Fragmentation analysis of optimized blasting rounds in the Aitik mine
- effect of specific charge
Vasileios Demenegas
Luleå University of Technology Master Thesis, Continuation Courses Mining and geotechnical engineering Department of Civil and Environmental Engineering
Division of Rock Engineering
OPTIMIZED BLASTING ROUNDS IN THE AITIK MINE - EFFECT OF SPECIFIC
CHARGE
VASILEIOS DEMENEGAS
Luleå University of Technology
This thesis summarizes the work done at the Swedish blasting research center at Luleå University of Technology. The supervisor for this thesis was Professor Finn Ouchterlony. The thesis is part of a related project of the Swedish blasting research center named “Model for bench blasting in open pits” and it was performed at Boliden’s Aitik copper mine.
The entire Project was sponsored by the Swedish blasting research center in LTU.
I would firstly like to thank my supervisor, Professor Finn Ouchterlony for his valuable guidance and support throughout the course of this project. Special thanks go to Ulf Nyberg of the Swedish blasting research center for all his help, advice and encouragement. The contribution of Boliden’s Peter Bergman and of the entire Aitik mine’s engineering staff in field data acquisition is gratefully acknowledged.
Finally my deep gratitude goes to my parents Αντώνιος and Παρασκευή for their invaluable support and patience throughout the course of my academic studies.
I detta Masters-arbete undersöks vilken effekt som en höjd specifik laddning har på styckefallet. Arbete är kopplat till Swebrecs projekt ”Modell för pallsprängning och förkross i dagbrott” och Boliden Minerals projekt ”G5 Optimerad sprängning i Aitik”.
Fältdelen utfördes i Boliden Minerals Aitikgruva i Gällivare. Målet kom att bli att mäta den skillnad i styckefall som den högre specifika laddningen, ca 1,35 kg/m3, orsakar i ena halvan av salva 5162 orsakar. Den andra halvan av salvan hade normal specifik laddning, 1,0-,1 kg/m3.
En kombination av bildanalys och siktning har använts för att bestämma styckefallet i de två salvhalvorna. För bildanalysen användes mjukvaran Split Desktop. Över 250 bilder av trucklass togs nära lastningen. Av dessa valdes 60, 30 från vardera salvahalvan, ut enligt ett kvalitetskriterium och analyserades med Split Desktop.
Dessutom togs fyra stickprov, två från vardera salvhalva, som siktades vid ett ackrediterat laboratorium.
I fältarbete ingick en detaljerad uppföljning av borrnings- och laddningsarbetet.
Denna plus övrig information från gruvans personal användes för att räkna fram den förväntade styckefallet i salvhalvorna enligt de teoretiska CZM och KCO-modellerna.
Resultaten pekar på betydande skillnader i finandelen medan skillnaderna i storstensområdet är betydligt mindre.
Styckefallsanalysen har gett ett blandat resultat. För medelstyckefallet x50 är skillnaden på 233 – 200 = 33 mm mellan hög och normal specifik laddning statistiskt säkerställd men detta gäller inte för alla skillnaden mellan 10%-percentiler. Runt hälften av dem innehåller värdet 0, dvs. skillnaden är inte säkerställd.
Å andra sidan så gäller att den enligt CZM- och KCO-modellerna förväntade skillnaden i t.ex. x50 och x80 är ungefär lika stor. Detta leder till slutsatsen att en utvärdering av fler foton, vilket skulle ge snävare konfidensintervall, förmodligen skulle kunna säkerställa skillnaderna.
medelkurva för styckefallet i de två salvhalvorna. Passningen blev god för båda halvorna och korrelationen hög, r2 > 0,999.
Boliden Mineral ställde också en modell för primärkrossen i Aitik till förfogande.
Dess förmåga att återge styckefallet för produkten testades när de olika fördelningarna för inmatat salvberg användes. Modellens beräknade utfall jämfördes med mätvärden som erhållits för respektive salvhalva genom systemets Split Online som finns installerat över bandet efter förkrossen.
Det är möjligt att krossmodellen underskattar bildandet av finmaterial i krossprocessen. Vidare så måste troligtvis den teoretiska CZM-modellen förbättras eftersom inmatat material innehåller mer fint än produkten mätt med Split Online.
This report investigates the effect increased specific charge has on the fragment size distribution of the blasted material. It is a part of a related project of the Swedish blasting Research center named “Model for bench blasting in open pits” and the field tests took place in Boliden’s Aitik copper mine in Gällivare.
The goal of this thesis work was to measure the difference in fragmentation caused due to increased specific charge. In order to achieve this, one bench i.e. bench 5162, was divided into two blasting domains. One domain was charged with the normal specific charge used for bench blasting in the mine which is approximately 1 to 1.1 kg/m3, while the other domain had a slightly elevated specific charge close to 1.35 kg/m3.
A combination of optical methods and lab sieving tests was used to evaluate the fragment size distribution of the blasted material in each blasting domain. The software used for the purposes of this investigation is “Split Desktop”. Over 250 images of truck – loads were acquired during the loading period of the material, from which, 60 were picked according to a quality criterion formulated and analyzed with the afore-mentioned software suite. In addition to the image analysis, four samples were taken from the muck pile, two from each blasting domain and they were sent for sieving in an accredited laboratory.
Included in the field work was detailed monitoring of the drilling and charging parameters. The results, along with additional information provided by the mine personnel, were used in order to obtain the fragment size distribution estimation of different theoretical models for each blasting domain. The models used were the Kuz- Ram model, the CZM and the KCO model. The results indicate significant differences in the model predictions for the finer ranges of the fragment size distribution curve, while the differences are reduced in the coarse range.
233 – 200 = 33 mm between the high and the low specific charge blasting domain.
Unfortunately, the same cannot be said for the rest of the passing sizes.
