similar reduced scale experiments
in dolomite benches. Results of the mentioned tests were based on muck pile screening of the
blasted materials. These attempts are together known as the “USBM Fragmentation Data”.
Katsabanis et al. (2014) examined the USBM data through normalization of the previously
mentioned Kuznetsov’s equation in order to investigate the effect of timing on the average
passing size. Since powder factor and the amount of charge per hole are known in Kuznetsov’s
equation, the ratio 𝑥50
𝑞−0.8𝑄1/6 can be considered as the normalized 50% passing size which
15
represents the effect of lithology and timing. Figure 2.3 displays the variation of the normalized
passing size with delay per meter of burden derived from the reduced scale tests.
Figure 2.3 Effect of Delay on Fragmentation – Reduced Scale Tests (Katsabanis et al., 2014)
A general trend line with an optimum delay can be obtained from the reduced scale tests. Full
scale tests, on the other hand, did not yield any tangible change in fragmentation as a result of
using different delays in the experiments. Figure 2.4 shows the results of full scale tests in which
no optimum delay was found. Neither of the tests showed any improvement in fragmentation at
short delays (<3 ms) between blast holes.
0
2
4
6
8
10
12
14
16
0 20 40 60 80 100 120 140
No
rmal
ized
x5
0
Delay time (ms/m of burden)
reducedscale
16
Figure 2.4 Effect of Delay on Fragmentation – Full Scale Tests Katsabanis et al., 2014)
Katsabanis and Liu (1996) tried to establish the effect of delay in a 2m bench of granite. High
speed filming of the blasts was used to analyze fragmentation. Despite inaccuracies of this
technique, they managed to develop the X50-Delay curve which answered some important
questions about the role of delay in the outcome of the blasts. Results of their work are shown
in Figure 2.5. At 0 ms delay the coarsest fragmentation was observed, while the optimum delay
appeared to be close to 8 ms.
Figure 2.5 Effect of Delay on Fragmentation (Katsabanis and Liu, 1996)
0
0.5
1
1.5
2
2.5
3
3.5
4
0 10 20 30 40 50 60
No
rmal
ize
d x
50
Delay time (ms/m of burden)
FullScaleTests
0
20
40
60
80
100
0 2 4 6 8 10 12 14
Ave
rage
siz
e (c
m)
Delay time (ms/m of burden)
17
Rossmanith (2003) tried to explain the mechanical fracturing process of the rock material using
the theory of stress waves and Lagrange diagrams. According to this theory, two types of stress
waves arise from detonation of an explosive charge: P-wave (longitudinal or primary wave) and
S-wave (shear or secondary wave). The waves are assumed to be planar and propagate in a one
dimensional fashion and a Lagrange diagram can be used to describe the waves along with a
crack generated by detonation. The three dimensional propagation of the waves is ignored in
this model (Figure 2.6).
Figure 2.6 Lagrange Diagram Representing the One Dimensional Propagation of Longitudinal (P) Wave,
Shear (S) Wave, and a Crack (C), Rossmanith (2002)
The tangents of the associated lines are the inverses of the speeds of the waves and the crack.
Any stress wave of pulse type with finite length and finite duration consists of a leading
(compressive) and a tailing (tensile) part. The leading compressive part is characterized by the
index “+”, whereas the tailing part is shown by the index “-”. Hustrulid (1999) states that the
positive pressure of the produced wave rapidly falls into negative values, which implies a change
from compression to tension. A stress pulse can usually be described in two ways: in space or in
18
time. This is shown in Figure 2.7 (Rossmanith, 2002), where ɅW and τW are the wave length and
wave duration, respectively.
Figure 2.7 Representation of a One Dimensional Stress wave /Pulse in the Space and Time Domain,
Rossmanith (2002)
For a single hole detonation, each wave is represented by its front and end as shown in Figure
2.8. Within the close vicinity of the blast hole the two waves overlap; however, they separate as
the waves travel further away from the hole with different speeds. Rossmanith considers
parallel lines for the front and the end of the P and S pulses, but he states that in reality the two
lines slightly diverge as they travel along the positive x-axis.
19
Figure 2.8 Representation of Fronts and Ends of a P-wave (PF, PE) and an S-wave (SF, SE) for a Short Pulse;
After Rossmanith (2002).
As explained by Rossmanith and shown in Figure 2.9, several types of stress wave interaction
can be identified for two adjacent blast holes separated by the spacing s. These interactions
include the following categories.
- PP interaction of the leading compressive parts of the P-waves
- PP interaction of the tailing tensile parts of the P-waves
- SS interaction of the S-waves
- and a range of mixed wave interactions, such as the overlap of the P-wave from blast
hole #1 and the S-wave from blast hole #2.
20
Figure 2.9 Lagrange Diagram of the Interaction Patterns of the Waves from Two Simultaneously-Initiated
Blastholes; After Rossmanith (2002).
Location and size of the interaction zones depend on the spacing distance between the blast
holes, the duration of the pulses, and the delay between the two charges. Longer stress waves
provide wider areas of stress wave overlap and increase the chance of superimposed
interactions. On the other hand, if the second blast hole is delayed the regime of stress wave
interaction becomes closer to the delayed blast hole. Rossmanith (2002) claimed that enhanced
fracturing can occur in the areas between blast holes where maximum interaction of stress
waves is obtained. Stress waves are known to propagate at large velocities; therefore, short
delay times are preferred to create zones of interactions between blast holes.
Since the tensile strength of rock is much lower than its compressive strength, Rossmanith’s
theory focuses on possible interaction and superposition of tensile tailings of stress waves. If the
delay between blast holes is longer that the time required for the P-wave to travel the spacing
21
distance, PP interaction is eliminated. In the same manner, if the delay is chosen shorter than
the P-wave arrival time at the second blast hole, PP interactions (compressional and tensional)
are achieved; thus, improved fragmentation is expected. This type of analysis supports the idea
of short delay and precise firings using electronic detonators in order to achieve better
fragmentation results.
Rossmanith (2002) also examined other types of interactions between stress waves and running
cracks. According to this model, cracks are created and driven by stress waves; however, when
the wave outdistances the crack, the initial crack comes to arrest. Further assistance from
another stress wave is required to re-initiate the first crack. The model suggests that there are
four possible interactions between stress waves and cracks as follows.
- P-wave interacts with a running crack
- Arrested crack interacts with P-wave and is re-initiated
- Re-initiated crack interacts with S-wave, and
- Re-arrested crack interacts with S-wave
As a result of above, one can assume that the inter hole delay, if chosen properly, would be a
good means to assist the stopped crack to re-initiate. For this purpose, the second hole should
be programmed to fire in a way that its P-wave arrives at the arrested crack at the moment the
crack stops and not prior to it.
McKinstry et al., (2004) conducted a drill-to-mill study to evaluate the potential benefits of
electronic detonators and precise timing at the Betz Post open pit gold mine. A part of this study
focused on maximizing fragmentation in a full-scale rock bench using proper delay timing
22
between blast holes. Among 8 drilled holes in a row of blast holes, 2 of them were selected to
measure P-wave arrival at the free face and the neighboring blast hole as well as the time
between the firings of the holes and the face displacement. The holes were 22 cm in diameter,
14 meter deep, and altogether contained 335 kg of explosive. According to the published study,
high speed cameras were used to define the time of the rock mass movement in order to
measure the face displacement velocity. Fragmentation was also evaluated using high standard
video cameras and image analysis. Piezoelectric accelerometers were placed in front of the blast
holes to record P-wave arrival and initial movement time of the rock mass. The P-wave readings
were later used to determine the allowable time to promote inner row wave collisions. Figure
2.10 shows the sequence of the post-blast events within the 36 ms of the first hole initiation.
The P-wave from the first blast hole was recorded to reach its free face at 3.7 ms with the
velocity of 1994 m/s, while it arrived at the next hole face at 5.56 ms with the velocity of 1935
m/s. The analysis showed an average P-wave velocity of 1981 m/s, suggesting the P-wave arrival
at the neighboring hole to be around 3.5 ms. The accelerometer data showed that the face
began to move at 11.7 ms; however, no visible face movement was observed by the video
cameras within 18 ms of initiation of the first hole. Since the second blast hole was set to
initiate with the delay of 25 ms from the first hole, no P-wave interaction between the two holes
occurred in the experiment. The video cameras also captured the displacement of the second
hole face 11 ms after its initiation implying that the key events took place in a timeframe of 36
ms. Based on the sequence of the events in the test and the analysis obtained from the
captured images, McKinstry recommended that using an inter-hole delay of 3 ms fragmentation
would be optimum with programmable electronic detonators. The reason for this delay
selection is not clear given the observations on the movement of the free face.
23
Figure 2.10 Sequence of Events from Two Detonating Blast Holes (McKinstry et al., 2004)
24
In continuation of Rossmanith’s work (2002), Vanbrabant and Espinosa (2006) made a series of
full-scale tests to determine proper delay time between blast holes. Unlike Rossmanith’s work,
delays were chosen to create a time window for negative tails of P-waves to overlap in this
study. The principle of overlapping is shown in Figure 2.11. In this approach delays are longer
than the time required for the P-wave to travel the spacing distance thus eliminating the
superposition of waves between blast holes. The desired superposition of tensile waves takes
place beyond the second blast hole in this model. In order to achieve the desired negative pulse
superposition, a few key parameters should be take into account as follows:
Figure 2.11 Desired Case for Overlap of Tensile (Negative) Pulses (Modified from Vanbrabant and
Espinosa, 2006, Johansson, 2011)
TDesired=Td + T1 – T0
25
where
Td = shock wave traveling time between the first hole and the neighboring hole.
T1 = duration of the first half wave (compressive) at the neighboring blast hole (at distance D =
spacing).
T0 = duration of the first half wave at the first hole when it detonates (at distance D = 0)
The idea of negative pulse superposition was tested by Vanbrabant and Espinosa (2006).
Fragmentation achieved in their experiments was evaulated by the use of image analysis and it
was claimed that a decrease of 45% in the average particle size was observed through their
approach. Electronic blasting was recommended as a precise and reliable tool to enhance
blasting results. However, no information on the actual delays was reported by them to provide
a comparison between electronic and non electronic fragmentation results.
Katsabanis et al (2006) made another effort to explain fragmentation results of blast holes with
a range of delays between 0 to 4000 μs, in a smaller scale. Delays between 0 to 100 μs were
achieved by different lengths of detonating cord between holes while longer delays were
generated using a sequential blasting machine and seismic detonators. Granodiorite blocks with
dimensions of 92 cm× 36 cm × 21 cm were chosen in the new study. Multiple rows of 11 mm
diameter blast holes were drilled in each block. The holes were in an equilateral triangular
pattern with the burden and spacing of 8.8 and 10.2 cm, respectively. The powder factor used in
the tests was constant to investigate the effect of timing. Eight tests were made with delays
under 1000 μs. In this range, as shown in Figure 2.12, instantaneous initiation had the coarsest
fragmentation whereas longer delays led to better results. The short delays, if examined closely,
show a horizontal line with little change in x50 in the range of 0 to 1.1 ms/m of burden (Figure
26
2.13). The 1000 μs experiment, which corresponds to an actual delay of 11 ms/m of burden
seems to have produced very close fragmentation to the 100 μs (1.1 ms/m) test. Unfortunately,
it was impossible to generate a delay between 100 μs and 1000 μs, since delays were achieved
by a sequential blasting machine, which had a resolution of 1 ms. Observing the results at
longer delays, it appears that there was no drastic change of fragmentation between the
experiments conducted at 22 and 45 ms/m delays.
Figure 2.12 Average Fragmentation as a Function of Delay in Granodiorite Blocks (Katsabanis et al. 2006)
Figure 2.13 Average Fragmentation from Short Delay Experiments (Katsabanis et al. 2006)
0
20
40
60
80
100
120
0 5 10 15 20 25 30 35 40 45 50
Ave
rage
par
ticl
e s
ize
(m
m)
Delay time (ms/m of burden)
0
20
40
60
80
100
120
0 0.2 0.4 0.6 0.8 1 1.2Ave
rage
Fra
gme
nta
tio
n (
mm
)
Delay (ms/m of burden)
27
Examining the results, Katsabanis concluded that delays between 0.11 to 11 ms/m of burden
would result in improved fragmentation. Based on the fact that at long delays (above 22 ms)
fragmentation becomes coarse, time delay does not seem to be effective on fragmentation after
a certain point. This could be due to no transmission of energy from the detonating charges to
the earlier detonated holes as cracks are fully open. This type of blasting was very inefficient due
to lack of stemming and decoupled blast holes. In addition, the blasted blocks had six free faces
which led to reflection of the blast generated stress waves. This could further complicate the
analysis of results. As explained by Blair (2009), in experiments such as this, the outgoing
compressive wave from each hole will have six secondary reflected tensile wave stress, one off
each face. Any reflection of the waves would either promote fragmentation or be transformed
into kinetic energy of fragments. The location of each hole relative to the free faces determines
the time interval between the primary and the secondary (reflected) waves. Blair (2006) also
believed that in this particular case, this time interval could lie in the range of 15 to 225 µs (0.17
to 2.5 ms/m). Katsabanis’ results clearly contradict this claim for the delays up to 100 µs.
However, since there is no experimental data available between 100 and 225 µs, no firm
conclusion can be made regarding the time interval suggested by Blair. If Blair’s assumption
about the time span of 100 to 225 µs is true, the fracturing mechanism and the resulting
fragmentation also involve a series of events such as the effect of reflected waves in addition to
the action of the primary waves interacting within the blast hole initiation delays. Since in full-
scale tests the rock mass is typically a continuous medium with no reflecting waves, generalizing
the results from small-scale tests to larger scales should be done with caution. Also, due to the
role of the reflected waves, drawing any definite conclusion regarding optimum delays may not
be of enough validity.
28
Johansson (2011) conducted a series of small-scale tests using confined samples to eliminate
surface reflections. The set-up of the tests included 15 magnetic mortar blocks with dimensions
of 650×205×300 mm. Magnetite powder, cement, quartz sand, and water were mixed to create
the blocks. The synthetic blocks had similar properties to the magnetite ore body extracted from
the Kiruna Mine in north Sweden. Two rows of blast holes, row 1 and 2, were drilled with five
holes in each row to examine the effect of delay on blasting products. In order to avoid
unwanted reflection of stress waves from free faces, the blocks were confined in a U shape
yoke. This confinement also helped to create situations similar to the Sub Level Caving method
(SLC) in underground mines. The spacing and burden were 110 and 70 mm, respectively. The
yoke was made from high strength concrete. The distance between the yoke and the placed
blocks was filled with a fine-grained expanding grout with similar density to the yoke to prevent
impedance mismatch. The first row of blast holes in each block was fired with a pre-determined
inter-hole delay while the same delay was used in the second row of holes to investigate
fragmentation in intact and pre-damaged blocks. A variety of delays between 0 to 146 µs were
chosen to examine different possibilities of shock wave interactions. Petropoulos et al., (2013)
completed Johansson’s work by conducting two more tests using the same set up and with a
longer delay (290 μs). The results of the two experiments are displayed in Figure 2.14.
29
Figure 2.14 Fragmentation Data from Johansson et al., (2012) and Petropoulos et al., (2013)
The two works proved that the use of simultaneous initiation would not improve fragmentation.
Results of the first row showed a large scatter in the delay interval 0<Δt<86 µs. This suggests
that no trend can be assumed for row 1, thus making it impossible to identify any minimum x50,
optimum fragmentation, in this range. The longest delay however, 146 µs, resulted in the best
fragmentation among the tested delays. In row 2, a remarkably finer fragmentation with less
scatter was obtained as opposed to the first row in all shots. A general tendency toward
improved fragmentation was observed with increasing delay time over the interval 0<Δt<146 µs.
The data published by Petropoulos extended this range to 290 µs. No more experiments were
made beyond this point to reach a possible optimum fragmentation. The improvement of
fragmentation in the second row was attributed to the accumulation of damage from the
previous shot in the same block. The influence of the first row also appeared in minimizing the
dust and boulders behaviour associated with blast products of row 1. By increasing the delay to
290 μs, Petropoulos observed better fragmentation in both rows. He claimed that no further
0
10
20
30
40
50
60
70
80
0 50 100 150 200 250 300 350
Ave
rage
par
ticl
e s
ize
(m
m)
Delay time (μs)
Row 1 - Johansson
Row 2 - Johansson
Row 1 - Petropoulos
Row 2 - Petropoulos
30
crack growth and consequently enhanced fragmentation can be achieved as each hole acts
independently at longer delays without influencing the neighboring blast holes. These two
studies created serious doubts on the role of stress wave interactions in generating
fragmentation and the recommendations made by Rossmanith (2002) on the use of short
delays. Nevertheless, the scatter in the experiments on intact blocks does not provide a clear
picture on the effect of delay on fragmentation. In addition, this investigation seems to be
incomplete since no definite conclusion can be drawn regarding the existence of an optimum
delay in either intact or pre-damaged material.
Schill et.al (2012) carried out an investigation to examine Rossmanith’s idea of improving
fragmentation by the use of 3D Finite Element simulations. The LS-DYNA1 computer code was
chosen to simulate fragmentation. In this work, a 2 blast hole model was designed to resemble
the Aitik Open Pit Mine in Sweden (Figure 2.15). The blast model was assumed to be an infinite
continuum; therefore, non-reflecting boundaries were predicted in the model (Figure 2.16).