Approximately 50 % of the values between x10 and top-size include 0 in the 95 % confidence intervals of the size difference between the two blasting domains therefore, it cannot be claimed that the existence of a distinct difference has been substantiated. On the other hand the values for the differences in fragment size between domains for e.g. x50 and x80, even though for the latter they are not statistically significant, agree rather well with the range of values predicted by theoretical models such as the Kuz-Ram model the CZM and the KCO model. This leads to the conclusion that an increase in the sample size would allow for a better determination of the sample mean differences which would in turn have a beneficial effect in reducing the range of the confidence intervals rendering more difference values statistically significant and allowing for a more consolidated view of the fragment size distribution of the material within each blasting domain.
A compilation of image analysis and laboratory sieving data was used in an attempt to describe the fragment size distribution curve for the material within each blasting domain with the use of the Swebrec function incorporated in the KCO model. The results were satisfactory with the Swebrec function obtaining a fit better than 0.999 for both domains.
For the last part of the investigation, a crusher model for the mine’s primary crusher was made available and its ability to reproduce the fragment size distribution of crushed rock was tested for feeds from different theoretical models. The output of the crusher model for different feeds was compared to the results of the fragmentation analysis of the crushed rock performed by the “Split Online” monitoring system installed after the mine’s primary crusher. It is possible that the crusher model under- predicts the amount of fine material generated during the crushing process.
Furthermore, the theoretical CZM model used as input for the crusher model probably needs to be improved, since the feed material appears to contain more fines than the crusher product as measured with “Split Online”.
Utökad sammanfattning ... iii
Executive Summary ... v
1 Introduction ... 1
2 Background theory... 3
2.1 BENCH BLASTING...3
2.1.1 Geometry ...3
2.1.2 Detonation ...5
2.2 BLAST FRAGMENTATION...6
2.2.1 Fragmentation’s influence in down-stream operations ...6
2.2.2 Blast fragmentation models ...7
2.2.2.1 The Kuz – Ram Model... 7
2.2.2.2 The JKMRC models... 10
2.2.2.2.1 Crushed Zone Model (CZM) ... 10
2.2.2.2.2 The Two Component Model (TCM)... 13
2.2.2.3 The KCO Model... 15
2.2.3 Discussion...16
2.3 IMAGE ANALYSIS...17
3 Aitik Mine ... 19
4 Background information on blast no. 5162 ... 20
4.1 GEOLOGY...20
4.2 DRILLING...23
4.3 CHARGING...25
4.4 JKSIMBLAST...26
5 Fragmentation analysis ... 28
5.1 CRITERION FOR CHOOSING WHICH IMAGES TO ANALYZE...29
5.1.1 Light conditions ...29
5.1.2 Presence of unwanted particles in the image...31
5.1.3 Other parameters...31
5.2 IMAGE PROCESSING...32
5.3 RESULTS...34
5.5 CONSTRUCTING THE FRAGMENT SIZE DISTRIBUTION CURVES...43
5.6 FRAGMENT SIZE DISTRIBUTION PREDICTION OF DIFFERENT MODELS...46
5.6.1 The Kuz – Ram model ...46
5.6.2 The CZM Model...47
5.6.3 The KCO model ...48
5.6.4 Collective model comparison...49
5.7 COMPARISON BETWEEN THE TWO DOMAINS...51
5.7.1 Discussion...55
5.8 COMPARISON WITH THE RESULTS FROM THE PREVIOUS INVESTIGATION...58
5.9 COMPARISON WITH SPLIT ONLINE DATA FROM THE CRUSHER...60
6 Conclusions and future work ... 71
References ... 75
Appendix 1 ... 77
Appendix 2 ... 91
1 Introduction
In open pit hard rock mining, rock blasting is by far the most cost effective way of extracting the ore. The purpose of rock blasting is to extract adequately fragmented rock in the most economically viable way while avoiding possible damage to mine infrastructure and the foot wall.
Blast fragmentation is one of the most important aspects of open pit blasting. The blasted rock should be easily loaded and hauled and the blasted rock fragments should be adequately pre-conditioned (i.e. weakened) in order to reduce the energy requirements in down-stream processes such as crushing and grinding.
In Boliden’s Aitik open pit cooper mine over 18 million tons of copper ore are excavated every year along with over 20 million tons of waste rock. An expansion has been scheduled which will double the ore production to an astounding 36 million tons per year.
In order to achieve this ambitious goal, special attention is paid to blasting and blast fragmentation. Since January 2007, the Aitik Mine is running the project: “G5 optimized blasting” with the goal of giving a statistically based conclusion of the potential benefit optimized fragmentation can have on loadability, wear and mill throughput for both the ore and the waste rock. The first part of this project investigates the influence of a raised specific charge in production blasting. During 2007, 5 test rounds have been blasted and the tests will continue (to a maximum of 20 test blasts) until a significant effect in mill throughput has been observed.
The Swedish Blasting Research center has a related sub-project named: “Model for bench blasting in open pits” with a goal of giving a description of how to blast in different geological domains within the mine, so that the mill throughput increases.
A report by Nyberg et. al., (2006) and a paper by Ouchterlony et al. (2006) summarize the follow up of test blast 4141-2 in the Aitik open pit mine. The work done entails modeling of the blast using the JKSimBlast software, structural mapping of the bench
fracture mapping of production blast holes, evaluating blast fragmentation using
“Split Desktop” and “Split Online” software (www.spliteng.com, Kemeny, 1999) along with sieved samples from the muck pile and the adjustment of the parameters of the Kuz – Ram model combined with the Swebrec function to fit Aitik’s conditions.
The results of this investigation pointed out several deficiencies in the image analysis methods such as different types of delineation errors, lighting conditions and possible camera effects. A correlation between “Split Desktop” and “Split Online”
fragmentation data could not be established and the authors conclude that the fragmentation results obtained by the two systems should be regarded with suspicion, for the latter more than for the former.
The fragment size distribution curve for the entire bench was constructed using a combination of sieved and image analysis data. The Swebrec function was used to describe the curve and it gave a fit better than 0.995.
The present research is a continuation of the work performed by Nyberg. The objective of the project is to investigate the effect specific charge has on blast fragmentation through the use of image analysis data complimented by sieved samples from the muck pile. In addition to investigating the effect of specific charge, the data is to be used to construct the fragment size distribution curve for the blasted material.
2 Background theory
2.1 Bench blasting
2.1.1 Geometry
The main purpose of bench blasting is to facilitate the fracturing and moving of the intact rock mass so that it can be loaded, hauled and further processed in an easy and efficient way.
There are several parameters that influence the fragmentation result of a bench blast.
Among the most significant ones are the rock mass properties and the geometrical features of the blast design. Secondary parameters include explosive and detonator type, initiation pattern and timing etc. A brief overview of the terminology used in bench blasting drilling patterns can be seen in the following figure.
Figure 2.1: Bench blasting geometry and terminology (Bergman, 2005)
Burden (B): The distance between the borehole and the free face or the distance between two consecutive rows of boreholes.
Spacing (S): The distance between two consecutive boreholes in the same row Bottom charge (BCL): When charging with non bulk explosive material, the bottom charge is often heavier to compensate for the increased confinement on the bench toe.
Column charge (CCL): The main volume of explosive distributed along the main section of the borehole.
Bench height (H): The vertical distance form the bench’s crest to the bench’s toe.
Sub-drill (U): The section of the borehole extending below the bench’s toe. Sub- drilling is necessary to achieve sufficient breakage and have a relatively smooth working surface for loading the muck pile.
Stemming (Ho): The top part of the borehole which is left uncharged and then filled with sand, drill cuttings and gravel rock. The stemming is left uncharged in order to reduce the risk of fly-rock and it is filled with sand and gravel in order to prolong the action of the gas masses generated after the detonation of the explosive material and improve breakage.
Specific charge is a unit used in bench blasting to define the quantity of explosive material used per units of mass or volume. In this report, specific charged is defined as mass of explosive material used per cubic meter of rock. The specific charge for a bench blast can be calculated through the following equation (equation 2.1)
q Q
B S H
= ⋅ ⋅ (2.1)
Where:
q: Specific charge (kg/m3)
B: Burden (m)
H: Bench height (m)
S: Spacing (m)
Q: Total amount of explosive material in blast hole (kg) All as defined above
The burden in bench blasting depends on a multitude of parameters ranging from hole diameter and rock properties to the density of the explosive material. A great variety of equations exist for the calculation of the burden, based mainly on empirical data.
Among the most widely used is the Langefors and Kihlström (1963) equation for the calculation of the maximum burden (Bmax) (equation 2.2)
( )
max 33
D p E
B c f SB
= ⋅ ⋅
⋅ ⋅ (2.2)
Where:
Bmax: Maximum burden (m)
D: Blasthole diameter (mm)
p: Density or degree of packing of explosive material (Kg / dm3) E: Weight strength of explosive material
SB : Spacing to burden ratio c: Rock constant
f: Degree of packing, 1 for vertical holes, 0.93 for 3:1 inclined holes
2.1.2 Detonation
The explosives are placed inside the blast hole and with a detonator and a primer which will be used to initiate the detonation sequence. The holes are fired sequentially with an in-row time delay between holes as well as an inter-row delay. The detonation delay is part of the blasting plan and it takes place in millisecond intervals. This is made possible through delay elements embedded in the blasting caps as well as delay elements in the inter-hole and inter-row connection points on the surface. Timing the detonation sequence is a very important part of the blast design which, if done right, will ensure a smooth initiation front and will minimize the risk for reverse firing order and blast hole overlapping. A failed detonation can result to unexploded holes or insufficient fragmentation of the material which complicates down stream processes such as loading and hauling an creates the need for further processing of oversize fragments through means of re-blasting or breaking with a hydraulic hammer.
2.2.1 Fragmentation’s influence in down-stream operations
Blasting is the first step in the rock comminution process and it has a major impact on subsequent operations such as loading, hauling, crushing and grinding. The uniformity of the muck pile benefits its digability which makes loading and hauling of the material easier and less time consuming. The amount of oversize boulders produced by a blast defines how much resources will be used to further decrease their size in order for them to be effectively handled by the mining equipment.
Crushing and grinding are examples of two more operations which are to a great degree influenced by blasting. The size distribution of the blasted fragments is the most obvious parameter to be examined here. An increased amount of coarse material in a muck pile will result to increased energy consumption in the crushing and grinding stages as well as reduced primary crusher throughput due to the volume of the material which has to be downsized.
The effect of blasting in the grinding stages of the comminution process has been investigated by Nielsen and Kristiansen, (1996) and Workman and Eloranta, (2003). It is suggested that apart from fragmenting the rock, blasting also preconditions the fragmented material through the development of micro-fractures within the individual fragments. These micro-fractures develop through and around mineral grains and they are small enough to survive the initial crushing stages
There is evidence, (Nielsen& Kristiansen, 1996, Workman and Eloranta, 2003, Paley
& Kojovic, 2001) that the micro-fractures weaken the individual fragments, which reduces the overall energy required in the grinding stages to achieve the desired fragment size (Bond’s work index).
2.2.2 Blast fragmentation models
Through the years, a number of different models developed to describe the size distribution of the fragments after blasting (Ouchterlony, 2003). Most of these models offer equations to calculate the average fragment size (x50) as well as the entire fragment size distribution curve. The input for such models includes explosive material properties such as the weight strength, geometrical design features from the blast such as burden, spacing and bench height as well as in situ rock properties like discontinuity spacing, orientation etc.
While explosive properties and blast geometrical features are relatively easy to obtain and can be quite accurate, the same cannot be said for rock properties. The consideration of the rock mass as homogenous as well as the existence and properties of discontinuities throughout the rock mass make the rock properties difficult to establish and, in most cases, assumptions have to be made which will reduce the model’s ability to accurately reproduce the fragment size distribution curve.
However, the trends indicated by the model’s predictions are assumed to be correct and are used to provide blast design guidelines.