Figure 2.15 Geometry of the Two Blast hole Model (Dimensions in m), Schill et.al (2012)
1 For more information refer to the LSTC Corporation website: http://www.lstc.com/products/ls-dyna
31
Figure 2.16 Non Reflecting Boundaries and Free Surfaces, (Schill et.al 2012)
The Finite Element discretization was performed with a total of 20 million hexahedron elements.
The rock material in the case of this study was Westerly granite with compressive, shear, and
uni-axial tensile strength of 200, 36, and 10 Mpa, respectively. The explosive type used in the
experiment was an emulsion with the density of 1180 kg/m3 and detonation velocity of 5850
m/s. This emulsion (known as Emulsion 682-b) was modeled with the explosive material in LS-
DYNA combined with the JWL (Jones-Wilkins-Lee) equation of state1. The stemming material
(gravel) was modeled by MAT_SOIL_CONCRETE as well as the granite part. The study was made
to determine the effect of initiation delay, the amount of explosives, and the distance between
blast holes on the subsequent fragmentation. Table 2.1 shows the parameters used in design of
the blasts.
1 Review of Jones-Wilkins-Lee equation of state, Baudin et al. (2010)
32
Table 2.1 Description of Simulations
#
Initiation time Amount of explosives Distance between blast holes
BH1 BH2 BH1 BH2
1 0 ms 0 ms 11 m 11 m 8.7 m
2 0 ms 1.5 ms 11 m 11 m 8.7 m
3 0 ms 5 ms 11 m 11 m 8.7 m
4 0 ms 0 ms 11 m 11 m 12.3 m
5 0 ms 0 ms 8 m 8 m 8.7 m
6 0 ms 0 ms 8 m 11 m 8.7 m
In order to observe fragmentation in different sections of the model, the entire model was
divided into 7 cuts as displayed in Figure 2.17. The fragmentation results of all cuts were
evaluated at 15 ms which by then, the tension waves are assumed to have passed. Figure 2.18
presents the overall crack pattern of the model at t = 15 ms.
Figure 2.17 Vertical Cuts used in the Results Presentation, Schill et.al (2012)
33
Figure 2.18 The Overall Crack Pattern Resulted from Finite Element Simulation (Delay = 0 ms) , Schill et.al
(2012)
In all tests, fragmentation was higher in areas around the blast holes. An effect of stress wave
interaction was observed at the top of the model around the symmetry line (V4). Also, around
this line, some interesting results can be found. This line is located where the primary stress
waves meet and interact in the model. If blast holes are initiated simultaneously, unlike
Rossmanith’s theory, fragmentation does not seem to be higher in comparison with delayed
tests. In addition, the adverse influence of increased blast hole distance and decreased amount
of explosives on fragmentation was seen in the experiments particularly around the symmetry
line. According to the simulations, it was also found that the highest fragmentation was
achieved at fairly long delay times. Since at such delays, the primary stress wave from the first
hole has already passed the second hole, the role of stress waves in improving fragmentation
was questioned by this research.
34
Johansson et al. (2013) conducted a series of numerical simulations to further determine the
effect of timing on blast performance. The previously performed small-scale test pattern
(Johansson, 2011) was employed with the same methodology as Schill (2012). The Finite
Element discretization was performed using hexahedron elements. The mesh size of 3×3×3 mm
was chosen for the concrete part. The yoke was discretized with coarser mesh. The detonation
initiation point of the holes was the top of the blocks. The concrete part was modeled with the
Riedel-Hiermaier-Thoma (RHT) concrete model (Borrvall, 2011) which is a plasticity model for
brittle materials such as concrete. The parameters used to model the explosives (PETN cords) in
the experiments were extracted from the AUTODYN material library (ANSYS, 2010). Crack
formation and propagation modeling was not directly possible in this work. Therefore, a
threshold damage value was considered for each element. An algorithm was developed to
identify fragments that exceeded the determined damage threshold (60%) and the area of each
fragment. The fragmentation area was then specified by measuring the fragments in a number
of vertical and horizontal cuts through the medium. The damage levels were evaluated at 1000
µs for all simulations. The remaining area and remaining volume of the model were also studied
to evaluate the blast effect. These two concepts were the residual area and volume of the
model which were determined after the fragments with damage level of above 60% were
blanked out. The three parameter (fragment area, remaining area, and remaining volume)
method was used to review the previous findings from Johansson’s experiments on small-scale
concrete blocks. Based on the simulations, it was concluded that:
- Simultaneous initiation always results in coarse fragmentation.
- The effect of delay timing on fragmentation is clear. Short delays improve fragmentation
as opposed to instantaneous firing; however, the best fragmentation was found at a
relatively long delay intervals where stress wave superposition was not possible.
35
- The optimal delay time could be in the interval of 73 to 86 µs.
It was also noted that, the row 1 simulations resulted in coarser fragmentation compared to row
2 shots. The initial damage induced by row 1 in the blocks seems to have significant influence on
the fragmentation.
36
Chapter 3
Material Properties
3.1. Material Selection
Fragmentation studies have usually been made on different rock types including granite,
limestone, dolomite, etc. One can assume that testing rock specimens may encounter structural
flaws such as pre-existing discontinuities in the specimens and lack of homogeneity of the rock
materials. In such cases, the pre-existing fractures dampen the energy of the blast-generated
wave and block its propagation once a blast-induced crack reaches a discontinuity. Also, gaseous
products of a blast will leak off through the passages existing in the rock, such as pre-blast
cracks, thus reducing the influence of gas pressure on developing more cracks in the rock.
Therefore, it seems reasonable that propagation of detonation products (stress waves and gas)
in rock will not be similar to media without pre-existing discontinuities. Consequently, a true
interpretation of blast results only with respect to effects of detonation products requires a
medium without pre-blast fractures. To provide such a medium and in order to create consistent
and similar test conditions in all the samples, it was decided to produce a series of small-scale
test blocks using a commercial high strength grout (Sika Grout 212 SR)1 with the following
composition.
Ingredient Weight % kg2
SikaGrout 212 SR 85.3 75
Water 14.7 12.9
1 http://can.sika.com/dms/getdocument.get/8c2f3ba0-f9b8-36a8-8cb2-0f2fe39b547f/SikaGrout212SR_pds.pdf 2 The amount of grout and water required to cast one block with the main design (Refer to Chapter 4).
37
The grout mixture was poured into a rectangular mold (wooden box) and the blast holes for
placing detonating cords were inserted by using wooden dowels based on the determined
burden and spacing pattern. The poured mixture required 28 days to reach the maximum
strength of 60 MPa (SikaGrout 212 SR Product Data Sheet, 2012).
3.2. Physical and Mechanical Properties of the Selected Material
3.2.1. UCS
Laboratory tests were conducted to determine physical and mechanical properties of the grout
in this research. 18 cylindrical samples were produced to measure density, Young’s Modulus,
and uniaxial Compressive Strength (UCS) of the samples. The length and diameter of the
samples were 12 cm and 5.2 cm, respectively. Samples were mounted in a 500 kN Material
Testing System (MTS) and were subjected to uniaxial pressure. All the tests were made in the
Rock Mechanics Lab at the Department of Mining, Queen’s University. Figure 3.1 shows some of
the samples before and after strength testing.
Figure 3.1 Cylindrical Samples Before and After Strength Testing
38
Table 3.1 illustrates the UCS results as well as more information on the grout specimens.
According to the results, the average UCS of the Grout SR212 samples is 50 MPa, which
represents a material with strength of medium to high as classified by ISRM (1978)1. Also, the
average density of the grout is 2.2 g/cm3.
Table 3.1 Some Physical and Mechanical Properties of the Grout Samples
Sample
#
Length
(cm)
Diameter
(cm)
Weight (g) Density
(g/cm3)
Young’s Modulus
(Gpa)
UCS
(Mpa)
1 12.68 5.12 590.1 2.26 10.97 51.41
2 12.78 5.17 595.6 2.22 10.54 47.29
3 12.7 5.15 603.1 2.28 11.27 44.72
4 12.72 5.2 614.1 2.27 15.26 56.92
5 12.62 5.21 588.2 2.18 11.32 44.01
6 12.69 5.17 609.6 2.28 12.91 49.73
7 12.8 5.19 604 2.23 13.29 58.75
8 12.67 5.2 577.2 2.14 5.57 40.54
9 12.9 5.22 580.4 2.1 8.01 33.05
10 12.7 5.17 587.6 2.2 13.70 48.98
11 12.78 5.17 599.6 2.23 13.95 56.73
12 12.76 5.18 599.6 2.23 14.57 53.65
13 12.8 5.21 619.5 2.27 12.31 51.37
14 12.66 5.15 594 2.25 15.45 59.91
15 12.8 5.19 603.7 2.23 12.86 56.28
16 12.8 5.2 604.4 2.22 11.99 46.95
17 12.76 5.17 605.9 2.26 13.95 55.76
18 12.79 5.16 608.3 2.27 8.51 40.3
1 International Society for Rock Mechanics
39
3.2.2. P-wave Velocity
When an explosive charge detonates in a blast hole, the rock surrounding the charge is fractured
and if the fracturing mechanism is strong enough, fractures extend to a level that where rock is
fully disintegrated. The energy liberated from a detonation propagates in the form of stress
waves. The most important types of stress waves are the P-wave, the S-wave, and the R-wave.
P-wave stands for primary wave. It is also called pressure wave or compressive wave. In this
type of wave, which is known as the longitudinal wave, particle motion is parallel to the
direction of wave propagation. A P-wave travels in all directions at velocities proportional to
mechanical characteristics of the material being travelled through. S-wave stands for secondary
wave or the shear wave which is known to travel at 50-60% of the velocity of the P-wave
(Richards, 2009). Particle motion in this type of wave is perpendicular to the wave propagation.
R-wave stands for Rayleigh wave and only travels on surfaces. This type of wave is of importance
in earthquake studies. Figure 3.2 demonstrates how the generated waves travel through the
rock material after detonation.
Figure 3.2 A General Representation of the Stress waves Travelling through Rock (Richards, 2009)
40
In general, wave velocity measurement is done by sending a mechanical pulse through the
sample and receving it at the other end. Typically a piezoelectric transducer is used to convert
voltage to a mechanical pulse and vice versa. As shown in Figure 3.3, a pulse generator sends a
square wave of short duration in the form of voltage to the transducer and simultaneosuly a
trigger is sent to the recording device to notify it when the pulse was sent. This is when the
transducer is excited and sends a mechanical pulse across the sample which is received by the
other transducer at the other end. The mechanical pulse is converted into voltage and the
oscilloscope records the received pulse as well as the start time from the trigger.
Figure 3.3 Experimental Set-up used to Measure P-wave Velocity
Velocity of the pressure wave can then be measured using the distance of the wave traveling
across the specimen and the time it requires for the second transducer to receive the pulse. The
wave recorded on the oscilloscope screen and the P-wave arrival time is shown in Figure 3.4.
41
Figure 3.4 Picking the Arrival Time of P-wave
For the purpose of this thesis, p-wave velocity measurement was performed to further-
determine the characteristics of the grout material used in this research. Eight blocks of
SikaGrout 212SR were cast with dimensions of 25 cm×20 cm × 25 cm. P-wave velocity was
measured every 1 cm along the length of blocks, providing 25 readings for each block (Figure
3.5).
Figure 3.5 A Plan View of the Grout Block Specimens Used for P-wave Velocity Measurements
42
The results of the measurements are shown in Appendix A. According to the readings from the
eight blocks, the p-wave velocity for Grout 212SR is 4075±45 m/s.
3.3. Determination of Shock wave Pressure and Duration
The eight grout blocks mentioned in the previous section were also used to examine blast shock
wave characteristics such as shock wave pressure at different distances from the explosives
charge and duration of the pulses. In order to do so, the eight samples were divided into two
sets of four blocks. In each block, one hole was drilled in the middle of the block and two holes
were drilled in the two sides of the center hole (blast hole). The diameter of the blast hole was 1
cm and different strengths of detonating cords were used to charge the blast holes. Table 3.2
shows the strength of the detonating cord in each experiment. The volume between the wall of
the blast hole and the detonating cord was filled with water to provide a continuous medium for
the propagation of the shock wave. The two side holes were drilled to place carbon resistor
gauges to record shock wave pressure at the different distances from the charge. The gauges in
this work were 120 Ω carbon composition resistors made by the Allen Bradley Corporation. The
carbon resistors were embedded and protected at the bottom of the pressure holes by
polyethylene shrink tubing and epoxy. Figure 3.6 shows the locations of the resistors in the two
block sets.
43
Figure 3.6 Locations of the Carbon Resistor Gauges
When a carbon resistor is subjected to shock waves from detonation, it undergoes compression
which leads to a change in resistance of the carbon composition resistor. This change in
resistance can be derived from the voltage readings that can be recorded on any suitable
data capture device (Mencacci and Chavez, 2005).
In the case of this study, the setup of the experiments consists of detonating cords of different
strengths, electric detonators to initiate the event, two 120 Ω Allen Bradley carbon resistors
embedded in the blocks, a PCB signal conditioner (Model 482C) to supply constant current of 4
mA to the resistors, and a Data Trap II manufactured by MREL to record voltage variations of the
sensors. The data acquisition device (Data Trap) was set to initiate recording by a trigger line
connected to the detonator in each experiment.
Typically, an experimental setup such as above is used to measure relative resistance change of
the sensors, caused by detonation, in order to calibrate the pressure response of the gauges.
Many researchers have conducted experiments using resistor gauges to produce calibration
44
equations for shock wave pressures of different amplitudes. Wieland (1987 and 1993) proposed
a calibration equation relating relative conductance (inverse of resistance) change to pressure
for amplitudes below 1.0 kbar (Equation 3.1).
P (kbar) =R0−R
R×
1
0.2 (Equation 3.1)
for 0 < 𝑃 < 1 𝑘𝑏𝑎r
where, R0 and R are the original (initial) and instantaneous resistances of the gauge respectively,
expressed in ohms. Katsabanis (2013, personal communications) presented another equation to
calculate shock wave pressure which was suggested to be reliable for amplitudes up to 3000 bar
(Equation 3.2).
P (bar) = e(8.54+0.9464ln(R0−R
R) for 0 < 𝑃 < 3000 bar (Equation 3.2)
In this study, the two mentioned equations were utilized in order to examine the shock waves at
different distances from the charge. The wave duration was then determined as well as the
shock wave peak amplitude using the pressure pulses in each experiment. Figure 3.7
demonstrates a typical recording of a pressure-time pulse obtained from carbon resistor gauges
in one of the measurements.
45
Figure 3.7 Typical Record for a Pressure-Time Pulse
Using the two relationships, the pressure-time profiles were graphed (Appendix B) and the
characteristics of the pulses were as displayed in Table 3.2.
Table 3.2 Pressure Results
Block#
Charge loading
(grams/m)
Distance between
gauge and blast hole (cm)
Pressure (Kbar)
Wieland Calibration
Pressure (bar)
Katsabanis Calibration
Pulse Duration
(µs)
1 5.25 1 - - -
1 0.29 329 19
2 3.15 1 - - -
2 0.14 166 21
3 3.15 1 0.26 295 3
3 0.33 41 12
4 3.15 1 0.1 120 9
4 0.1 128 7
5 3.15 1 0.08 94 9
1 0.11 128 7
6 3.15 1 0.9 110 10
2 0.09 114 9
7 21 1 1.74 1843 150
3 0.26 297 30
8 21 1 0.57 624 74
4 0.23 259 34
0
0.05
0.1
0.15
0.2
0.25
0.3
0.134 0.139 0.144 0.149 0.154 0.159 0.164
Pre
ssu
re (
kbar
)
Time (ms)
46
Figure 3.8 Pressure as a Function of Distance
One conclusion from the pressure-distance graph (Figure 3.8) is that the pressure attenuates as
the wave moves away from its generating source. Another characteristic of the pressure waves
as shown in Figure 3.9 is the pulse duration obtained at different distances from the borehole.
Although different loadings were used in the experiments, it can be claimed that an average
pulse duration of 19 µs was achieved 2 to 4 cm from the charge. It is worthy of noting that in
the case of 21 g/m detonating cords (similar to the strength used in fragmentation tests in this
study) 30 µs duration pulses were produced at 3 to 4 centimeters from the borehole. This is of
importance, if one intends to draw Lagrangian diagrams to examine areas of overlap between
stress waves to modify fragmentation as discussed in the literature. Assuming this pulse
duration (30 µs), a P-wave velocity of 4075, an S-wave velocity of 2500 m/s, and a spacing
between boreholes of 10 cm, the Lagrangian diagram can be shown for two boreholes initiating
simultaneously, as shown in Figure 3.10. It is evident that a large area between the two
boreholes is covered by the interactions of the stress waves arising from each hole. According to
Rossmanith’s theory (Rossmanith, 2002), these interactions could strongly contribute to the
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 1 2 3 4 5
Pre
ssu
re (
bar
)
Distance (cm)
Pressure-Distance (3.15g/m)
Pressure-Distance (5.25g/m)
Pressure-Distance (21g/m)
47
process of fragmentation, while others have suggested to use time delay in order to move the
wave interactions closer to the delayed hole or even beyond the spacing distance. In any case,
such diagrams, using the velocity and duration of the pulses, are helpful to identify the areas of
stress wave interactions under various delayed and non-delayed blast conditions. Based on the
type of interactions, their locations, and the fragmentations achieved, positive impacts of stress
waves could be examined more accurately.
Figure 3.9 Pulse Duration as a Function of Distance
0
20
40
60
80
100
120
140
160
0 1 2 3 4 5
Du
rati
on
(µ
s)
Distance (cm)
Distance-Pulse Duration(3.15 g/m)
Distance-Pulse Duration(5.25 g/m)
Distance-Pulse Duration (21g/m)
48
Figure 3.10 Lagrangian Diagram to Show the Interaction of Stress waves. PCF1: Front of Compressive Wave from 1st Borehole; PCE1: End of Compressive Wave from 1st Borehole; SF1: Front of S-wave from 1st
Borehole; SE1: End of S-wave from 1st Borehole; PCF2: Front of Compressive Wave from 2nd Borehole; PCE2: End of Compressive Wave from 2nd Borehole; SF2: Front of S-wave from 2nd Borehole; SE2: End of S-wave from 2nd Borehole; PTE1: End of Tensile Wave from 1st Borehole; PTE2: End of Tensile Wave from 2nd
Borehole.
0
30
60
90
120
0 0.02 0.04 0.06 0.08 0.1
Tim
e (
µs)
Distance (m)
PCF1
PCE1
SF1
SE1
PCF2
PCE2
SF2
SE2
PTE1
PTE2
49
Chapter 4
Fragmentation Test Set-up
A series of small-scale blasts were conducted to study the effect of timing sequence on
fragmentation. Using the idea of confinement by Johansson and Ouchterlony (2013) it was
decided to place the testing blocks in a concrete yoke to minimize the impacts of free face
reflections. The yoke simulated a condition similar to bench blasting in open pit mines, resulting
in attenuation of the stress waves as they traveled inside the yoke without reflecting at the
boundaries to interact with the blocks.
4.1. Testing Blocks
As shown in Figure 4.1, the dimensions of the testing blocks (main design) were 60 × 25 × 24 cm
(L×H×W). The burden and spacing were 7.5 and 10.5 cm, respectively. The length and diameter
of the blast holes were chosen to be 23 and 1 cm. Wooden dowels were used to create the
holes in their specified locations.
The shape and dimensions of the yoke are demonstrated in Figure 4.2. A fast-curing concrete
with a density of 2.3 g/m3 was used to fill the gap between the blocks and the yoke. This density
is close to the density of the grout, thus minimizing the possibility of impedance mismatch
between the two mediums.
50
Figure 4.1 Dimensions of the Grout Blocks (main design)
Figure 4.2 Dimensions of the Yoke
51
4.2. Charging, Initiation, and Test Environment
The blast holes were loaded with two strands of detonating cord, with the exception of the first
six tests where single strands were used. Each detonating cord consisted of 10.5 g/m (50
grain/ft) of PETN, providing a powder factor of 2.4 kg/m3 based on the pattern of the blast. The
powder factor for the first six tests was 1.2 kg/m3. The blast holes were coupled with water prior
to the blasts. A wide range of delays was chosen from 0 to 2000 μs (0 to 26.6 ms/m of burden)
between blast holes to fully investigate the effect of initiation delay on blast fragmentation.
As demonstrated earlier in Figure 3.18, the P-wave front arrives at the neighboring blast hole
24.5 μs after initiation. Assuming the pulse duration of 30 µs, the end of the compressional
wave reaches the second hole at t = 54.5 μs. If the two blast holes are simultaneously initiated, a
wide area of PP interaction is generated covering the spacing distance between blast holes.
Lagrangian diagrams also suggest that other interactions of waves such as overlap of tensional
pulses or the overlap of tensional pulses and S-waves can occur between two adjacent blast
holes. Using shorter duration pulses, one can assume that the wave interaction zones would
become smaller. In the same manner, initiation delay can change the areas of interaction
bringing them closer to the delayed blast hole with narrower zones of overlap. Other
interactions of shock waves may take place beyond the spacing distance. Johansson (2011)
selected a number of inter-hole delays to investigate such interactions. Some delays were also
chosen slightly longer than the arrival time of the shock wave from the first blast hole at the last
hole to ensure no possible wave interaction would occur.
A different type of interaction takes place when a wave arrives at an outgoing crack which is
initially driven by another stress wave and is later assisted by gas. The cracks come to arrest
52
immediately after the stress intensity factor at the crack tip falls below the critical value
(Rossmanith, 2002). Lagrangian diagrams can be helpful in describing how waves and cracks
interact and thus lead to re-initiation of the arrested crack. As displayed in Figure 4.3 a crack
propagating at the velocity of (680 m/s)1 reaches the free face (Burden = 7.5 cm) at t ≈ 130 µs.
This will cause the arrest of outgoing cracks due to the venting and loss of gas as a driving factor
in developing fractures. Under such circumstance, if a tensional pulse from a second blast hole
arrives at the moment the crack stops, it can be concluded that the arrested crack will resume
its movement. In order to do so, the second blast hole has to detonate 124 µs after the first
hole. This delay provides the required time for a tensional pulse from the second hole to arrive
at the moment the mentioned crack stops to re-initiate it. Unlike stress wave interaction
assumptions, this model suggests that a certain delay is needed between blast holes, if
fragmentation optimization is desired.
Figure 4.3 Lagrangian Diagram to Show Interaction of a Shock Wave with an Arrested Crack from a
Previously Detonated Hole.
1 Crack Velocity ≈ (1/6) × P-wave Velocity, Katsabanis et al., (2006)
0
30
60
90
120
150
180
210
240
270
300
0 0.02 0.04 0.06 0.08 0.1
Tim
e (
µs)
Distance (m)
PCF1
PCE1
SF1
SE1
PTE1
Crack
PCF2
PCE2
SF2
SE2
PTE1
53
Considering the velocity of detonation of 7000 m/s for the detonating cord, short delays (< 100
μs) were achieved by using appropriate lengths of detonating cord between successive holes. An
upgraded version of the Orica electronic initiation system (I-kon I) was used to obtain delays
longer than 100 μs (Figure 4.4). The I-kon I initiation system showed an accuracy of ± 20 µs
(Katsabanis et al., 2014) which seems to be adequate for the range of delays in which electronic
detonators were used (>100 µs). The sub-millisecond system is composed of the following
components:
- A logging and testing device (Logger A3) with the capability of programming up to 400
detonators,
- A blasting device (Blaster 400 A3) to issue the fire command according to the timing
sequence information stored in the logger, and
- Sub-millisecond electronic detonators connected to each charge to initiate them based
on the signal received from the blaster.
This initiation technology delivers benefits such as: high timing accuracy with regard to delays
assigned for each detonator, programmability of detonators in increments/multiples of 0.1 ms
between 0 to 250 ms, independence of detonators in receiving their fire signal which minimizes
the risk of possible cut-offs and concerns with respect to early initiations, and capability of
detonators to communicate with the logger at any time prior to firing which allows the user to
identify possible problems associated with the detonators (I-kon II Electronic Blasting Manual,
2013).
54
Figure 4.4 The Components of the Electronic Initiation System (i-konTM II Technical Data Sheet, 2013)
Considering the closeness of the holes, a lot of care was taken to separate the detonating cords
and detonators of the neighboring holes using wooden boards to avoid cut-offs or unwanted
initiation of charges due to possible contacts between charges (Figure 4.5).
55
Figure 4.5 Set-up for a Block Placed in the Yoke
Experiments were done in a 76 m3 chamber at the Alan Bauer Explosives Laboratory. The
chamber was used to contain the flying fragments after each blast. The walls and floor of the
chamber were covered with 2.5 cm thick rubber mats to minimize further breakage of the
fragments due to impact.
4.3. Analysis of the Blasted Material
The blasted material was collected after each blast and was transported to the Mineral
Processing Laboratory in the Mining Department at Queen’s University. Sieving analysis was
done to achieve the particle distribution curves as well as the average fragment size and several
other fragment sizes for further examination of the results. Fragments were sieved in two steps.
56
The larger particles were size-measured individually using a measuring tape. The finer material
was then passed through the following standard size sieves: 63; 53; 45; 37.5; 31.5; 26.5; 22.4;
18.85; 13.33; 9.5; 6.73; 4.76; 3.36; 2.38; 1.7; 1.18; 0.84; 0.425 mm.
Fragmentation can be evaluated using different methods. One of the measures for evaluation of
fragmentation is the average fragment size (x50) that can be achieved using the particle
distribution results from the sieved material. A simple interpolation between the two particle
sizes with passing percentages close to 50% can be used to predict the average fragment size.
However, the best fragmentation model is the Swebrec function that enables one to construct a
comprehensive size distribution fit from the sieved material with a high accuracy to approximate
the desired fragment sizes other than x50 (x10, x60, x80, etc).
In this study, the Swebrec function (Equation 2.4) was used as the main fragmentation model.
This function uses the 50% passing size particle as the central parameter while introducing an
upper limit, xmax, to the fragmentation distribution and a curve undulation parameter (b). It has
been found that this fragmentation distribution gives excellent fits to hundreds of
fragmentation data with correlation coefficients of (r2 > 0.995) or better (Ouchterlony, 2005).
In addition to the Swebrec curves, the Rosin-Rammler function was used to describe the
cumulative distribution of fragments. The results are given in Appendix C. The Swebrec and
Rosin-Rammler parameters (xmax, x50, b, n, and xc) were calculated through least squares fitting.
57
Chapter 5
Fragmentation Results from Powder Factor of 1.2 kg/m3
5.1. Experimental Work
In the beginning of the project, it was decided to use one strand of 10.5 g/m detonating cord
with the pattern mentioned in Section 4.1. This provided a powder factor of 1.2 kg/m3 which
appears to be close to practical blasts. The first three test blocks were cast with a slight
difference from the main design. The dimensions of the initial blocks were 60 × 25 × 40 cm
(L×H×W), thus enabling us to perform more than one blast in the blocks. The blast holes were
drilled manually in the first three blocks using masonry drill bits with a diameter of 1 cm. The
burden, spacing, and length of the holes were as discussed in Chapter 4.
In the first block, the first row of blast holes was drilled and the holes initiated with no delay
using an electric detonator to initiate all detonating cords in order to study fragmentation under
a simultaneous firing condition. After blasting the first row and collecting the fragments,
another row of blast holes was drilled with 4 holes in the block under the same burden and
spacing. The blasts continued in the same manner with but different inter-hole delays and
number of blast holes in the remainders of the block. Table 5.1 shows the number of blasts
performed in the first block along with the applied delay between the blast holes.
Table 5.1 Initial Blasts
Row # Number of blast holes Delay (μs) Powder factor (kg/m3)
1 5 0 1.2
2 4 5 1.2
3 5 20 1.2
4 3 40 1.2
58
5.2. Initial Results
The fit of the Swebrec function and its parameters were obtained for the four shots (Table 4.2).
The coefficient of determination obtained by the Swebrec fit was with one exception (∆t = 40
μs) above 0.9995.
Table 5.2 Swebrec Parameters from First Block
Block and Row # Delay (μs) x50 (mm) xmax (mm) b r2
B1R1 0 182.2 - 5.4 0.9999
B1R2 5 111.6 205.7 1.4 0.9995
B1R3 20 70.9 255.9 2.36 0.9996
B1R4 40 46.8 193 2.84 0.9964
The first test with 0 μs delay between blast holes produced a very large fragment constituting
approximately 75% of the total weight of the obtained material, which made it very difficult to
describe fragmentation by a continuous sieving curve and predict the fragment sizes of interest
including x50, x80, and xmax (See Appendix C). However, the Swebrec function gave a very good fit
for fragments up to 75 mm. Figure 5.1 displays the condition of the first block after several
blasts until the block fully disintegrated.
59
Figure 5.1 Block #1 After Successive Blasts
As shown in Table 5.2, the average fragmentation improved as the delay time increased;
however, it is not clear if this was merely due to the influence of timing. It seems necessary to
note that the blast in row #1 was carried out under an intact material condition as opposed to
the next rows in which possible radial cracks existed before blasting. Petropoulos et al., (2013)
described this as a preconditioned material caused by previous blasting in the block.
The next set of fragmentation data using a powder factor of 1.2 kg/m3 was achieved from two
blasts in separate blocks with the same blasting pattern. The delays chosen in these two
experiments were 40 and 200 μs. The first delay provided a comparison between the two
experiments with the same timing factor under two different material conditions (damaged and
intact). Interestingly, the two major fragment sizes (x50 and x80) became coarser by 255% and
60
216%, respectively in the repeated 40 μs experiment. Table 5.3 illustrates the Swebrec
parameters from
the two tests.
Table 5.3 Swebrec Parameters for Second Block
Block and Row # Delay (μs) x50 (mm) xmax (mm) b r2
B2R1 40 119.3 267.2 1.92 0.9537
B3R1 200 69.5 262.3 1.76 0.9991
The Swebrec fits from the blasts in the two blocks were plotted together (Figure 5.2). The
distribution curve of the 200 μs experiment has moved toward the finer range of fragments, if
compared to the 40 μs test. In the 40 µs experiment, the fit of the Swebrec function is rather
poor, especially for fragments larger than 100 mm (boulders). However, in the longer delay test
(200 µs), the Swebrec model seems to have predicted fragments of different sizes with better
accuracy to their experimental values.
Figure 5.2 An Example of Two Distribution Curves
0
20
40
60
80
100
0 50 100 150 200
Pas
sin
g (%
)
Size (mm)
Particle Size Distribution
40 μs - Swebrec
200 μs - Swebrec
40 μs - Experiment
200 μs - Experiment
61
Another point worthy of noting is that the initial powder factor of 1.2 kg/m3 produced average
fragments larger than half of the burden. In blast practice, this type of fragmentation is known
as dust and boulders (Johansson, 2012) which is indicative of poor blasting. Producing oversize
fragments (boulders) suggests that the blast has not been successful in breaking the rock into
suitable sizes for the cycle of excavation, loading, hauling, and finally the crushing plant. Also,
very fine particles (dusts) resulting from blasting can become both an environmental issue and
an economical loss to the producers (Parihar et al., 2012). The remedy to this situation can be
achieved by increasing powder factor or making changes to the blast design including burden
and spacing (Singh et al., 2012). For the purpose of this project, powder factor was doubled,
although it is much higher than the powder factors normally used in bench blasting. Significant
losses of energy and gas, released by blasting, due to lack of stemming as well as decoupling of
the blast holes justifies this decision. In addition, increasing powder factor makes it possible to
compare results from similar delays under different loadings of blast holes.
62
Chapter 6
Fragmentation Results from Powder Factor of 2.4 kg/m3
6.1. Experimental Work
The blast holes in this research project were top initiated and did not allow for using any
stemming material. Under such blast conditions, there will be premature escape of blast-
generated-gases which can lead to poor fragmentation qualities (Rajpot, 2009). To compensate
for the energy lost due to the escape of gas, two strands of PETN cord were used in each hole to
double the powder factor of the blasts (2.4 kg/m3).
Twenty blocks of grout were cast with dimensions of the main design, 60 × 25 × 24 cm (L×H×W),
and they were blasted with a variety of delays from 10 to 2000 microseconds. This choice of
delay generated more data points in the range of interest and could provide a better answer to
questions about fragmentation and delay. In the shots with delays below 100 μs (10, 40, and 80
μs), pieces of detonating cord with the lengths that corresponded to the VOD of 7000 m/s and
the desired delays (7, 28, and 56 cm of PETN cord between holes) were cut to achieve the
delays. These pieces of detonating cord connected the charges inside the blast holes to an
electric detonator and the firing line. In longer delays, it was difficult to use the same method
due to the short distance between the holes. Two tests were implemented with a delay of 2000
μs. A sequential blasting machine (REO model BM-175-10ST-M) was used to create this delay for
one of the tests. The sequential blasting board failed to initiate all of the charges. The last two
holes did not fire which was assumed to be due to a cut-off in the circuit. A new technology
(sub-millisecond electronic detonators, ikon detonators manufactured by Orica) was used to
obtain delays in all other 16 blocks.
63
6.2. Results
Results of the failed test did not seem to be a true representation of the parameters used in
evaluating fragmentation; therefore, this shot was repeated with the new electronic initiation
system. Table 6.1 presents the results from the Swebrec fits of the 20 tests. The Swebrec
function fit runs very well through the experimental data with r2 of above 0.997 at delays equal
to 80 μs and longer. At delays ∆t = 10 and 40 μs, discrepancy between the sieved data and the
Swebrec curves can be observed in the range of fine particles, coarse fragments, and around
average fragment sizes (Figures 6.1 and 6.2).