Although the blast fragmentation models predict the mesh size of the individual fragments, they give no prediction for their shape or the degree of preconditioning due to the generation of micro-cracks from blasting.
A brief description of the most popular blast fragmentation models follows.
2.2.2.1 The Kuz – Ram Model
The Kuz – Ram model is by far the most widely used fragmentation model to date.
The model is based on the expression for the average fragment size x50 constructed by Kuznetsov in 1973 and a Rosin – Rammler distribution (Cunningham 1983, 1987, 2005). The model basically consists of 4 equations, from which, one describes the fragmentation curve, one gives the value for x50 in cm as a function of the blasting parameters, the third gives a value for the rock mass factor A and , the last gives a
( )
1 x50P x = −e ⋅⎜⎝ ⎟⎠ (2.3)
Where:
P(x): Percentage of material below size x
X: Size of material (m)
x50: Average fragment size (m) n: Uniformity index
1 1930
50 0.8 6
1 115
ANFO
x A Q
q S
⎛ ⎞
⎛ ⎞
= ⋅⎜ ⎟⋅ ⋅⎜ ⎟
⎝ ⎠ ⎝ ⎠
(2.4) Where:
x50: Average fragment size (cm)
A: Rock mass factor
q: Specific charge (kg/m3)
Q: Total amount of explosive material in blast hole (kg) SANFO: Strength of explosive used, % ANFO equivalent
0.06 ( )
A= ⋅ RMD RDI HF+ + (2.5)
Where:
10, if powdery, friable
RMD: Rock mass description: JF, if joints are vertical
50, if rock mass is massive
JF: Joint factor = JPS + JPA
10, if average joint spacing Sj<0.1m JPS: Joint plane spacing 20, if Sj<X0 oversize fragment
50, if Sj>X0 oversize fragment 20, if the joints dip out of the face JPA: Joint plane angle 30, if strike is perpendicular to the face
40, if the joints dip into the face RDI: Rock density influence:
(
0.025⋅ −p)
50 (kg/m3)1 0.1
2.2 14 1 0.1
2
tot tot
S
B SD B BCL CCL L
n D B L H
⎛ + ⎞
⎜ ⎟ ⎛ ⎞
⎛ ⎛ ⎞⎞ ⎛ ⎛ ⎞⎞ − ⎛ ⎞
=⎜⎝ − ⋅⎜ ⎟⎝ ⎠⎟ ⎜⎠ ⎝⋅ −⎜⎝ ⎟⎠⎟⎠⋅ ⎜⎜ ⎟ ⎜⎟⋅⎝ + ⎟⎠ ⋅⎜⎝ ⎟⎠
⎝ ⎠
(2.6)
Where:
B: Burden (m)
D: Drillhole diameter (mm)
SD: Standard deviation of drilling accuracy (m)
S: Spacing (m)
BCL: Length of bottom charge (m) CCL: Length of column charge (m) Ltot: Total charge length (m)
H: Bench height (m)
The above equations indicate certain trends some of which are briefly summarized below.
The 50 % passing fragment size (x50) appears to be mainly influenced by explosive- related parameters. Improved fragmentation (i.e. smaller x50 value) can be achieved by using an explosive with higher weight strength of with higher density, which has an impact on specific charge. If the specific charge is increased by means of shrinking the blasting pattern (but maintaining hole diameter D and spacing to burden ratio constant) fragmentation will improve (i.e. become finer) and the uniformity index will increase as well according to the model.
The uniformity index (n) appears to be mainly influenced by blast geometry parameters as well as charge length. An increase in the uniformity index will result to a more uniform fragmentation with less fines and oversize material (Cunningham, 1983). A decrease in the burden to hole-diameter ratio
( )
BD will have a positive impact on the uniformity of the muck pile. An increase in parameters such as drilling accuracy, spacing to burden ratio, total charge length to bench height ratio will also case an increase of the uniformity index. Finally it is suggested by Cunningham, although it is not derived from the mathematical expression of the model, that aindex by 10 %.
2.2.2.2 The JKMRC models
The Julious Kruttsnitt Mineral Research Center has developed two blast fragmentation models, the crushed zone model (CZM) and the two component model (TCM), both of which are essentially based on the Kuz – Ram model. The main assumption behind those models is that there are two discrete mechanisms causing the fragmentation of blasted rock. The models assume that the fine material in generated within a circular zone (crushed zone) around the charge where the failure mode is predominately compressive, while the coarse part of the fragment size distribution is attributed to tensile fracturing and preexisting fractures in the rock mass. The following figure illustrates the concept of the crushed zone
Figure 2.2: Schematic illustration of processes occurring in the rock around a blast hole, showing formation of crushing zone, fracture zone and fragment formation zone (Essen, 2003)
2.2.2.2.1 Crushed Zone Model (CZM)
The crushed zone model uses two different Rosin – Rammler functions to describe the entire fragment size distribution curve. One function describes the fines part of the curve while the second describes the coarse part of the curve. The two curves join at a characteristic fragment size Xc which depends on the rock mass properties. The coarsest particle size in the crushed zone is assumed to be 1 mm and the characteristic fragment size Xc ranges from x50 for strong rocks (UCS>50 MPa) to X90 for very soft rocks (UCS<10 MPa) (Kanchibotla et al, 1999).