Table 6.1 Swebrec Results for Main Design Tests
Block # Delay (μs) x50 (mm) xmax (mm) b r2
1 10 78.4 229.4 1.65 0.9986
2 40 89 145.5 1.5 0.9993
3 80 34.3 192.1 2.53 0.9997
4 100 28.7 154.3 3.07 0.9995
5 100 23.5 124.2 2.41 0.9993
6 200 34.6 520.6 5.59 0.9996
7 200 21.7 98.6 2.18 0.9967
8 400 28.7 177.1 3.75 0.997
9 500 21.3 165.7 3.23 0.9999
10 600 21.8 100.1 2.46 0.9999
11 700 16.8 102.4 2.83 0.9996
12 800 27.1 81 2.2 0.9997
13 800 17.9 115.8 3.03 0.998
14 1000 19.8 168.8 3.04 0.9993
15 1000 19.4 96.7 2.74 0.9999
16 1400 28.2 318.3 3.36 0.9982
17 1500 22.3 99.5 2.17 0.9997
18 1800 30.2 152.5 2.84 0.9995
19 2000 50.8 227.6 2.5 0.9998
20 2000 31.7 357.8 3.21 0.9978
64
Figure 6.1 Distribution Curves from the 10 µs Test
Figure 6.2 Distribution Curves from 40 µs Test
Considering x50 as an indicator for fragmentation, a general tendency toward size reduction can
be seen with an increase in the inter-hole-delays. Regardless of the small scatter, this constant
size reduction continues to ∆t = 200 μs rapidly, where the trend seems to reach a plateau. At
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120 140 160
Pas
sin
g (%
)
Size (mm)
Experiment
Swebrec
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120 140
Pas
sin
g (%
)
Size (mm)
Experiment
Swebrec
65
this point forward, a slight variation in the x50 values can be observed with x50 (mm) = 26.1 ± 8.7
mm (mean ± std-dev). Within the delay interval of 200 to 2000 μs an optimum fragmentation
appears to be obtained at ∆t = 700μs.
Figure 6.3 Average Fragment Size as a Function of Delay
Reviewing the results from the two different powder factors, a comparison can be made in
terms of the role of this factor in improving fragmentation (Figure 6.3). Using a similar delay
(200 μs), doubling the powder factor has reduced the average fragment size by more than 50%.
Figure 6.4 provides a one-by-one comparison between two tests with the same delay but where
different powder factors were used. It is clear that fragmentation enhances as the powder
factor is increased. In addition, the figure shows that different fragmentation results can be
expected even with the same blast pattern and powder factor but different initiation delays.
Therefore, despite the importance of powder factor, it is evident that powder factor is not the
0
20
40
60
80
100
120
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
x 50
(mm
)
Delay (μs)
Delay - x50PF=2.4kg/m3PF=1.2kg/m3
∆t=700 μs
66
only parameter contributing to fragmentation. In other words, parameters such as delay can be
utilized to improve fragmentation as desired in this study.
The higher powder factor (PF=2.4 kg/m3) appears to have produced very few boulders, thus
reducing the average fragment sizes below half of the burden. At delays shorter than 200 μs,
however, a number of large fragments were still obtained suggesting that fragmentation was
poor even using fairly large powder factors.
Figure 6.4 Effect of Powder Factor on Fragmentation
0
20
40
60
80
100
120
1 2 3
x 50
(mm
)
Powder Factor (kg/m3)
Powder Factor - x50
PF=2.4 kg/m3
PF=1.2 kg/m3
Delay = 40 µs
Delay =200 µs
67
Chapter 7
Fragmentation Results from Copper-lined Blast-holes
7.1. Effect of Gas on Fragmentation
The process of fragmentation is usually attributed to the combined effect of stress and gas.
Upon detonation, a large amount of energy is released which immediately pressurizes the wall
of the blast hole, generating radial compressive stress around the hole. This stress is much
higher than the compressive strength of the rock which breaks the rock and creates a thin
crushed zone around the blast (Esen et al., 2003). Depending on the compressive strength of the
rock, the extent of the crushed zone can reach twice the diameter of the borehole (Sharma,
2009).
The stress pulse propagates beyond the crushed zone in the form of radial compression and
circumferential tension. As the tensile stress exceeds the tensile strength of the rock, it creates a
radial pattern of fractures. The amplitude of the stress wave rapidly attenuates such that after a
distance no further fracturing and propagation of the cracks can occur. Depending on the size of
the burden, if the blast-induced stress wave reaches a free face, it will be reflected and the
compressive component of the pulse travels back as a tensile wave. The newly generated tensile
wave may be of sufficient amplitude to create surface spalling in the rock. The stress waves are
normally followed by a quasi-static gas pressurization generated by gas products of detonation.
The liberated gas travels through the widened borehole, crushed zone, and finds its way
through the stress wave induced cracks, resulting in further extension of the fracturing into a
wider area (Bozic, 1998). This is the zone where most of the fragmentation process takes place
(Figure 7.1) and produces the coarsest fraction of rock whereas, the fine fraction of
68
fragmentation normally originates from the process of compressive crushing within the crushed
zone (Sharma, 2009 and Iqbal, 2013).
Figure 7.1 A Schematic of Crushed Zone, Fracture Zone, and Fragment Formation Zone, (Sharma, 2009)
Multiple interactions between the components of stress waves, generated cracks, and
reflections of the stress waves from free faces can be assumed as discussed by (Rossmanith,
2002). Many researchers (Rossmanith, 2000; Rossmanith and Kouzniak, 2004) have tried to
explain positive effects of stress wave interactions on fragmentation; however, this idea has
been challenged by others such as (Blair, 2006), who claimed that stress wave interactions are
very localized in distances between the blast holes and the stress waves from neighboring blast
holes are not necessarily similar in amplitude to interact constructively to maximize damage and
fragmentation. Blair also indicates that, a very comprehensive model is required to describe the
role of stress wave propagation and the subsequent gas interactions with the stressed rock to
clarify both aspects of rock fragmentation.
69
7.2. Experimental Work
In order to investigate the effect of gas penetration on blast-induced fragmentation, it was
decided to make a series of small-scale tests using the same pattern as discussed in the earlier
chapters. The new tests were carried out in blocks using the same or very close delays as in
Chapter 6, but with copper lined holes. Blasting under such conditions, with a copper lining, is
assumed to prevent or reduce gas penetration into the blast stressed zone and the radial cracks,
thus changing the process of fracturing in the blocks. To achieve this goal, copper pipes with a
diameter of 11 mm and thickness of 0.7 mm were purchased and annealed in an oven at the
temperature of 932 (ᵒF) for 45 minutes. Annealing1 the copper pipes increases their ductility and
strengthens them against gas pressures. Eight blocks of grout were prepared and copper pipes
were placed in the blast holes. To create consistency between the blast conditions and to obtain
comparable results, blast holes were loaded in similar fashion as explained in Chapter 4.
Different delays were chosen among the range of 40 to 1200 μs.
7.3. Results
After each shot, the fragments were sieved and the fragmentation distribution was described by
the Swebrec function as shown in Table 7.1. The new set of data was plotted together with the
identical unlined blocks to examine if the new set up would make a difference in the average
fragment size (Figure 7.2).
1 For more information refer to http://heattreatment.linde.com/international/web/lg/ht/like35lght.nsf/repositorybyalias/wp_annlg_13/$file/13.pdf
70
Table 7.1 Swebrec Results for Copper-lined Blasts
Block # Delay (μs) x50 (mm) xmax (mm) b r2
1 40 32.9 3016.1 5.1 0.9844
2 80 50.8 342.5 2.71 0.9993
3 100 24.7 162.3 3.31 0.9986
4 200 26.7 221.4 3.58 0.9979
5 200 27.4 224 2.92 0.9964
6 700 20.9 2748.5 6.75 0.9841
7 800 27.3 1878.3 5.36 0.9878
8 1200 34.6 2171 5.88 0.9952
For delays as long as 200 μs no firm conculsion can be reached regarding the influence of gas on
the average fragmentation. While at ∆t = 80 μs a considerable coarser fragmentation was
achieved than the unlined block with the same delay, no such behaviour was seen at ∆t = 40 or
100 μs. In fact, at these two delays fragmentation unexpectedly became fine or resulted in no
different x50 values from the unlined condition.
Figure 7.2 Average Fragmentation, Lined and Unlined Conditions
0
10
20
30
40
50
60
70
80
90
100
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
Ave
rage
par
ticl
e s
ize
(m
m)
Delay time (μs)
unlined
Cu lined
Δt1 = 200 µs
Δt2 = 200 µs
71
As demonstrated in Lagrangian diagrams (Figure 3.10) stress wave generated cracks travel at
velocities around 680 m/s. This implies a minimum required time of around 155 µs for the cracks
to arrive at the neighboring blast hole. As stated by Daehnke et al. (1997), this is a phase where
the fracturing mechanism is mostly dominated by the effect of stress waves. Then, in the second
phase, the gases become the main driving force in extending the initial fractures which are
generated by the stress waves. The experiments show that in the short delays stress waves from
subsequent holes form a combined system of cracks and the gases vent through them. On the
contrary, in the long delays, there is no cooperation of stress waves reulting in formation of
independent networks of cracks due to the action of stress and gas.
The two phase approach appears to be in agreement with the results of the short delay tests
from the copper lined holes. At short delays below 200 µs, the effect of gas is not significant;
therefore, the average fragmentations appears not to differ drastically from the unlined
condition. For longer delays a change in fragmentation can be observed as a result of
eliminating or reducing the effect of gas pressure in the process of fragmentation by copper
lining the holes. With one exception (∆t1 = 200 μs), all other delays gave coarser x50 values under
the lined condition. The unlined borehole test at the delay of 200 μs was repeated and gave an
x50 smaller than the x50 with copper lined holes. Therefore, it can be claimed that a general trend
of increase in fragmentation occurred for delays > 200 μs, when gas penetration was inhibited
by the copper pipes. This also proves the importance of the effect of gas pressure at long delays.
At such delays, each hole creates a damage zone and radial fractures around it under the
influence of stress waves. Since there is sufficient delay time between blast holes, the damage
will expand by the action of gases, resulting in better fragmentation. Under such conditions, if
72
gas is controlled by copper pipes, less damage will be created as observed in the long delay tests
with lined blast holes.
The average fragmentation was in the range of 27.4 ± 4.9 mm (mean ± std-dev). Although the
blocks were blasted under a different rock fracturing process in the new tests, the minimum
average fragmentation was again achieved at the delay of ∆t = 700 μs between holes.
73
Chapter 8
Fragmentation Results from a Medium-scale Granite Bench
8.1. Experimental Work
In previous chapters, fragmentation was studied with different delays in small-scale blocks. The
medium in which the tests were made was homogeneous, ensuring the repeatability of blast
conditions. Typically, the delay timing results from different burden sizes are scaled up to real
dimensions and are expressed as ms/m of burden. For the purpose of this study, it was decided
to conduct a few tests in a medium-scale granite bench to reach a better understanding of
fragmentation in rock materials existing in nature. In addition to the chosen scale, heterogeneity
of the granite bench, altered rock type due to weathering, and the pre-existing fractures in the
rock were also influential to create a different sample condition from the previous tests.
However, the bench shape and size as well as its confined condition seemed to be appropriate
for blast experiments (Figure 8.1).
Figure 8.1 The Granite Bench
74
The diameter of the holes, length of the holes, burden, and spacing were 12 mm, 56 cm, 20 cm,
and 30 cm respectively. The blast holes were loaded using 85 g/m detonating cords with a
length of 30 cm, resulting in a powder factor of 0.76 kg/m3 of burden based on the blast pattern.
Multiple single row blasts were performed in the bench. At first, a 0 μs delay test was made to
create a proper and smooth face. As predicted, very large fragments were produced in this test,
making it impossible to easily move them in order to measure their size. Three main shots were
carried out with 500, 1000, and 2000 μs interhole delays. Similar to the first main test, clean-up
shots, ∆t = 0 μs, were implemented prior to each main shot to obtain an appropriate new face.
The generated fragments were collected for sieving analysis after the three tests.
8.2. Results
Table 3.1 shows summary of the Swebrec parameters obtained from the experiments. The x50
values were also plotted as a function of time (Figure 8.2). Only three data points were achieved
from the granite bench which do not show a clear pattern; however, the longest delay, 2000 μs,
gave the finest fragmentation which seems to be in agreement with the general trend from the
small-scale tests.
Table 8.1 Swebrec Parameters for the Granite Bench
Row # Delay (μs) x50 (mm) xmax (mm) b r2
1 500 107 303.8 1.94 0.9992
2 1000 141.3 340 1.73 0.996
3 2000 56.8 1266.3 4.08 0.995
75
Figure 8.2 Results from Granite Bench
As displayed in Figure 8.3, among the results from the bench, the 2000 μs test clearly yielded
the finest particle distribution curve with good consistency between the experimental data and
the predicted distribution from the Swebrec fit.
Figure 8.3 Fragmentation Distribution Curves from Bench Blasting
0.0
40.0
80.0
120.0
160.0
0 500 1000 1500 2000 2500
x 50
(mm
)
Delay (μs)
Delay - x50
Average Fragment Size
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200 250
Pas
sin
g (%
)
Size (mm)
500 μs - Swebrec
2000 μs - Swebrec
500 μs - Experiment
2000 μs - Experiment
76
As mentioned earlier, fragments from the instantaneous shots were not included in the analysis
due to their very coarse sizes (a few times of that burden size). All observations showed that the
zero microsecond blasts gave the coarsest fragmentation which, together with other data,
empowers the assumption regarding the gradual improvement in fragmentation by increasing
interhole delays. Figure 8.4 shows the condition of the bench before the experiments (a) and
after a few tests. It also demonstrates a very large fragment was produced after an
instantaneous test (b), and large back-break occurred after a delayed shot (c). The powder
factor used in the experiments was good enough to produce fragments smaller than half of the
burden in the delayed shots.
Figure 8.4 Granite Bench, Before and After Blasts
77
Chapter 9
Analysis of Results and Discussion
9.1. Blasting and Fragmentation
The importance of blast results to the efficiency of the downstream processes has been of
interest to many blast designers and mill specialists in the past few decades. Mackenzie (1967)
presented a series of conceptual curves to determine the cost dependence of different mining
operations on fragmentation at the Quebec Cartier Iron Mine. The study suggested that costs
associated with loading, hauling, and crushing are directly influenced by the degree of
fragmentation; therefore, the overall mining costs can ultimately reduce under an optimum
fragmentation condition. More studies by Nielsen and Kristiansen (1996) focused on the effect
of blasting on the subsequent crushing and grinding aspects of mining. The results indicated that
blasting as the first phase of size reduction could have positive impacts on the optimization of
mine operations. Eloranta (1997) compared energy requirements between blasting, crushing,
and grinding. Using the Bond equation as the indictor of energy usage, he concluded that
blasting could have a cost advantage of 3:1 over grinding. Another investigation by Grundstrom
et al. (2001) showed that achieving a finer fragmentation delivers many benefits to the
downstream process of mineral recovery. In addition to cost reductions in crushing and grinding,
he concluded that the following can be obtained through improved fragmentation:
- Improvements in excavator productivity through increase in muckpile digability and
increased bucket factor
- Increase in crusher throughput due to reduction of feed size distribution
- Reduction in ore dilution and potential for increased liberation of valuable minerals
leading to more mill recoveries.
78
The main concentration in the mentioned investigations was on optimizing blast results through
increasing powder factor. Other studies including Rossmanith (2002), Rosenstock (2004), and
Miller et al. (2007) selected a newer approach toward optimization of fragmentation. Their
research mainly targeted the results of blasts performed by electronic detonators in open pit
and quarry industries. Not only did all these researchers confirm the improvements mentioned
earlier in downstream processes, but also some of them addressed other advantages of using
electronic detonators as follows:
- Programmability, flexibility, and accuracy of electronic detonators compared to electric
and non-electric detonators
- A potential for minimizing vibration levels where possible damage to the neighboring
structures are concerned as well as environmental control
- Higher safety of blast operators since the risk of unintended detonation is minimized
with electronic initiation system.
Using the means of precision timing (electronic detonators), increased powder factor , or both,
any optimization in fragmentation typically involves the following aspects (Wuchi, 2010):
Minimizing oversize boulders to reduce secondary breaking costs
Minimizing ultra-fine products
Maximizing lump products with proper degree of uniformity
Ensuring efficient digging and loading through decreasing fragment sizes.
In the following , the results from recent experiments will be discussed with emphasis on size
reductions obtained when fragmentation appears to be optimal.
79
9.2. New Approach toward Optimization of Fragmentation
Various researchers have long tried to establish a relationship between fragmentation and the
parameters used in blast design. The quantity of explosives, burden, spacing, hole diamater,
sequence of firing and the associated timings, etc have been discussed in several works by
different blast specialists. Among all the different parameters, the role of delay has always been
a challenging topic with several unanswered questions. A variety of approaches have been
proposed from experimental methods to numerical modelling aiming at defining a time window
between blast holes in which the blast damage on the surrounding rock is maximized. In this
research project, an attempt was made to find a proper delay time with respect to results from
actual blasts. In order to do so, several blocks of grout were cast with mechanical properties
close to rock to generate blast fragmentation. The influence of reflective boundaries, normally
observed in free blocks, were minimized using a new experimental set –up , simulating open pit
blasting. For this purpose, a yoke was designed to confine the blocks from three free faces to
absorb the blast generated stress waves when they reached the face.
9.2.1. Effect of Timing on Fragmentation
The current study has examined the possible effects of timing factor on maximizing
fragmentation by the use of electronic initiation in the grout samples. The produced blocks were
blasted with a wide range of delay timing from 0 to 2000 μs between holes to ensure that all
rock fracturing mechanisms were taken into account. This choice of delay helped to evaluate
suggestions regarding fast initiation benefits of blasting made by Rossmanith (2004) and
Vanbrabant and Espinosa (2006) as well as assumptions about fracturing mechanisms of blasts .
80
The results of the new work appear to contain less experimental scatter compared to the
previous studies by Katsabanis et al., (2006), Johansson (2012), and others. The most scatter
seems to appear in the range of 0 to 200 μs (0 to 2.7 ms/m of burden); however, a continuous
reduction of the 50% passing size is obtained with increase in delay time. At delays above ∆t =
200 μs, the “x50 – Delay” plot reaches a steady zone which continues up to 1000 μs. This trend
indicates that in the scaled up delay interval of “2.7 to 13.3 ms/m of burden” no substantial
change in the value of x50 occurs while the finest mean fragment size (x50 = 16.8 at ∆t = 9.3
ms/m) falls in this range. This can be considered as the optimum range of delay, knowing that
beyond the delay of 1000 μs fragmentation becomes slowly coarser again.
The extent of this optimum range appears to be somewhat in agreement with the previous
experiments in granodirite blocks (Katsabanis et al., 2006) and the USBM data (Stagg and Rholl,
1987; Otterness et al, 1991) but certainly is not compatible with the idea of improving
fragmentation through simultaneous initiation or the use of very short delays. Moreover, if the
results are compared to suggestions made by Cunningham in South Africa’s mines
(Cunningham, 2005) and Johansson’s fragmentation data, some very interesting similarities and
differences can be found. Cunningham suggested that the proper interhole delay time to obtain
maximum fragmentation can be calculated by the use of the following formula.
𝑇𝑏𝑒𝑠𝑡 (𝑚𝑠) = 15.6
𝐶𝑃 𝐵
where, CP is the compressional stress wave velocity (km/s) and B is the burden (m). The Tbest in
this formula corresponds to a time window where the fracture network around the blast holes
evolves optimally due to the action of stress waves. In support of the Tbest concept, Cunningham
compared some previously found fragmentation data by Bergmann et al. (1974) from full-scale
tests, where delays longer than Tbest led to coarser fragmentation. He also claimed that if delays
81
shorter than Tbest are selected, stress waves from the delayed blast hole would destructively
interfere with the fractures from the earlier hole, thus suppressing the growth of the fracture
network. As a result such delays would not be assisting in improving fragmentation. If
Cunningham’s recommendation is used, the appropriate delay time to enhance fragmentation
would be equal to 3.8 ms/m of burden. This lies inside the range of delays where relatively fine
fragmentation was achieved, according to the findings from the small-scale tests. However, at
longer delays, blasts produced even finer fragmentation.
Johansson et al. (2013) re-examined their small-scale experimental data (Johansson et al., 2012)
using a numerical FEM code. The laboratory tests were modeled to identify the influence of
superposition of stress waves at different inter hole delays as tested in the experimental work.
The numerical simulations of the concrete blocks demonstrated that simultaneous initiation or
very short delays are useless in improving fragmentation and the optimum delay is in the range
of 73 to 86 μs for the burden size of 7 cm. Comparing these two results with the findings of this
research, the first conclusion is clearly in agreement with the current data. The optimum
fragmentation, however, seems to have been produced at very longer delays, thus questioning
the hypothesis that stress waves and their interactions are the only cause for creating
fragmentation.
The change in the 80% passing sizes with delay time is another topic of value to discuss if
fragmentation is evaluated from the comminution design viewpoint in mills. The importance of
x80 becomes evident since the energy required for the primary crusher is dependent on the
muckpile 80% passing size (Bond, 1961). The current study shows that the x80 reaches its
minimum value (33.83 mm) at the delay of ∆t = 700 μs (Figure 9.1).
82
Assuming that the results can be converted to real scale blasts, there is a potential for energy
cost saving through providing the mill with a feed size produced by a delay in the range of 2.7 to
13.3 ms/m of burden. The behaviour of the 10% passing size is also shown in the figure with the
least variation compared to other particle sizes. This is rather expected as the 10% fragments
are typically products of the crushed zone in which the fragmentation is under the influence of
compression from detonation and the the finest fraction is formed within this region. In all
passing sizes, the Swebrec values are very close to the experimental observations, thus proving
the capability of this model to predict different fragment sizes with acceptable accuracy. The
very fine fraction, below 1 mm, varies between 1% to 8% of the total collected fragments in the
experiments (Figure 9.2). Due to the large scatter in the distribution of the very fine fragments,
it is impossible to draw any reasonable conclusion regarding the effect of timing on the
formation of fines.
Fig 9.1 The Variation of Different Fragment Sizes with Time
0
20
40
60
80
100
120
140
160
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
Frag
me
nt
size
, (m
m)
Delay (μs)
Fragmentation - PF = 2.4 kg/m3
50% Passing Size -Swebrec
80% Passing Size -Swebrec
10% Passing Size -Swebrec
50% Passing Size -Experimental
80% Passing Size -Experimental
10% Passing Size -Experimental
83
Figure 9.2 Fines Below 1 mm
9.2.2. Uniformity and Delay
Another interesting point is the effect of timing on the slope at the 50% passing sizes obtained
from the fragmentation distribution curves. It seems logical that a steep slope at the average
size, in the distrbution curves, is indicative of the closeness of the fragments around x50.
Similarly, if the slope of the line that passes through two desired fragment sizes becomes
steeper, it can be concluded that those two fragments are closer to each other in size. The
closeness of different fragment sizes is typically described as the uniformity of fragmentation.
Higher uniformity suggests fewer coarse fragments, less fines, and more efficient blast products
for mill purposes. Therefore, uniformity can be considered as another measure to evaluate
fragmentation along with x50. Interestingly, at some delays used in this research, it was found
that uniformity was optimum in the same manner as the average fragment size. As displayed in
Figure 9.3, the increasing pattern of the slope values at x50 starts from short delays and
continues toward the upper limit of the delay range that was previously found to be optimum in
0
1
2
3
4
5
6
7
8
9
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
% p
assi
ng
Delay time, μs
Fines ≤ 1mm - PF = 2.4 kg/m3
84
terms of the average fragment size. It is then followed by a declining trend in uniformity,
particularly beyond Δt = 1000 µs. In agreement with the x50 evaluation, the optimum uniformity
(peak slope value) was found at Δt = 700 µs. A similar trend is observed if the slopes through
different fragment sizes of interest are drawn. For instance, Figures 9.4 and 9.5 illustrate the
slopes of the lines connecting the x80, x20 and x60, x40 passing sizes . All the peak slope values lie
inside the range within which fragmentation was optimum from the average size analysis
viewpoint. This suggests that as the delay increases, the produced fragments from different
sizes become finer and form a distribution curve with a higher uniformity.
Figure 9.3 Slope at x50
0
0.005
0.01
0.015
0.02
0.025
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
Slo
pe
at
x 50
Delay time (μs)
Slope at x50
unlined
Cu lined
85
Figure 9.4 Slope through x80 and x20
Figure 9.5 Slope through x60 and x40
0
0.5
1
1.5
2
2.5
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
Slo
pe
th
rou
gh x
80,
x2
0
Delay time (μs)
Slope through x80 and x20
unlined
Cu lined
0
0.5
1
1.5
2
2.5
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
Slo
pe
th
rou
gh x
60,
x4
0
Delay time (μs)
Slope through x60 and x40
Unlined
Cu lined
86
The figures also reveal that, the slopes through the average fragment size as well as the slopes
through the x80, x20 and x60, x40 passing sizes are lower when blast holes were lined with copper
tubes at delays above 200 µs. As a result, uniformity appears to be generally poorer in the case
of the lined blasts where the effect of gas is reduced. The poorer uniformity is even more
noticebale in the case of longer delays where fragmentation is highly dependent on the action
of gases.
The traditional Rosin-Rammler uniformity index (n) obtained from the small-scale tests (Figure
9.6) does not appear to show an obvious trend with delay time. Therefore, no comment can be
made on the impact of timing on this type of uniformity. Another type of expression of
uniformity (x60/x10), commonly used in soil mechanics studies, is plotted in Figure 9.7. The large
scatter in this graph also suggests no tangible effect of timing. Given the results of the two
known uniformity indices, the author suggests using other methods such as assessment of the
slopes obtained from distribution curves in order to perform fragmentation uniformity analysis.
Figure 9.6 Rosin-Rammler Uniformity Index vs. Delay
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
Un
ifo
rmit
y in
de
x (n
)
Delay time (μs)
Uniformity index - Rosin-Rammler
87
Figure 9.7 Uniformity Expressed as x60/x10 vs. Delay
9.2.3. Effect of Stress waves on Creating Fragmentation
Considering the compressive wave velocity of 4075 m/s, the arrival time of the P-wave at the
neighboring blast hole is assumed to be (105 mm) / (4 mm/μs) ≈ 26 μs. If the second hole
detonates at a delay equal to this or later, no P-wave interaction between the spacing distance
can be achieved and any PP-wave interactions will occur only at the second hole and distances
beyond that. Theoretically, a five times longer delay (130 μs) would lie outside the range of PP-
interaction between the waves arising from the blast holes in the block. This logic was chosen by
Johansson (2011) to determine the shortest and longest delays in his work. Apart from one
experiment at a delay of 0 μs, all other tests were made at a delay range from “P-wave
interaction at the neighboring hole” to “no P-wave interaction”. Johansson also used the idea of
superposition of pulses beyond the hole detonating later. At first, Johansson initiated the
second charge at the delay of 37 µs which coincided with the stress wave arrival from the first
hole. He then increased the delay to 46, 56, 73, and 86 µs to obtain different tensile pulse
interactions near neighboring holes. This attempt is simplified in Figure 9.8.
0
5
10
15
20
25
30
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
x60
/x1
0
Delay time (μs)
Uniformity
88
Figure 9.8 Interaction of Tensile Waves
The shaded area in this figure represents the zone where tensile pulses from two neighboring
holes interact. Clearly, the extent of this zone is controlled by the delay used between the holes.
Johansson then chose a delay time of 146 µs between blast holes to investigate fragmentation
when no stress wave interaction was possible. Fragmentation improvements were seen as the
inter hole delays increased; however, this study remains restricted to the range of stress wave
interactions. Johansson’s approach was continued by Petropoulos et al., (2013) to study the
effect of longer delays (218 and 290 μs) on fragmentation. More improvements were observed
as the delay increased. Using these two delays, he concluded that with a crack propagation
velocity of 500-600 m/s, the generated crack moved past the neighboring hole before it is
initiated and no more improvement in fragmentation is possible as the burden starts moving
250 μs after initiation of the first hole. Katsabanis et al. (2014) also presented Lagrangian
diagrams (Figure 9.9) to display tensile wave interaction in the case of a blast with the P-wave
velocity of 4200 m/s, the compressional tail velocity of 2000 m/s, and the tensional tail velocity
of 1000 m/s. The pulse duration was also assumed to be 50 µs in compression and tension, close
to what was previously measured using carbon resistor gauges. The diagram suggests that in a
case such as this, if the second hole initiates at the delay of 50 µs, the tension pulses from the
89
two holes fully overlap with each other, creating maximum tension in the areas past the delayed
charge. This approach along with other findings from Johansson (2011) recommends the use of
short delays but certainly does not explain the observations in this study where much longer
delays yielded better fragmentation results.
Figure 9.9 Lagrangian Diagrams to Create Zones of Maximum Tension (Katsabanis et al., 2014)
The current study agrees with the improving trend of fragmentation with time from
Johansson’s work; however, it shows that results can still change toward the formation of finer
fragments as observed in the delay span of 200 to 1000 μs, where average fragment size has
reached a plateau. This longer range of improvement could be due to the accumulation of
damage caused by stress waves when they have passed the consecutive blast holes and
subsequently the role of gas pressurization in expanding the damage into a wider extent before
venting. According to Stagg and Rholl (1987), the blast generated gas travels at the rate of 6% of
the P-wave velocity. In the present work, this would be equal to 240 m/s suggesting that gas
pressurization continues for about 430 μs before venting. Since the blast holes were left
0
50
100
150
200
250
300
0 0.1 0.2 0.3 0.4
Tim
e (
µs)
Distance (m)
PF1
PE1
PF2
PE2
PF2R
PE2R
TT1
Superposition of tensile pulses from 1st and 2nd
Compression from 2nd hole
Compression from 1st hole
Tensile tail from 1st and 2nd hole
90
unstemmed, this velocity can be even lower. As mentioned in Chapter 7, upon detonation of the
explosives the stress waves are initially the dominant mechanism to create fractures. This type
of fracturing could take up to 130 µs (refer to 9.2.3) in the case of these experiments.
Subsequently, as the fractures develop, the gas entering the fractures becomes the driving force
to generate further fragmentation. This seems to account for the long delay window required
for the action of fracturing mechanisms to create close to optimum fragmentation.
9.2.4. Effect of Gas Pressure on Formation of x10, x50, and x80 under Lined and Unlined
Conditions
A new approach toward determining the effect of gas pressure was tested by placing copper
pipes in the blast holes. The pipes were assumed to act as a trap to minimize penetration of the
blast gases into the stress wave-created cracks. Comparing the copper lined experiments with
the non-lined blasts,the average fragmentation showed an increase at delays between 200 to
1000 µs. This increase in the average fragment size was in the order of 25% for the 200 and 700
µs tests, whereas, at Δt = 800 µs, the x50 increased by 52%. However, at delays below 200 µs no
such increase was obtained. This could be attributed to the role of gas only at long delays where
the blast gases have sufficient time to further pressurize the stress-created damage zone and
develop the fractures before venting. On the contrary, in the short delay tests, the
superposition of stress waves most likely creates a large crack along the plane connecting the
axes of the boreholes. This major crack provides a path for the gases to escape through reducing
the effect of gas on pressurizing the block. The copper lined blast holes produced larger 80%
passing sizes of fragmentation in the range of 200 µs – 800 µs compared to the unlined tests in
the same range. The 80% passing size showed an increase of 36%, 52%, and 58% at delays equal
to 200, 700, and 800 µs, respectively when gas penetration was inhibited by copper pipes
91
(Figure 9.10). This seems to be of importance considering that large fragments, such as x80, are
likely produced in the zones with the most distance from the stress wave fracturing zone and
their formation is mainly under the influence of gas pressure released from a blast.
Figure 9.10 Effect of Copper Lining on x10, x50, and x80
The figure also indicates the non-sensitivity of the 10% passing sizes to gas pressurization since
the results of the lined holes did not change significantly from that of the unlined condition. This
is rather expected since the small particles such as the 10% passing size are most likely
originated from the thin crushed zone around the blast holes as shown in Chapter 7. This zone is
believed to be the product of the initial compressive stress, within which the influence of other
fracturing mechanisms such as gas is expected to be minimum.
9.2.5. Fragmentation Distribution Curves under Lined and Unlined Conditions
The effect of copper lining the blast holes on the fragmentation distribution curves is displayed
in Figures 9.11 to 9.14. The impact of reducing the gas flow on the overall fragmentation
0
20
40
60
80
100
120
140
160
0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200
Ave
rage
par
ticl
e si
ze (
mm
)
Delay time (μs)
Effect of Copper lining on Fragmentation - PF = 2.4 kg/m3
50% unlined
50% Cu lined
80% unlined
80% Cu lined
10% unlined
10% Cu lined
92
becomes apparent as explained earlier at long delays. The distribution curves clearly suggest
that fragmentation deteriorates remarkably under lined hole condition in terms of obtaining
much larger particles in a wider size range (lower uniformity).
Figure 9.11 Effect of Copper Lining on Distribution Curves, Delay = 100 µs
Figure 9.12 Effect of Copper Lining on Distribution Curves, Delay = 200 µs
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120 140
Pas
sin
g (%
)
Size (mm)
Delay = 100 μs
No Copper
Copper
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120 140
Pas
sin
g (%
)
Size (mm)
Delay = 200 μs
No Copper
Copper
93
Figure 9.13 Effect of Copper Lining on Distribution Curves, Delay = 700 µs
Figure 9.14 Effect of Copper Lining on Distribution Curves, Delay = 800 µs
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120 140
Pas
sin
g (%
)
Size (mm)
Delay = 700 μs
No Copper
Copper
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120 140
Pas
sin
g (%
)
Size (mm)
Delay = 800 μs
No Copper
Copper
94
9.3. Back-break
Any blasting operation is associated with damage around the blast holes. A portion of this
damage, occurring in the burden area, is the desired fragmentation produced by the effect of
the blast. Typically, blast researchers investigate the possibilties of maximizing this type of
damage in order to gain benefits in the downstream processes as discussed in Chapter 2.
Another type of damage in the blasted material is known as back break, which is an undesirable
phenomenon and may cause instability of walls in surface mine benches. In this research, this
phenomenon was seen in most of the small-scale blocks as well as in the granite bench shots.
According to the observations in the post blast blocks, there seems to be a direct relationship
between increase in the interhole delay and the extent of the back break. Figure 9.15 shows a
block condition after a zero delay test. The experiment resulted in formation of very large
fragments with the minimum damage to the left-overs of the block.
Figure 9.15 Block Condition After a Simultaneous Initiation Shot
As the delay was increased to Δt = 40 µs, breakage emerged in the back of the block. The effect
became larger at longer delays. For example, at Δt = 1000 µs , although a better fragmentation
95
was obtained, the back break in the block was large (Figure 9.16). In this experiment, not only
was the entire block damaged, but the yoke seemed to have moved due to exposure to the
energy liberated from the blast. A simple explanation for this could be the effect of gas that can
remain inside the block and pressurize the blast zone for a longer period of time; whereas, at
very short delays gas is escaping through the opening created by interaction of stress waves on
the plane where the blast holes are located. This is in agreement with observations from two
blocks blasted at the same delay (200 µs) but with copper lined and unlined blast holes (Figure
9.17). In the unlined block, more back break is visible after the blast, while the copper lined
block, which is not as much affected by gas penetration, appears to be less influenced by
detonation.