The coarse part of the fragmentation curve is given by the following equation:
( )
1 ln 1( ( ))ncoarse c
c
P x x
P x e x
⎛ ⎛ ⎞ ⎞
⎜ − ⋅⎜ ⎟ ⎟
⎜ ⎝ ⎠ ⎟
⎝ ⎠
= − (2.7)
Where:
P(x): Percent of material passing sieve size x (%) P(xc): Percent of material passing characteristic size xc (%)
x: Sieve size (m)
xc: Characteristic size (m)
ncoarse: Uniformity index for the coarse part of the curve
1 2.2 14
2
coarse tot
S L
B B
n D H
⎛ + ⎞
⎜ ⎟
⎛ ⎛ ⎞⎞ ⎛ ⎞
=⎜⎝ − ⋅⎜ ⎟⎝ ⎠⎟⎠ ⎜⋅ ⎜ ⎟⎟⋅⎜⎝ ⎟⎠
⎝ ⎠
(2.8)
Where:
B: Burden (m)
D: Drillhole diameter (mm)
S: Spacing (m)
Ltot: Total charge length (m)
H: Bench height (m)
The fine material is assumed to originate from a cylindrical crushed zone around the blast hole, within which the particles are generated by the crushing of the rock due to compressive – shear failure (Kanchibotla et al, 1999). The radius of the crushed zone is assumed as the distance from the blast hole to the point where radial stresses exceed the compressive strength of the rock mass and is given by the following equation:
d c
c
r r P
= ⋅ σ (2.9)
rc: Crushed zone radius (m)
r: Blast hole radius (m)
Pd: Detonation pressure (Pa) σc: Compressive strength of the rock (Pa) The detonation pressure is given by the equation:
2
4
d
d c
P =ρ ⋅C (2.10)
Where:
Pd: Detonation pressure (m) Cd: Velocity of detonation (m/s)
ρc: Density of explosive material (kg/m3)
The fraction of the crushed material is calculated through equation 2.11.
c c b
F V
=V (2.11)
Where:
Fc: Fraction of crushed material
Vc: Volume of crushed rock (m3) Vb: Volume of blasted rock (m3)
The Fine part of the size distribution curve is given by the following equation:
( )
1 ln 1( ( ))n fine c
c
P x x
P x e x
⎛ ⎞
− ⋅⎜ ⎟
⎝ ⎠
= − (2.12)
Where:
P(x): Percent of material passing sieve size x (%) P(xc): Percent of material passing characteristic size xc (%)
x: Sieve size (m)
xc: Characteristic size (m)
nfine: Uniformity index for the fine part of the curve
( )
( ( ) )
ln ln 1 ln 1
ln 1
c c fine
c
F n P x
x
⎛ − ⎞
⎜ ⎟
⎜ − ⎟
⎝ ⎠
= ⎛ ⎞
⎜ ⎟
⎝ ⎠
(2.13)
Where:
Fc: Fraction of crushed material
P(xc): Percent of material passing characteristic size xc (%)
xc: Characteristic size (mm)
nfine: Uniformity index for the fine part of the curve
2.2.2.2.2 The Two Component Model (TCM)
The two component model (Djordjevic, 1999) uses two simultaneous Rosin – Rammler functions to describe the fine and the coarse components of the size distribution curve which results to a curve with a uniform slope unlike the CZM
model’s size distribution curve which has a breaking point in the characteristic size xc. The fragmentation curve is given by the following equation:
( )
100 1 1( )
ln 2 ln 2b d
x x
a c
c c
P x F e F e
⎛ ⎞ ⎛ ⎞
− ⋅⎜ ⎟⎝ ⎠ − ⋅⎜ ⎟⎝ ⎠
⎛ ⎞
⎜ ⎟
= ⋅ − − ⋅ − ⋅
⎜ ⎟
⎝ ⎠
(2.14)
Where:
P(x): Percentage of material below size x (%)
x: Size of material (m)
Fc: Fraction of crushed material
a: Mean fragment size outside the crushed zone (m) b: Uniformity coefficient outside the crushed zone c: Mean fragment size within the crushed zone (m) d: Uniformity coefficient within the crushed zone
The parameters c and d are determined through blast chamber tests where samples are blasted and the fragments are then sieved to obtain the desired values.
are determined using the same equations with slight modifications of JPS and RDI.
The fraction of the crushed material is determined the same way it is calculated for the CZM.
The radius of the crushed zone for the TCM in calculated through the following equation:
24 si c
in tu b
r r r
TS P
⎛ ⎞
⎜ ⎟
⎜ ⎟
=⎜⎜ ⋅ ⎟⎟−
⎜ ⎟
⎝ ⎠
(2.15)
Where:
rc: Crushed zone radius (m) r: Blasthole radius (m) Pd: Detonation pressure (Pa) TSin situ: In situ tensile strength (Pa)
The detonation pressure is calculated using the same equation as the CZM, while the in situ tensile strength is determined as follows:
0.05 0.18 in situ
TS =στ⋅⎜⎛mean block size⎞⎟
⎝ ⎠ (2.16)
Where:
στ: Tensile strength of rock (MPa) And the mean block size is given in meters.
2.2.2.3 The KCO Model
The KCO model (Ouchterlony, 2005a) is an extended version of the Kuz – Ram model. The model essentially replaces the Rosin – Rammler function used to describe the fragmentation curve in the Kuz – Ram model with a new function, the Swebrec function. The Swebrec function includes 3 parameters, the 50 % passing size x50, the maximum size Xmax and b which is a curve undulation parameter similar to n in the Kuz – Ram model. The expression for x50 remains the same as for the Kuz – Ram model while the expressions for b and the Swebrec function can be seen bellow.
( )
max
max 50
1 ln 1
ln P x b
x x x
x
=⎧⎪⎪⎨⎪⎪⎩ +⎡⎢⎢⎢⎢⎢⎣ ⎛⎜⎝⎛⎜⎝ ⎞⎟⎠⎞⎟⎠⎤⎥⎥⎥⎥⎥⎦ ⎫⎪⎪⎬⎪⎪⎭
(2.17)
max 50
2 ln 2 ln x
b n
x
⎡ ⎛ ⎞⎤
=⎢ ⋅ ⋅ ⎜ ⎟⎥⋅
⎢ ⎝ ⎠⎥
⎣ ⎦ (2.18)
Where:
P(x): Percent of material passing sieve size x (%) b: Curve undulation parameter
x: Sieve size (cm)
x50: 50 % passing size (same as in Kuz – Ram model) (cm) Xmax: Maximum in situ block size (cm)
n: Uniformity index (same as in Kuz – Ram model)
The KCO model also suggests an alternative expression for x50 with an addition of a pre - factor originally derived by Spathis (2004), which can be seen below.