Figure 9.16 Block Condition After 40 µs and 1000 µs Shots
96
Figure 9.17 Block Condition After 200 µs Shots, Lined and Unlined
9.4. Analysis of the Granite Bench Experiments
In order to examine the effect of delay time on fragmentation in a larger scale, a series tests
were conducted in a granite bench located in the explosives laboratory. Fragments obtained
from three of the tests were collected and analyzed as in the small-scale grout blocks. At the
longest delay experiment (2 ms), the best fragmentation was achieved while shorter delays (0.5
ms and 1 ms) resulted in coarser fragmentations . Since too few data points were achieved, and
also due to the unusual coarse fragmentation obtained in the 1 ms shot, it is not possible to
draw a firm conclusion regarding the existence of a trend in the variation of delay-x50 in the
medium scale experiments. However, very interesting facts were revealed from frame-by-frame
review of the high-speed videos captured in the three experiments.
To start, the first blast in the bench was performed with no delay between the holes in order to
create a clean and even free face. This test was filmed by a high-speed video camera. As shown
97
in Figure 9.18, it is obvious that the burden starts to move with formation of very large
fragments as expected where simultaneous initiation is used.
Figure 9.18 Two Frames from Granite Bench 6 ms and 30 ms After Initiation, Delay = 0 ms
The 0.5 ms test was also analyzed by reviewing some frames obtained with intervals of 2 ms.
Burden movement and gas venting started less than 2 ms after initiation of the first hole.
Detonation gases appeared to vent initially from the collar region rather than the free face, thus
indicating that cracks developed between the holes provide a proper passage for gases to flow.
The simultaneous shot further confirmed this gas venting process as burden displacement
coincided with the escape of a considerable volume of gas and dust from the top of the holes
along the new generated free face (Figure 9.19)
98
Figure 9.19 Two Frames from Granite Bench 0 ms and 8 ms After Initiation, Delay= 500 ms
The sequential frames captured in the 2 ms delay experiment are also displayed in Figure 9.20.
Venting of gas and dust occurred in less than 2 ms after initiation. Similar to the 0.5 ms test,
burden movement started less than 2 ms after initiation of each hole. This time corresponds to
the 700 µs delay test in the small-scale blocks. Therefore, it can be assumed that no interaction
of gas with stress waves takes place at longer delay detonations. As a result, fragmentaion will
not be benefited by the action of gas in blasts with delays longer than 700 µs.
99
Figure 9.20 Six Frames from Granite Bench, Delay = 2 ms
100
Chapter 10
Conclusions
The results of this study shows that interhole delay influences the blast produced
fragmentation. No improvement in fragmentation was observed in simultaneous initiations or
very short delays. In these initiations, the blasts resulted in production of very large fragments
with low uniformity. However, short delays were associated with the least amount of back
break. The average fragmentation and the 80% passing size constantly improved as the inter-
hole delay increased from 0 to 200 µs (0 to 2.7 ms/m of burden). At delays between 200 to 1000
µs (2.7 to 13.3 ms/m) very small variations in the trend of the 50% passing sizes were obtained.
The 80% passing sizes, however, seem to be more affected by time in this delay range. Among
all the tested delays, the optimum 50% and 80% passing sizes were achieved from an
experiment with 700 µs (9.3 ms/m) delay between blast holes. This delay is very close to the
best fragmentation from the granite bench (10 ms/m).
The tests conducted in the range of 200 to 1000 µs showed the best performance in terms of
the uniformity obtained from the slope of the distribution curves. In agreement with the results
of the average and 80% passing sizes, the 700 µs shot yielded the highest uniformity in terms of
the slope at the 50% passing size among all other delays. This indicates an optimum delay both
from the size analysis and uniformity viewpoints.
The copper-lined blasts produced coarser fragmentation compared to the non-lined
experiments. It was noted that the effect of gas flow reduction on the size of the generated
101
fragments was larger at longer delays. The uniformity expressed as the slope of the distribution
curves was also much poorer under lined conditions, particularly at long delays.
Back break increased as longer delays were used. Delays longer than 1000 µs did not benefit
fragmentation and were in favor of excessive back break. Uniformity, expressed in terms of the
slope of the fragmentation curves is affected by delay time and appears to be optimum in the
delay range of 200 to 1000 µs. The results of the experiments challenge the ideas on rock
fracturing mechanisms presented by Rossmanith (2002) and Vanbrabant and Espinosa (2006)
and do not confirm fragmentation enhancement suggestions merely based on the interaction of
stress waves. According to the experimental data achieved in this study, a combination of
fracturing effects of stress waves along with blast generated gas pressure seems to serve as the
mechanism by which fragmentation is produced. To draw a better conclusion regarding the
fracturing mechanisms, crack velocity is suggested to be measured accurately as well as the gas
propagation velocity. These two factors will help determine the time window within which gas
can pressurize and develop the fractures induced by stress waves. In the small-scale tests, the
extensive back-break particularly at long delays caused difficulties to separate burden fragments
from other broken materials. Extra care should be taken in such blasts to collect the desired
fragments. In addition, burden displacement behaviour is another important restriction in this
type of test. Considering that any fracturing effect of stress waves and gases could be possible
only before the burden is displaced, the time that burden starts to move needs to be
determined. As reported by Petropoulos et al., (2013), the burden starts moving 250 µs after
initiation of the first hole; however, the current study shows further improvement in
fragmentation for delays up to 700 µs. To find a proper explanation for this, it is recommended
to study the behaviour of the burden using ultra-high speed cameras. Finally, it should be noted
that the small-scale experiments were conducted in a homogeneous medium without any flaws
102
existing in natural rocks. Also, the powder factor used in these tests was fairly high as compared
to actual bench blasting. Thus, it seems logical that the results of the small-scale tests are not
fully representative of real scale blasts.
103
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Appendices
Appendix A - P-wave Velocities
Figure A1. P-wave Velocity, Block 1
Figure A2. P-wave Velocity, Block 2
3.8
3.9
4
4.1
4.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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P-wave Velocity
3.8
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4
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P-wave measurements
P-wave Velocity
114
Figure A3. P-wave Velocity, Block 3
Figure A4. P-wave Velocity, Block 4
3.8
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4
4.1
4.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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P-wave Velocity
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P-wave Velocity
115
Figure A5. P-wave Velocity, Block 5
Figure A6. P-wave Velocity, Block 6
3.8
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4.2
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P-wave Velocity
116
Figure A7. P-wave Velocity, Block 7
Figure A8. P-wave Velocity, Block 8
3.8
3.9
4
4.1
4.2
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km/s
Points
P-wave measurements
P-wave Velocity
117
Appendix B – Shock wave Records
Figure B1. 5.25 gr/m, 1 cm from Borehole
Figure B2. 5.25 gr/m, 1 cm from Borehole
0
50
100
150
200
250
300
350
400
450
0.073 0.078 0.083 0.088 0.093
Pre
ssu
re (
bar)
Time (ms)
Katsabanis Calibration
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.073 0.078 0.083 0.088 0.093
Pre
ssu
re (
kBar
)
Wieland Calibration
Series1
118
Figure B3. 3.15 gr/m, 2 cm from Borehole
Figure B4. 3.15 gr/m, 2 cm from Borehole
0
20
40
60
80
100
120
140
160
180
0.024 0.029 0.034 0.039 0.044
Pre
ssu
re (
bar)
Time (ms)
Katsabanis Calibration
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.024 0.029 0.034 0.039 0.044
Pre
ssu
re (
kbar
)
Time (ms)
Wieland Calibration
119
Figure B5. 3.15 gr/m, 3 cm from Borehole
Figure B6. 3.15 gr/m, 3 cm from Borehole
0
10
20
30
40
50
60
0.057 0.059 0.061 0.063 0.065 0.067
Pre
ssu
re (
bar)
Time (ms)
Katsabanis Calibration
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
0.057 0.059 0.061 0.063 0.065 0.067
Pre
ssu
re (
kbar
)
Time (ms)
Wieland Calibration
120
Figure B7. 3.15 gr/m, 1 cm from Borehole
Figure B8. 3.15 gr/m, 1 cm from Borehole
0
20
40
60
80
100
120
140
0.163 0.165 0.167 0.169 0.171 0.173
Pre
ssu
re (
bar)
Time (ms)
Katsabanis Calibration
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.163 0.165 0.167 0.169 0.171 0.173
Pre
ssu
re (
kbar
)
Time (ms)
Wieland Calibration
121
Figure B9. 3.15 gr/m, 4 cm from Borehole
Figure B10. 3.15 gr/m, 4 cm from Borehole
0
20
40
60
80
100
120
140
0.024 0.026 0.028 0.03 0.032 0.034
Pre
ssu
re (
bar)
Time (ms)
Katsabanis Calibration
0
0.02
0.04
0.06
0.08
0.1
0.12
0.024 0.026 0.028 0.03 0.032 0.034
Pre
ssu
re (
kbar
)
Time (ms)
Wieland Calibration
122
Figure B11. 3.15 gr/m, 1 cm from Borehole
Figure B12. 3.15 gr/m, 1 cm from Borehole
0
20
40
60
80
100
120
140
0.077 0.079 0.081 0.083 0.085 0.087
Pre
ssu
re (
bar)
Time (ms)
Katsabanis Calibration
0
0.02
0.04
0.06
0.08
0.1
0.12
0.077 0.079 0.081 0.083 0.085 0.087
Pre
ssu
re (
kbar
)
Time (ms)
Wieland Calibration
123
Figure B13. 3.15 gr/m, 1 cm from Borehole
Figure B14. 3.15 gr/m, 1 cm from Borehole
0
20
40
60
80
100
120
140
0.025 0.027 0.029 0.031 0.033
Pre
ssu
re (
bar)
Time (ms)
Katsabanis Calibration
0
0.02
0.04
0.06
0.08
0.1
0.12
0.025 0.027 0.029 0.031 0.033
Pre
ssu
re (
kbar
)
Time (ms)
Wieland Calibration
124
Figure B15. 3.15 gr/m, 1 cm from Borehole
Figure B16. 3.15 gr/m, 1 cm from Borehole
0
20
40
60
80
100
120
0.01 0.015 0.02 0.025
Pre
ssu
re (
bar)
Time (ms)
Katsabanis Calibration
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.01 0.012 0.014 0.016 0.018 0.02 0.022 0.024
Pre
ssu
re (
kbar
)
Time (ms)
Wieland Calibration
125
Figure B17. 3.15 gr/m, 2 cm from Borehole
Figure B18. 3.15 gr/m, 2 cm from Borehole
0
20
40
60
80
100
120
0.054 0.055 0.056 0.057 0.058 0.059 0.06
Pre
ssu
re (
bar)
Time (ms)
Katsabanis Calibration
0
0.02
0.04
0.06
0.08
0.1
0.12
0.054 0.055 0.056 0.057 0.058 0.059 0.06
Pre
ssu
re (
kbar
)
Time (ms)
Wieland Calibration
126
Figure B19. 21 gr/m, 1 cm from Borehole
Figure B20. 21 gr/m, 1 cm from Borehole
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0.09 0.14 0.19 0.24 0.29
Pre
ssu
re (
bar)
Time (ms)
Katsabanis Calibration
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0.09 0.14 0.19 0.24 0.29
Pre
ssu
re (
kbar
)
Time (ms)
Wieland Calibration
127
Figure B21. 21 gr/m, 3 cm from Borehole
Figure B22. 21 gr/m, 1 cm from Borehole
0
50
100
150
200
250
300
350
0.134 0.139 0.144 0.149 0.154 0.159 0.164
Pre
ssu
re (
bar)
Time (ms)
Katsabanis Calibration
0
0.05
0.1
0.15
0.2
0.25
0.3
0.134 0.139 0.144 0.149 0.154 0.159 0.164
Pre
ssu
re (
kbar
)ar
)
Time (ms)
Wieland Calibration
128
Figure B23. 21 gr/m, 1 cm from Borehole
Figure B24. 21 gr/m, 1 cm from Borehole
0
100
200
300
400
500
600
700
0.084 0.104 0.124 0.144 0.164
Pre
ssu
re (
bar)
Time (ms)
Katsabanis Calibration
0
0.1
0.2
0.3
0.4
0.5
0.6
0.084 0.104 0.124 0.144 0.164
Pre
ssu
re (
kbar
)
Time (ms)
Wieland Calibration
129
Figure B25. 21 gr/m, 4 cm from Borehole
Figure B26. 21 gr/m, 4 cm from Borehole
0
50
100
150
200
250
300
0.118 0.128 0.138 0.148
Pre
ssu
re (
bar)
Time (ms)
Katsabanis Calibration
0
0.05
0.1
0.15
0.2
0.25
0.118 0.123 0.128 0.133 0.138 0.143 0.148 0.153
Pre
ssu
re (
kBar
)
Time (ms)
Wieland Calibration
130
Appendix C – Fragmentation Distribution Curves, Powder Factor = 1.2 kg/m3
Table B1: Size Distribution for Test B1 – Delay = 0 µs (Block#1)
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
179 99.0 99.0 99.0
90 25.2 25.7 28.4
75 22.1 21.3 17.7
63 16.3 17.8 15.5
53 14.7 14.9 13.7
45 13.8 12.6 12.1