( )
1 16 193050 0.8
ln 2 1 115
1 1
n
ANFO
x A Q
q S
n
⎛ ⎞
⎜ ⎟ ⎛ ⎞ ⎛ ⎞
⎜ ⎟
=⎜⎜⎝Γ +⎛⎜⎝ ⎞⎟⎠⎟⎟⎠⋅ ⋅⎜⎝ ⎟⎠⋅ ⋅⎜⎝ ⎟⎠
(2.19)
The above expression shifts the fragment size distribution to smaller values for x50,
The Kuz – Ram model has been the dominant model in prediction the fragment size distribution for blasted rock for nearly 25 years. Through the course of those years several shortcomings, such as the inability to adequately reproduce the fines part of the distribution curve, have been observed and it has become clear that very few sieved samples follow the models fragment size distribution curves.
The JKMRC models were made to compensate for the Kuz – Ram models poor ability reproduce the fines part of the size distribution curve. The CZM model has been successfully incorporated in the JKSimBlast blasting management software suite and the results have been checked against image analysis software such as “Split”.
However, evidence exists that the assumption that all the fine material comes from a crushed zone around the blast hole is mistaken and that a fraction closer to 25 % actually comes from that region (Svahn, 2003). In addition to the above, very few sieving curves have been noted to have break points such as the one in the Xc the CZM model predicts (Ouchterlony, 2007).
The KCO model is the most recent of the above models and its ability to accurately reproduce the entire range of the fragment size distribution curve for both blasted and crushed rock appears to be promising. The model is compatible with the already widespread Kuz – Ram model and it counteracts its basic draw back i.e. the poor predictive capacity in the fines range. One additional advantage of the KCO model is that it introduces a finite top – size for the fragment size distribution.
2.3 Image analysis
Image analysis is a method to measure blast fragmentation through the use of digital photography. The fragmentation achieved by blasting is often assessed qualitatively as
“good”, “too fine” or “too coarse”. This is a distinction made by people with relative experience and the criteria used for this empirical assessment are vague and difficult to quantify. The most reliable way for fragmentation to be assessed is through sieving of the entire muck pile or, of representative samples. This of course is nearly impossible given the volume of material being handled in modern day operations.
Bench blasts of thousands of m3 of rock make sieving costs astronomical and the entire process of sieving is known to be “intrusive” in terms of interfering with the production process.
Image analysis has several inherent advantages (Maerz & Zhou, 1998):
• The measurements can be completely automated eliminating several process- related expenses
• A great number of measurements can be made, which increases the overall statistical reliability through the reduction of sampling errors
• It is a non- intrusive to production method since it requires no interruption of the production process
• It offers a way to evaluate the fragment size distribution of materials which are too coarse to be sieved such as riprap material.
The disadvantages of image analysis are related to errors, which can be divided into the following main categories:
• Errors related to the method of analysis of the images
• Errors related to the sample presentation
• Errors related to the imaging process
• Errors related to the sampling process
It is accepted that all the above errors can be minimized through carefully established sampling methods, proper sampling environment and site-specific calibration of the software (Maerz & Zhou, 1998, 2000, Katsabanis, 1999).
As mentioned above, image analysis is a “non intrusive” method. Images of the material are acquired and used as input for image analysis software. The image is delineated (i.e. lines are drawn along the boundaries of the individual fragments) through the use of a special delineation algorithm. The size of the individual fragments is then measured and, a size distribution curve is constructed. The images can be acquired either from a fixed camera located e.g. above a conveyor belt or, photographs of muck piles or truck loads taken by an individual user can be used as input.
The software used for the purposes of this analysis is “Split Desktop” (Potts &
Ouchterlony, 2005). Apart from the standard functions of delineating images and constructing fragment size distribution curves, the program offers an editing suite and allows the user to edit the images before the delineation takes place as well as after the delineation process and prior to the fragment size measurement. This option enables the user to correct false delineations and outline and characterize patches of fine material within the muck pile.
3 Aitik Mine
The Aitik mine is one of the biggest open pit mines in Europe. The mine is situated 60 km north of the Arctic Circle near the town of Gällivare in the northernmost part of Sweden. The mine is owned and operated by Boliden AB and the main product is cooper with gold and silver as by-products.
The pit is approximately 2.5 km long, 500 m wide and more than 300 m deep.
The ore body has a strike of N20oW with a 45o dip to the west.
The mining area is divided in three main zones, the foot-wall, the ore zone and the hanging-wall. The division is made on the basis of the actual tectonic boundaries as well as the cooper grades. A map of the mining area along with the different rock types can be seen below.
Map 3.1: Geological map of the Aitik mining area.
A detailed description of the site geology, main rock type properties, process and monitoring systems has been made by Peter Bergman in his Licentiate thesis titled
“Optimization of fragmentation and comminution at Boliden mineral, Aitik mine”
(Bergman, 2005). The relevant chapter can be found as an appendix to this work (Appendix 1) with Bergman’s permission.
4 Background information on blast no. 5162
Bench 5162 is located on the 300 m level of the Aitik mine. It has an area of 10627 m2 and a height of approximately 15 m. The total volume of the bench is 159405 m3. Loading of the bench will take place in the 315 m level. An overview of the open pit mine can be seen below with the position of bench 5162 marked.
Map 4.1: Overview of the Aitik Mine, the position of bench 5162 can be seen marked with a red dot (source: Google Maps)
4.1 Geology
Bench 5162 consists mainly from biotite schist and pegmatite with a small amount of muscovite schist located in the northeast edge (local coordinate system) as suggested by diamond drilling data. An analysis of the drill cuttings from 95 holes out of a total of 177 indicated mainly biotite schist and biotite gneiss with some pegmatite and only one occurrence of muscovite schist. An older geological interpretation suggested that the bench consisted from muscovite schist and pegmatite. The above is illustrated in the following maps (maps 4.2 – 4.4) . Pegmatite is considered waste rock and
therefore it is not processed. The polygon which can be seen in maps 4.2–4.4 outlines an area where mainly pegmatite can be found which is going to be loaded separately and disposed in the waste rock dump.
Map 4.2: Older geological model of bench 5162. Muscovite schist marked with yellow color, Pegmatite with red, biotite schist with green and biotite gneiss with turquoise.
Map 4.3: Diamond drilling results. Different colors on individual line signify different rock types along the drill cores. Muscovite schist marked with yellow color, Pegmatite with red, biotite schist with
green, biotite gneiss with turquoise and biotite amphibole gneiss with dark blue.
Map 4.4: Drill cuttings analysis Muscovite schist marked with yellow color (1 hole), Pegmatite with red ( 10 holes), biotite schist with green (41 holes), biotite gneiss with turquoise (43 holes) and biotite
amphibole gneiss with dark blue (0 holes). The red circle designates holes with some, or only, pegmatite found in the drill cuttings.
A block model of the bench can be seen map 4.5. The low-grade pegmatite region is again outlined.
Map 4.5: Block model of bench 5162, local north noted on the map.
4.2 Drilling
The drilling pattern for blast 5162 consisted of a total of 177 production holes with a diameter of 311 mm divided in two blasting domains. The first domain was the “low specific charge” domain. 81 holes were drilled in a rectangular pattern, with planned values of 7.5 m and 9.5 m for burden and spacing respectively. The spacing-to-burden ratio for this domain is 1.27. In the “high specific charge” domain, 96 holes were drilled in a rectangular pattern. The planned values for burden and spacing were 6.5 m and 8.1 m respectively, with a spacing-to-burden ratio of 1.25.
Statistical information about the drilled holes can be seen in the following table (table 4.1). The design of the blast can be seen in Figure 4.1.The boundary between the blast domains as well as the planned values for burden and spacing can also be seen in the figure. The east and north faces of the bench are the free faces, while the south and west faces (local coordinate system) are the confined faces by benches 51621 and 5163 respectively.
Low specific
charge domain High specific charge domain Bench height (m) 15.0 15.0 Hole diameter (mm) 311 311 Hole angle vertical holes vertical holes
Number of rows 11 12
Number of holes 81 96
Planned hole depth (m) 16.8 ± 0.9 16.6 ± 0.7 Measured hole depth (m) 17.1 ± 0.8 17.0 ± 0.7 Maximum hole depth (m) 18.9 18.8 Minimum hole depth(m) 13.8 14.7 Planned drilling (m) 1364 1589 Total drilled (m) 1381 1630
Approximate domain area (m2) 5350 5277 Approximate domain volume (m3) 80250 79155 Specific drilling (m/ m3) 0.0172 0.0206
Burden (m) 7.5 6.5
Spacing (m) 9.5 8.1
Table 4.1: Statistical information about the drilled blast holes ± standard deviation
Figure 4.1: The blast design for blast 5162 the boundary between the blast domains can be seen in magenta color, along with the planned values for burden and spacing
The top part of the drilled hole is not charged with explosives. It is filled with drill cuttings and aggregates in order to minimize the risk of fly-rock and improve breakage by prolonging the action of the gas masses generated during the detonation of the explosive material. The length of the stemming was measured for 146 out of 177 holes and the results are presented in the following table.
Low specific
charge domain High specific charge domain
Measurements 68 78
Minimum length (m) 2 2.5 Maximum length (m) 7 6.1 Mean value (m) 5.4 4.9 Std deviation (m) 0.8 0.8
Table 4.2: Statistical information about the length of the stemming section of the blast holes
4.3 Charging
The explosive used in blast 5162 is TITAN 8070, a site sensitized emulsion with a content of 30 % of AN prills. The density before gassing is 1330 kg/m3 while after gassing it drops to approximately 1050 kg/m3. The explosive’s velocity of detonation (VOD) is close to 5200 m/s and the explosive energy is 3.34 MJ/kg. The weight strength compared to ANFO is calculated to 85 %.
Inside each blast hole, two primers are placed. One in the bottom of the hole and one approximately one meter above in order to ensure detonation. The primers are Dynamex 1,7 cartridges with a 66 mm diameter and 361 mm length. The theoretical explosive energy is approximately 5.5 MJ/ kg and the velocity of detonation is close to 6500 m/s. The detonators used with the primers are NONEL U 500, which have the equivalent strength of a standard no 8 detonator. An inter – hole delay of 42 ms and an inter – row delay of 176 ms is dictated by the blasting plan.
The planned values indicated a total of 178105 kg of emulsion was to be charged in a total of 177, 311 mm production holes. However, there was a deviation of 8.6 % (15346 kg) from the planned values and the quantity of emulsion used was 193451 kg. More information about the quantity of explosive material charged can be seen in table 4.3.
Quantity of explosive material
Planned (kg) Measured (kg) Deviation (kg) Deviation % Planned Specific charge (kg/m3)
Actual Specific charge(kg/m3) High Specific
charge domain 99446 107088 7642 7.7 1.26 1.35
Low specific
charge domain 78659 86363 7704 9.8 0.98 1.08
Total values for
the entire blast 178105 193451 15346 8.6 1.12 1.21
Table 4.3: Summary of explosive material charged in the holes of each blast domain
It is apparent from the previous table that there is a clear difference in the specific charge of the individual blast domains. The planned values dictated a 28.6 % increase in the high specific charge domain. However the actual values indicate that the difference was in the vicinity of 25 %.
A model of the entire blast was constructed with the use of the blast simulation software JKSimBlast (www.jksimblast.com). Data from the MWD system was used to position the blast holes within the bench and the charging data provided was used to charge the holes with explosives. The primers and detonators used in the simulation were identical to the ones used for the actual blast and the initiation pattern was plotted unchanged. An effort was made to keep the model as close to the real conditions as possible. A depiction of the model and the parameters used to build the model can be seen in the following figures (figures 4.2, 4.3).