37.5 11.6 10.5 10.7
31.5 9.8 8.8 9.3
26.5 7.2 7.4 8.2
18.85 5.0 5.4 7.2
13.33 3.1 3.9 5.5
6.73 1.6 2.2 4.2
4.76 1.3 1.7 2.5
3.36 1.1 1.3 1.9
2.38 1.0 1.0 1.5
1.7 0.8 0.8 1.1
1.18 0.7 0.6 0.9
0.84 0.5 0.5 0.6
0.425 0.2 0.3 0.5
131
Figure C1. Size Distribution Curve for Test B1
0
20
40
60
80
100
0 50 100 150 200
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
132
Table C2: Size Distribution for Test B2 – Delay = 5 µs (Block#1)
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
146 71.5 73.2 65.9
124 66.0 58.2 57.3
111 45.2 49.6 51.6
100 39.4 42.9 46.5
79 29.1 31.5 36.0
53 25.5 20.1 22.3
45 17.3 17.1 18.0
37.5 15.6 14.5 14.2
31.5 12.4 12.5 11.3
26.5 10.2 10.9 8.9
18.85 9.4 8.6 5.6
13.33 7.8 6.9 3.4
6.73 5.1 4.8 1.3
4.76 3.3 4.1 0.8
3.36 2.9 3.5 0.5
2.38 2.2 3.1 0.3
1.7 1.2 2.7 0.2
1.18 1.0 2.4 0.1
0.84 0.7 2.2 0.1
0.425 0.3 1.8 0.0
133
Figure C2. Size Distribution Curve for Test B2
0
20
40
60
80
100
0 50 100 150 200
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
134
Table C3: Size Distribution for Test B3 – Delay = 20 µs (Block#1)
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
129 84.5 81.5 76.9
113 73.2 74.4 71.6
94 68.2 64.2 63.8
88 59.6 60.7 61.0
82 51.5 57.1 58.0
70 47.1 49.4 51.4
63 42.9 44.8 47.2
53 38.2 38.2 40.7
45 35.9 32.9 35.1
37.5 31.3 27.9 29.5
31.5 26.0 24.0 24.9
26.5 21.5 20.7 20.9
18.85 17.2 15.8 14.6
13.33 12.3 12.3 10.0
6.73 7.8 7.9 4.7
4.76 4.3 6.5 3.1
3.36 3.5 5.4 2.1
2.38 2.8 4.5 1.4
1.7 2.4 3.9 1.0
1.18 1.9 3.3 0.6
0.84 1.4 2.9 0.4
0.425 1.0 2.2 0.2
135
Figure C3. Size Distribution Curve for Test B3
0
20
40
60
80
100
0 20 40 60 80 100 120 140
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
136
Table C4: Size Distribution for Test B4 – Delay = 40 µs (Block#1)
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
135 100 98.0 95.1
76 75.3 76.7 75.0
63 66.5 66.1 66.0
53 56.1 56.5 57.4
45 47.6 48.1 49.6
37.5 40.2 39.9 41.5
31.5 35 33.2 34.5
26.5 27.9 27.8 28.5
18.85 20.2 19.7 19.1
13.33 13.2 14.2 12.4
6.73 6.3 8.0 5.2
4.76 5.5 6.1 3.3
3.36 4.5 4.8 2.1
2.38 4.2 3.9 1.3
1.7 3.5 3.2 0.8
1.18 2.8 2.6 0.5
0.84 2.3 2.2 0.3
0.425 1 1.5 0.1
137
Figure C4. Size Distribution Curve for Test B4
0
20
40
60
80
100
0 50 100 150
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
138
Table C5: Size Distribution for Test B5 – Delay = 40 µs (Block#2)
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
180 79.3 82.3 74.9
128 65.1 54.9 55.4
119 58.2 49.8 51.3
115 41.4 47.6 49.4
103 28.9 41.1 43.6
76 27.1 27.8 29.8
72 23.8 26.0 27.8
63 20.8 22.2 23.2
45 18.1 15.4 14.4
37.5 16.7 12.9 11.0
31.5 14.6 11.0 8.5
26.5 11.6 9.4 6.5
18.85 7.3 7.2 3.9
13.33 4.7 5.6 2.2
6.73 2.5 3.7 0.8
4.76 2.0 3.1 0.4
3.36 1.6 2.6 0.3
2.38 1.3 2.2 0.2
1.7 1.1 1.9 0.1
1.18 0.9 1.6 0.0
0.425 0.3 1.1 0.0
139
Figure C5. Size Distribution Curve for Test B5
0.0
20.0
40.0
60.0
80.0
100.0
0 50 100 150 200
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
140
Table C6: Size Distribution for Test B6 – Delay = 200 µs (Block#2)
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
142 93.6 92.4 91.1
123 90.5 86.0 85.0
118 87.1 83.8 83.0
111 82.6 80.3 79.7
105 69.5 76.9 76.6
97 65.9 71.8 71.9
89 63.7 66.0 66.7
72 57.5 52.1 53.6
63 45.1 44.2 45.8
53 35.4 35.4 36.7
45 30.6 28.6 29.4
37.5 22.7 22.5 22.5
31.5 17.1 18.1 17.3
26.5 14.5 14.6 13.3
18.85 9.4 9.8 7.7
13.33 5.2 6.8 4.4
6.73 2.2 3.6 1.4
4.76 1.7 2.7 0.8
3.36 1.3 2.1 0.4
2.38 1.2 1.6 0.2
1.7 1.0 1.3 0.1
1.18 0.8 1.1 0.1
0.425 0.3 0.6 0.0
141
Figure C6. Size Distribution Curve for Test B6
0.0
20.0
40.0
60.0
80.0
100.0
0 50 100 150
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
142
Appendix D – Fragmentation Distribution Curves, Powder Factor = 2.4 kg/m3
Table D1: Size Distribution for Test C1 – Delay = 10 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
151 90.7 82.6 75.7
137 77.9 77.1 72.6
130 71.7 74.1 70.8
110 62.4 65.2 65.2
103 58.3 61.9 63.0
100 56.1 60.5 62.0
94 51.0 57.6 59.9
70 48.4 45.9 50.1
63 44.5 42.4 46.8
53 42.0 37.4 41.6
45 37.7 33.4 37.0
37.5 33.8 29.7 32.4
31.5 29.7 26.6 28.3
26.5 25.9 24.0 24.7
22.4 22.3 21.8 21.6
18.85 19.6 19.9 18.7
13.33 14.8 16.7 14.0
9.5 11.9 14.2 10.4
6.73 9.1 12.3 7.7
4.76 7.4 10.7 5.7
3.36 6.1 9.4 4.1
2.38 5.3 8.4 3.0
1.7 4.6 7.5 2.2
1.18 3.8 6.7 1.6
0.84 3.2 6.1 1.2
0.45 1.4 5.2 0.7
143
Figure D1. Size Distribution Curve for Test C1
0
20
40
60
80
100
0 50 100 150 200
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
144
Table D2: Size Distribution for Test C2 – Delay = 40 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
130 91.5 90.1 78.4
128 82.7 88.2 77.4
111 77.0 71.0 68.5
108 71.2 67.9 66.7
103 66.1 62.9 63.6
99 64.4 59.0 61.0
95 58.9 55.3 58.3
92 44.6 52.6 56.2
89 42.1 50.0 54.1
84 40.4 45.8 50.4
82 38.3 44.2 48.9
74 35.8 38.3 42.8
63 32.9 31.0 34.3
53 31.0 25.4 26.5
45 25.6 21.3 20.6
37.5 22.3 17.9 15.3
31.5 18.8 15.4 11.5
26.5 17.8 13.4 8.5
18.85 11.1 10.6 4.7
13.33 6.7 8.5 2.6
6.73 3.2 6.0 0.8
4.76 2.5 5.2 0.4
3.36 1.9 4.5 0.2
2.38 1.5 4.0 0.1
1.7 1.2 3.6 0.1
1.18 0.9 3.2 0.0
0.84 0.7 2.9 0.0
0.425 0.2 2.4 0.0
145
Figure D2. Size Distribution Curve for Test C2
-20
0
20
40
60
80
100
0 20 40 60 80 100 120 140
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
146
Table D3: Size Distribution for Test C3 – Delay = 80 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
103 94.8 92.9 89.9
99 92.7 91.8 88.9
87 86.7 87.8 85.5
82 84.5 85.7 83.7
78 81.4 83.8 82.2
63 76.2 75.1 75.1
53 70.0 67.7 68.8
45 59.5 60.7 62.7
37.5 53.6 53.4 55.9
31.5 46.8 47.0 49.6
26.5 41.3 41.3 43.7
22.4 36.4 36.4 38.4
18.85 32.1 32.0 33.4
13.33 24.0 24.9 24.8
9.5 19.9 19.6 18.3
6.73 15.1 15.7 13.2
4.76 12.7 12.6 9.5
3.36 10.7 10.3 6.8
2.38 9.2 8.6 4.8
1.7 8.0 7.2 3.4
1.18 6.5 6.0 2.4
0.84 5.3 5.2 1.7
0.425 2.0 3.9 0.8
147
Figure D3. Size Distribution Curve for Test C3
0
20
40
60
80
100
0 20 40 60 80 100 120
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
148
Table D4: Size Distribution for Test C4 – Delay = 100 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
82 96.2 96.6 92.4
63 90.1 89.7 86.2
53 83.8 83.4 81.2
45 76.0 76.7 75.8
37.5 68.4 68.8 69.4
31.5 60.7 61.4 63.1
26.5 55.0 54.4 56.9
22.4 49.5 48.2 50.9
18.85 43.0 42.5 45.1
13.33 32.5 33.0 34.7
9.5 25.6 25.9 26.2
6.73 19.5 20.5 19.4
4.76 16.0 16.5 14.2
3.36 13.3 13.4 10.3
2.38 11.3 11.0 7.4
1.7 9.8 9.2 5.4
0.84 7.6 6.6 2.7
0.425 4.9 4.9 1.4
149
Figure D4. Size Distribution Curve for Test C4
0
20
40
60
80
100
0 20 40 60 80 100
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
150
Table D5: Size Distribution for Test C5 – Delay = 100 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
94 98.6 97.7 96.6
84 96.1 95.8 94.6
76 93.6 93.4 92.3
71 91.5 91.5 90.4
63 89.6 87.3 86.5
53 79.0 80.1 79.8
45 69.6 72.2 72.6
37.5 61.5 62.9 64.0
31.5 55.3 54.3 55.7
26.5 46.3 46.4 47.8
22.4 41.6 39.5 40.7
18.85 35.5 33.5 34.1
13.33 23.4 24.0 23.4
9.5 17.1 17.5 15.7
6.73 11.4 12.9 10.4
4.76 8.5 9.7 6.7
3.36 6.4 7.4 4.3
2.38 5.4 5.8 2.8
1.7 4.4 4.6 1.8
1.18 3.3 3.7 1.1
0.84 2.7 3.0 0.7
0.425 1.1 2.1 0.3
151
Figure D5. Size Distribution Curve for Test C5
0
20
40
60
80
100
0 20 40 60 80 100
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
152
Table D6: Size Distribution for Test C6 – Delay = 200 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
63 92.8 93.5 92.8
53 87.8 87.5 87.8
45 81.1 80.8 81.1
37.5 72.6 72.7 72.6
31.5 65.3 65.0 65.3
26.5 57.7 57.7 57.7
22.4 51.4 51.2 51.4
18.85 46.0 45.2 46.0
13.33 33.7 35.3 33.7
9.5 27.4 27.9 27.4
6.73 22.5 22.3 22.5
4.76 18.2 18.0 18.2
3.36 15.2 14.8 15.2
2.38 12.7 12.3 12.7
1.7 10.9 10.4 10.9
0.84 7.8 7.6 7.8
0.425 5.3 5.8 5.3
153
Figure D6. Size Distribution Curve for Test C6
0
20
40
60
80
100
0 10 20 30 40 50 60 70
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
154
Table D7: Size Distribution for Test C7 – Delay = 200 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
101 97.6 94.3 95.5
96 93.9 93.3 94.4
90 89.9 91.9 92.8
63 79.8 80.2 79.7
53 69.5 72.2 71.4
45 64.4 63.9 63.0
37.5 55.6 54.2 53.6
31.5 46.8 45.3 45.2
26.5 36.9 37.2 37.6
18.85 24.0 24.4 25.3
13.33 14.5 15.6 16.4
6.73 6.2 6.7 6.6
4.76 4.8 4.4 4.1
3.36 3.8 3.0 2.5
2.38 3.4 2.1 1.6
1.7 2.8 1.5 1.0
1.18 2.2 1.1 0.6
0.84 1.8 0.8 0.4
0.425 0.8 0.5 0.1
155
Figure D7. Size Distribution Curve for Test C7
0
20
40
60
80
100
0 20 40 60 80 100 120
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
156
Table D8: Size Distribution for Test C8 – Delay = 400 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
93 96.6 98.0 97.7
63 91.5 89.3 88.5
53 80.2 82.4 81.7
45 74.8 74.4 73.9
37.5 64.7 64.5 64.6
31.5 54.1 55.0 55.6
26.5 48.4 46.0 47.0
18.85 31.2 31.5 32.5
13.33 19.3 21.1 21.4
6.73 9.1 10.0 8.7
4.76 7.0 7.1 5.4
3.36 5.5 5.1 3.4
2.38 4.7 3.8 2.1
1.7 3.9 2.9 1.3
1.18 3.2 2.2 0.8
0.84 2.6 1.7 0.5
0.425 1.2 1.1 0.2
157
Figure D8. Size Distribution Curve for Test C8
0
20
40
60
80
100
0 20 40 60 80 100
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
158
Table D9: Size Distribution for Test C9 – Delay = 500 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
63 90.4 91.9 90.2
53 85.9 87.0 85.4
45 82.2 81.2 80.1
37.5 75.4 73.9 73.5
31.5 67.5 66.4 66.7
26.5 58.4 59.0 59.8
22.4 51.0 52.0 53.3
18.85 46.0 45.3 46.8
13.33 32.3 33.9 35.3
9.5 25.7 25.4 26.0
6.73 18.4 19.1 18.8
4.76 14.5 14.5 13.3
3.36 11.4 11.1 9.4
2.38 9.4 8.7 6.6
1.7 7.9 6.9 4.6
1.18 6.1 5.5 3.1
0.84 4.8 4.5 2.2
0.425 1.8 3.1 1.1
159
Figure D9. Size Distribution Curve for Test C9
0
20
40
60
80
100
0 10 20 30 40 50 60 70
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
160
Table D10: Size Distribution for Test C10 – Delay = 600 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
63 96.4 94.9 90.9
53 90.3 89.6 86.3
45 81.9 83.0 81.2
37.5 73.0 74.7 74.6
31.5 66.9 66.4 67.9
26.5 58.4 58.4 61.1
18.85 46.3 44.5 48.0
13.33 33.0 33.5 36.3
6.73 19.4 19.7 19.5
4.76 15.3 15.4 13.9
3.36 12.3 12.3 9.7
2.38 10.6 9.9 6.8
1.7 8.6 8.2 4.8
1.18 6.8 6.7 3.3
0.84 5.4 5.7 2.3
0.425 2.0 4.2 1.1
161
Figure D10. Size Distribution Curve for Test C10
0
20
40
60
80
100
0 10 20 30 40 50 60 70
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
162
Table D11: Size Distribution for Test C11 – Delay = 700 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
63 98.0 97.6 95.5
53 93.9 94.6 92.3
45 88.3 90.3 88.3
37.5 83.8 84.0 82.8
31.5 77.2 77.0 76.7
26.5 71.4 69.4 70.1
22.4 63.4 62.0 63.4
18.85 55.6 54.6 56.5
13.33 38.6 41.5 43.5
9.5 30.4 31.4 32.7
6.73 22.4 23.8 23.8
4.76 17.9 18.2 17.0
3.36 14.5 14.1 12.0
2.38 12.5 11.1 8.4
1.7 10.6 8.9 5.9
1.18 8.5 7.2 4.0
0.84 98.0 97.6 95.5
0.425 93.9 94.6 92.3
163
Figure D11. Size Distribution Curve for Test C11
0
20
40
60
80
100
0 10 20 30 40 50 60 70
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
164
Table D12: Size Distribution for Test C12 – Delay = 800 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
63 96.1 96.8 94.8
53 93.9 93.3 91.3
45 90.0 88.7 87.0
37.5 79.8 82.1 81.1
31.5 75.4 74.8 74.6
26.5 68.0 67.1 67.7
22.4 59.9 59.5 60.9
18.85 51.6 52.0 53.9
13.33 37.2 39.0 41.0
9.5 30.0 29.1 30.4
6.73 22.5 21.7 21.9
4.76 17.3 16.4 15.5
3.36 11.9 12.5 10.8
2.38 9.6 9.7 7.5
1.7 8.0 7.7 5.2
1.18 6.0 6.1 3.5
0.84 4.9 5.0 2.4
0.425 2.3 3.4 1.1
165
Figure D12. Size Distribution Curve for Test C12
0.0
20.0
40.0
60.0
80.0
100.0
0 10 20 30 40 50 60 70
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
166
Table D13: Size Distribution for Test C13 – Delay = 800 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
63 94.8 96.3 91.0
53 88.7 89.0 85.1
45 78.8 79.8 78.2
37.5 71.5 68.5 69.6
31.5 60.7 58.1 60.9
26.5 46.0 48.9 52.4
18.85 33.3 34.7 37.3
13.33 22.5 25.0 25.2
6.73 15.0 14.1 10.8
4.76 12.1 10.9 6.9
3.36 10.1 8.7 4.4
2.38 8.7 7.0 2.7
1.7 7.2 5.8 1.7
1.18 5.7 4.8 1.1
0.84 2.8 4.1 0.7
0.425 1.5 3.1 0.3
167
Figure D13. Size Distribution Curve for Test C13
0
20
40
60
80
100
0 10 20 30 40 50 60 70
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
168
Table D14: Size Distribution for Test C14 – Delay = 1000 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
63 90.9 91.4 89.2
53 87.0 86.7 84.9
45 81.8 81.4 80.2
37.5 74.2 74.7 74.3
31.5 68.0 67.9 68.3
26.5 61.2 61.0 62.3
18.85 49.1 48.4 50.6
13.33 36.4 37.5 39.7
6.73 21.3 22.5 23.2
4.76 17.7 17.5 17.2
3.36 14.5 13.8 12.7
2.38 11.7 11.0 9.3
1.7 10.0 8.9 6.8
1.18 7.8 7.2 4.9
0.84 5.9 6.0 3.5
0.425 2.0 4.2 1.9
63 90.9 91.4 89.2
53 87.0 86.7 84.9
169
Figure D14. Size Distribution Curve for Test C14
0.0
20.0
40.0
60.0
80.0
100.0
0 10 20 30 40 50 60 70
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
170
Table D15: Size Distribution for Test C15 – Delay = 1000 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
63 97.4 96.3 92.7
53 91.9 91.9 88.7
45 83.6 86.2 83.9
37.5 78.1 78.6 77.8
31.5 71.4 70.8 71.4
26.5 65.5 62.9 64.7
22.4 56.4 55.7 58.1
18.85 49.4 48.8 51.5
13.33 34.3 37.2 39.4
9.5 28.0 28.6 29.5
6.73 21.4 22.2 21.5
4.76 17.2 17.4 15.4
3.36 14.1 13.8 10.9
2.38 12.2 11.2 7.7
1.7 10.4 9.2 5.4
1.18 8.4 7.6 3.7
0.84 6.9 6.4 2.6
0.425 2.7 4.7 1.3
171
Figure D15. Size Distribution Curve for Test C15
0.0
20.0
40.0
60.0
80.0
100.0
0 10 20 30 40 50 60 70
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
172
Table D16: Size Distribution for Test C16 – Delay = 1400 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
141 98.4 97.5 97.1
115 95.0 94.9 94.4
106 94.1 93.5 93.0
85 91.5 88.6 88.1
77 85.6 85.9 85.5
63 77.8 79.6 79.4
53 70.7 73.4 73.5
45 65.9 67.3 67.7
37.5 59.7 60.4 61.0
31.5 55.1 54.0 54.6
26.5 49.8 47.9 48.6
22.4 44.7 42.5 43.0
18.85 39.2 37.4 37.7
13.33 27.5 28.8 28.5
9.5 21.3 22.3 21.2
6.73 15.6 17.3 15.6
4.76 12.2 13.6 11.3
3.36 8.6 10.7 8.1
2.38 7.3 8.6 5.8
1.7 6.2 7.0 4.2
1.18 4.6 5.6 2.9
0.84 3.4 4.7 2.1
0.425 1.3 3.3 1.1
173
Figure D16. Size Distribution Curve for Test C16
0.0
20.0
40.0
60.0
80.0
100.0
0 50 100 150
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
174
Table D17: Size Distribution for Test C17 – Delay = 1500 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
63 92.9 92.9 87.4
53 88.3 86.8 82.7
45 80.4 79.9 77.6
37.5 69.7 71.7 71.6
31.5 62.5 63.9 65.5
26.5 57.1 56.6 59.4
22.4 50.8 50.2 53.6
18.85 44.7 44.2 47.8
13.33 34.4 34.5 37.3
9.5 28.3 27.3 28.6
6.73 21.4 21.8 21.5
4.76 17.9 17.6 15.9
3.36 14.7 14.5 11.7
2.38 12.5 12.0 8.5
1.7 10.7 10.2 6.3
1.18 8.6 8.6 4.5
0.84 7.0 7.4 3.2
0.425 2.6 5.7 1.7
175
Figure D17. Size Distribution Curve for Test C17
0.0
20.0
40.0
60.0
80.0
100.0
0 10 20 30 40 50 60 70
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
176
Table D18: Size Distribution for Test C18 – Delay = 1800 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
110 97.3 98.9 97.2
85 94.9 94.7 92.6
81 92.2 93.5 91.4
63 85.9 84.8 83.4
53 78.4 77.0 76.6
45 68.6 69.0 69.5
37.5 59.8 60.0 61.3
31.5 51.2 51.8 53.5
26.5 44.5 44.5 46.1
22.4 38.1 38.2 39.5
18.85 32.7 32.6 33.4
13.33 22.9 23.8 23.3
9.5 17.8 17.8 16.0
6.73 12.6 13.4 10.8
4.76 11.5 10.3 7.2
3.36 9.6 8.1 4.7
2.38 8.1 6.4 3.1
1.7 5.9 5.2 2.1
1.18 4.8 4.2 1.3
0.84 3.6 3.5 0.9
0.425 1.3 2.5 0.4
177
Figure D18. Size Distribution Curve for Test C18
0.0
20.0
40.0
60.0
80.0
100.0
0 20 40 60 80 100 120
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
178
Table D19: Size Distribution for Test C19 – Delay = 2000 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
115 95.0 87.7 86.0
109 83.9 85.5 84.2
104 79.6 83.5 82.4
88 74.9 75.8 75.7
80 71.9 71.1 71.6
77 67.0 69.2 69.9
75 64.1 67.9 68.7
63 62.3 59.5 60.9
53 55.2 51.8 53.2
45 45.8 45.1 46.2
37.5 38.4 38.7 39.1
31.5 33.5 33.3 33.0
26.5 29.1 28.9 27.6
18.85 19.6 21.9 19.2
13.33 13.0 16.9 13.0
6.73 7.5 10.6 5.8
4.76 5.9 8.6 3.8
3.36 4.9 7.0 2.5
2.38 4.3 5.8 1.7
1.7 3.5 4.9 1.1
1.18 2.8 4.1 0.7
0.84 2.3 3.6 0.5
0.425 1.0 2.7 0.2
179
Figure D19. Size Distribution Curve for Test C19
0.0
20.0
40.0
60.0
80.0
100.0
0 20 40 60 80 100 120 140
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
180
Table D20: Size Distribution for Test C20 – Delay = 2000 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
110 95.3 91.0 89.2
98 85.7 88.3 86.5
63 71.9 74.5 73.8
53 67.3 68.3 68.1
45 63.5 62.3 62.7
37.5 56.3 55.8 56.6
31.5 50.1 49.8 50.9
26.5 44.8 44.3 45.6
22.4 40.6 39.4 40.7
18.85 36.0 34.9 36.0
13.33 25.9 27.2 27.8
9.5 21.0 21.4 21.3
6.73 15.9 16.9 16.1
4.76 12.9 13.5 12.0
3.36 10.6 10.8 8.9
2.38 9.0 8.8 6.6
1.7 7.8 7.3 4.9
1.18 6.5 6.0 3.5
0.84 5.2 5.0 2.6
0.425 2.3 3.6 1.4
181
Figure D20. Size Distribution Curve for Test C20
0.0
20.0
40.0
60.0
80.0
100.0
0 20 40 60 80 100 120
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
182
Appendix E – Fragmentation Distribution Curves, Copper lined Blast-holes
Table E1: Size Distribution for Test D1 – Delay = 40 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
149 92.3 88.8 89.4
114 86.8 83.7 83.8
110 77.9 82.9 83
104 75.4 81.7 81.6
63 72.5 68.8 68.2
53 65.6 63.8 63.3
45 60.2 59 58.6
37.5 55.1 53.7 53.4
31.5 48.5 48.8 48.7
26.5 42.9 44.1 44.2
22.4 39.1 39.7 40
18.85 34.7 35.6 36
13.33 26.8 28.3 28.92
9.5 22.1 22.5 23
6.73 16.9 17.7 18.1
4.76 13.8 14 14.1
3.36 11.4 11.1 11
2.38 9.9 8.8 8.5
1.7 8.4 7.1 6.6
1.18 6.9 5.6 5
0.84 5.4 4.6 3.8
0.425 2.1 3.1 2.3
183
Figure E1. Size Distribution Curve for Test D1
0
20
40
60
80
100
0 50 100 150 200
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
184
Table E2: Size Distribution for Test D2 – Delay = 80 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
124 93.4 84.7 81.3
102 73.1 77.4 75.3
85 71.0 70.1 69.2
81 63.5 68.2 67.6
69 60.7 61.7 62.1
63 55.6 58.1 59.0
53 49.5 51.5 53.2
45 45.8 45.9 47.9
37.5 42.2 40.1 42.3
31.5 38.3 35.3 37.3
26.5 34.3 31.1 32.8
22.4 29.6 27.5 28.8
18.85 25.8 24.4 25.1
13.33 18.8 19.2 18.9
9.5 15.4 15.3 14.1
6.73 11.1 12.4 10.5
4.76 8.8 10.1 7.7
3.36 7.0 8.3 5.6
2.38 5.8 7.0 4.1
1.7 4.8 5.9 3.0
1.18 3.6 5.0 2.2
0.84 2.8 4.3 1.6
0.425 1.0 3.2 0.8
185
Figure E2. Size Distribution Curve for Test D2
0
20
40
60
80
100
0 20 40 60 80 100 120 140
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
186
Table E3: Size Distribution for Test D3 – Delay = 100 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
120 97.5 99.8 99.2
63 92.9 90.7 89.0
53 82.3 84.8 83.4
45 78.5 78.1 77.1
37.5 69.5 69.6 69.4
31.5 61.5 61.2 61.8
26.5 53.3 53.1 54.2
22.4 46.5 45.8 47.2
18.85 39.4 39.1 40.5
13.33 27.3 28.1 29.0
9.5 19.4 20.4 20.4
6.73 14.3 14.9 14.0
4.76 11.3 11.1 9.5
3.36 9.0 8.4 6.3
2.38 7.3 6.4 4.2
1.7 6.0 5.1 2.9
0.84 4.6 3.2 1.2
0.425 - 2.2 0.5
187
Figure E3. Size Distribution Curve for Test D3
0
20
40
60
80
100
0 20 40 60 80 100 120 140
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
188
Table E4: Size Distribution for Test D4 – Delay = 200 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
118 97.3 98.7 98.1
93 94.2 96.1 95.1
63 87.3 86.6 85.4
53 78.6 80.3 79.3
45 75.5 73.4 72.8
37.5 66.9 65.2 65.2
31.5 58.1 57.3 57.8
26.5 49.3 49.7 50.7
22.4 41.0 42.9 44.1
18.85 36.5 36.7 37.9
13.33 25.3 26.6 27.3
9.5 18.3 19.4 19.4
6.73 14.1 14.2 13.5
4.76 11.9 10.6 9.2
3.36 8.8 8.0 6.3
2.38 7.8 6.1 4.2
1.7 6.5 4.8 2.9
0.84 4.3 3.0 1.3
0.425 - 2.0 0.6
189
Figure E4. Size Distribution Curve for Test D4
0
20
40
60
80
100
0 20 40 60 80 100 120 140
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
190
Table E5: Size Distribution for Test D5 – Delay = 200 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
120 96.6 97.2 95.1
92 93.2 92.5 90.4
84 91.2 90.3 88.3
71 87.3 85.4 83.9
63 79.9 81.4 80.4
53 73.2 75.1 74.8
45 67.9 68.7 69.2
37.5 61.6 61.6 62.8
31.5 55.8 55.0 56.7
26.5 49.5 48.9 50.8
22.4 43.6 43.4 45.3
18.85 39.4 38.3 40.0
13.33 28.9 29.7 30.7
9.5 23.3 23.3 23.3
6.73 17.6 18.3 17.3
4.76 14.4 14.5 12.8
3.36 11.8 11.7 9.3
2.38 10.1 9.5 6.8
1.7 8.5 7.8 5.0
1.18 6.8 6.4 3.5
0.84 5.1 5.4 2.5
0.425 1.9 3.9 1.3
191
Figure E5. Size Distribution Curve for Test D5
0
20
40
60
80
100
0 20 40 60 80 100 120 140
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
192
Table E6: Size Distribution for Test D6 – Delay = 700 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
120 93.8 95.2 97.3
98 90.8 92.9 94.9
63 83.8 85.0 85.9
53 82.8 80.7 80.9
45 76.0 76.1 75.8
37.5 70.3 70.3 69.6
31.5 65.9 64.4 63.5
26.5 59.5 58.4 57.5
22.4 53.0 52.4 51.7
18.85 46.4 46.5 46.1
13.33 33.2 35.6 35.8
9.5 25.6 26.7 27.4
6.73 18.1 19.6 20.6
4.76 13.9 14.3 15.3
3.36 11.0 10.4 11.2
2.38 8.9 7.7 8.2
1.7 7.3 5.7 6.0
1.18 5.9 4.2 4.3
0.84 4.7 3.2 3.1
0.425 2.0 1.9 1.6
193
Figure E6. Size Distribution Curve for Test D6
0
20
40
60
80
100
0 20 40 60 80 100 120 140
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
194
Table E7: Size Distribution for Test D7 – Delay = 800 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
132 89.6 92.4 93.5
114 86.8 90.1 90.9
90 84.5 85.5 85.8
79 83.3 82.5 82.5
63 80.1 76.5 76.1
53 73.4 71.4 70.8
45 68.9 66.3 65.6
37.5 61.0 60.3 59.8
31.5 52.9 54.6 54.3
26.5 48.1 49.1 49.0
22.4 42.7 43.9 44.1
18.85 38.2 38.9 39.3
13.33 27.8 30.2 30.9
9.5 23.1 23.2 24.0
6.73 17.1 17.8 18.4
4.76 14.1 13.5 14.0
3.36 11.5 10.4 10.5
2.38 9.9 8.0 7.9
1.7 8.3 6.3 6.0
1.18 6.2 4.8 4.4
0.84 3.4 3.8 3.3
0.425 1.7 2.5 1.8
195
Figure E7. Size Distribution Curve for Test D7
0
20
40
60
80
100
0 20 40 60 80 100 120 140
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
196
Table E8: Size Distribution for Test D8 – Delay = 1200 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
139 91.2 91.8 93.3
108 84.4 86.9 87.9
83 81.7 80.2 80.3
77 79.4 78.0 77.9
63 72.5 71.5 71.0
53 64.9 65.5 64.8
45 59.5 59.5 58.8
37.5 52.4 52.9 52.4
31.5 47.1 46.7 46.4
26.5 41.1 40.9 40.9
22.4 35.1 35.7 36.0
18.85 29.4 30.9 31.3
13.33 22.8 22.8 23.4
9.5 18.0 16.8 17.4
6.73 12.6 12.3 12.7
4.76 9.4 9.1 9.2
3.36 6.9 6.7 6.6
2.38 5.8 5.0 4.7
1.7 4.7 3.8 3.4
1.18 3.5 2.9 2.4
0.84 2.5 2.2 1.7
0.425 1.1 1.4 0.9
197
Figure E8. Size Distribution Curve for Test D8
0.0
20.0
40.0
60.0
80.0
100.0
0 50 100 150
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
198
Appendix F – Fragmentation Distribution Curves, Granite Bench
Table F1: Size Distribution for Test E1 – Delay = 500 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
228 97.5 92.4 85.1
220 90.4 90.7 83.9
201 83.8 85.8 80.5
191 80.7 82.8 78.5
170 78.1 75.7 73.6
160 76.8 72.0 71.0
159 75.5 71.6 70.7
155 73.1 70.0 69.6
153 71.0 69.3 69.0
151 69.3 68.5 68.4
148 68.1 67.3 67.5
145 64.5 66.1 66.6
142 63.2 64.9 65.7
140 61.9 64.0 65.1
138 61.1 63.2 64.4
133 57.4 61.1 62.8
129 55.9 59.4 61.4
125 53.1 57.7 60.0
120 50.9 55.6 58.2
116 49.5 53.9 56.7
110 48.8 51.3 54.4
106 46.8 49.6 52.7
103 45.7 48.3 51.5
85 44.3 40.5 43.6
80 43.3 38.3 41.3
75 43.0 36.2 38.9
70 40.0 34.1 36.4
199
63 35.3 31.1 32.8
53 29.9 27.0 27.6
45 25.1 23.7 23.2
37.5 22.1 20.6 19.1
31.5 19.5 18.2 15.7
26.5 15.5 16.2 13.0
22.4 12.8 14.5 10.7
18.85 11.4 13.0 8.8
13.33 7.9 10.7 5.8
9.5 5.7 8.9 3.9
6.73 4.7 7.5 2.6
4.76 4.2 6.4 1.7
3.36 3.8 5.6 1.1
2.38 3.3 4.9 0.7
1.7 2.8 4.3 0.5
1.18 2.1 3.8 0.3
0.84 1.4 3.4 0.2
0.425 0.5 2.8 0.1
200
Figure F1. Size Distribution Curve for Test E1
0
20
40
60
80
100
0 50 100 150 200 250
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
201
Table F2: Size Distribution for Test E2 – Delay = 1000 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
340 95.9 100 90.8
238 93.1 82.7 77.3
230 89.4 80.3 75.8
228 87.8 79.6 75.4
225 82.2 78.7 74.8
214 75.6 75.2 72.4
208 70.7 73.2 71.1
204 69.2 71.9 70.2
185 68.1 65.4 65.4
180 66.3 63.6 64.1
178 65 62.9 63.6
175 62.2 61.9 62.7
170 60.3 60.1 61.3
163 58.4 57.6 59.3
160 54.4 56.6 58.4
158 51.2 55.9 57.8
155 50.4 54.8 56.8
150 49.6 53.1 55.3
148 48.9 52.4 54.6
145 46.3 51.3 53.7
140 45.9 49.6 52.0
132 44.9 46.8 49.3
130 43.4 46.1 48.6
127 42.5 45.1 47.5
125 41.2 44.4 46.8
122 40.6 43.3 45.8
120 39.8 42.7 45.0
115 39.2 41.0 43.2
113 38.4 40.3 42.5
202
109 37.1 39.0 41.0
97 36.5 35.0 36.3
95 36.1 34.4 35.5
88 35.1 32.1 32.7
73 34.8 27.5 26.6
63 27.6 24.4 22.5
53 24 21.4 18.3
45 21.2 19.1 15.0
37.5 19.2 16.9 12.0
31.5 17.5 15.1 9.7
26.5 16.1 13.6 7.8
22.4 14.9 12.4 6.3
18.85 13.9 11.3 5.0
13.33 11.7 9.4 3.2
9.5 10.2 8.1 2.1
6.73 8.3 7.0 1.3
4.76 7 6.1 0.8
3.36 5.7 5.3 0.5
2.38 4.8 4.7 0.3
1.7 4.1 4.3 0.2
1.18 3.2 3.8 0.1
0.84 2.5 3.5 0.1
0.425 1.3 2.9 0.0
203
Figure F2. Size Distribution Curve for Test E2
0
20
40
60
80
100
0 100 200 300 400
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
204
Table F3: Size Distribution for Test E3 – Delay = 2000 µs
Size
(mm)
Passing %
(Experimental)
Passing %
(Swebrec)
Passing % (Rosin-
Rammler)
215 96.5 90.8 90.7
209 91.8 90.2 90.1
185 87.5 87.6 87.4
170 86.0 85.5 85.3
160 83.9 84.0 83.7
155 81.2 83.1 82.8
145 79.7 81.2 81.0
135 78.8 79.1 78.9
132 77.8 78.5 78.2
128 73.8 77.5 77.2
125 73.2 76.8 76.5
115 70.9 74.1 73.9
109 70.2 72.3 72.1
105 69.7 71.1 70.9
101 68.4 69.8 69.6
95 67.9 67.7 67.6
90 67.0 65.8 65.8
84 65.1 63.4 63.5
80 64.3 61.7 61.8
75 63.8 59.5 59.6
70 63.3 57.1 57.3
63 55.7 53.5 53.9
53 48.1 47.8 48.3
45 42.3 42.7 43.4
37.5 38.0 37.5 38.2
31.5 34.5 33.0 33.7
26.5 24.2 29.0 29.6
22.4 21.4 25.6 26.0
18.85 19.4 22.5 22.6
205
13.33 16.1 17.3 17.1
9.5 13.9 13.5 12.8
6.73 11.5 10.6 9.5
4.76 10.0 8.4 7.0
3.36 8.4 6.7 5.2
2.38 7.1 5.4 3.8
1.7 6.1 4.4 2.8
1.18 4.8 3.6 2.0
0.84 3.2 2.9 1.5
0.425 1.6 2.1 0.8
Figure F3. Size Distribution Curve for Test E3
0.0
20.0
40.0
60.0
80.0
100.0
0 50 100 150 200 250
Pas
sin
g (%
)
Size (mm)
Size Distribution
Experiment
Swebrec
Rosin-Rammler