Figure 4.2: The JKSimBlast model. The drilling parameters used can be seen .
Figure 4.3: The JKSimBlast model. The charging parameters used can be seen
After running the detonation simulation, the software gave a depiction of the explosive energy distribution across the entire area of the bench on the 315 m level (bench bottom level). The explosive energy distribution can be seen in the following figure.
Figure 4.4: Explosive energy distribution across the entire area of the bottom of bench 5162.
Figure 4.4, illustrates a higher explosive energy in the high specific charge part of the bench with several “hot spots” where holes are placed very close together or, are overcharged with explosives. The explosive energy is clearly lower in the perimeter of the bench in order to avoid excessive damage to the surrounding rock. The explosive energy seems to be evenly distributed along the biggest part of the bench with the exception of the northwest corner (local coordinate system) where the energy levels are significantly reduced.
5 Fragmentation analysis
A total of 264 pictures of truck trays were taken for the purpose of the analysis in a period of 7 days from 10/03/2008 to 16/03/2008. From those, 60 were chosen to be analyzed with “Split Desktop”. The criteria for deciding which images would be analyzed and which would be discarded is discussed more in detail later in this report.
The entire round was loaded within 8 days from 10/03/2008 to 17/03/2008 into approximately 1500 truck loads.
The mine’s truck fleet consists of Caterpillar trucks with a tray capacity of approximately 200 ton. Loading was done with a P & H electric shovel which could load each truck in three dumps.
The images were acquired from an appropriate location with a Canon EOS 350 D digital camera with a 75 – 300 mm lens. The tray of the truck was photographed with an image resolution of 3456⋅2304 pixels. The distance from the truck to the camera was approximately the same for all the images acquired. Only images of trucks hauling ore were acquired. Trucks headed to the waste rock dump followed a different route therefore the distinction between them was easily made.
Before the image was analyzed it was cropped in order to remove all the unnecessary background elements such as the sky, the ground and all the truck elements besides the truck tray and the hauled material. An example of an image prior to, and after cropping can be seen in the following figure.
Figure 5.1: Example of cropped (right) and un-cropped image (left)
The image was scaled (i.e. creating a relationship between the pixels of the image and an actual physical distance) with the “Split Desktop” software using the width of the truck tray as a known physical distance. Mainly, two types of trucks were used to haul the material Cat 793 C and Cat 793 D. The width of the truck tray was measured and, with a deviation of ± 4 cm the results can be seen in the following table
Truck type Inner tray diameter ( cm ) Outer tray diameter ( cm )
Cat 793 C 638 670
Cat 793 D 647 680
Table 5.1: Truck tray diameters
5.1 Criterion for choosing which images to analyze
From the 264 images acquired, not all were of the same quality. Lighting conditions as well as weather conditions play a significant part in the image quality and throughout the 7 days during which the images were acquired, the dynamic nature of these parameters created a significant variation in image quality. It was decided that a set of criteria was to be formulated in order for the quality of the images to be assessed. The criteria would take into consideration the parameters which influence the image quality and particularly those parameters which influence the capacity of the “Split Desktop” software to effectively delineate the individual fragments of the analyzed material.
5.1.1 Light conditions
Since the images where acquired in an outdoors environment, the light conditions varied depending on the weather conditions and the time of day. Different light intensities across a region of interest i.e. the material on the truck tray, are often misinterpreted by “Split Desktop” as fragment boundaries causing mistakes in the fragment delineation. In addition to that, shadows on the material can be confused as large areas of fine material when the program’s thresholding algorithm is applied on the grayscale image in order to turn it into a binary image (Potts & Ouchterlony,
on the material were disregarded while images taken under diffused sunlight were favored.
Another issue is the amount of light present in the environment at the time the image was taken. Images taken in a reduced light environment (i.e. under a very cloudy sky, too early in the morning or too late in the afternoon) appear somewhat dark and the software would have a problem in delineating them correctly. Due to that, images which appear somewhat dark were discarded, while images taken with enough light present in the environment were favored. Examples of images taken under good and bad lighting conditions can be seen in the following figures (figures 5.2, 5.3).
Figure 5.2: Example of image taken under direct sunlight (left) and of image taken under diffused lighting conditions (right)
Figure 5.3: Example of image taken under reduced lighting conditions and of image taken under satisfactory lighting conditions
5.1.2 Presence of unwanted particles in the image
There were several images acquired under heavy snowfall. The distribution of snowflakes across the image combined with the reduced visibility render those images unsuitable for further processing since snowflakes can be misinterpreted for fine material and distort the outcome of the fragment size distribution analysis.
Dust is another example of unwanted particles within an image. Apart from concealing and distorting part of the material, it can also be misinterpreted by “Split Desktop” for fine material and create a fragment size distribution which is too fine for the material on the truck tray. An example of unwanted particles within an image can be seen in figure 5.4.
Figure 5.4:
Example of image with a lot of unwanted particles in the frame (left) and of a clear image (right)
5.1.3 Other parameters
Different material colors within the same pile also have an adverse effect on image analysis software’s capacity to delineate an image,(Maerz & Zhou, 1998) therefore, images with similar material colors were favored over images which contained multi – colored material such as pegmatite.
Images which were acquired in a non perpendicular position to the material were discarded due to possible scaling errors which might lead to a mistaken estimation of the fragment size.
between the high and low specific-charge domains were discarded since the transition zone between the two domains would contain mixed material, deemed not useful for the purposes of this investigation.
Examples of images taken at an angle to the truck tray and of images of loads containing multi-colored material can be seen in the following figures (figures 5.5- 5.6)
Figure 5.5:
Example of image taken at an angle to the truck tray (left) and perpendicular to the truck tray (right)
Figure 5.6: Example of image containing multi colored material (left) and of image containing uniformly colored material (right)
5.2 Image processing
The images were cropped, and all the unnecessary elements were removed leaving only the material and the edges of the truck tray required for editing. If the image after cropping was larger than 1640⋅1400 pixels, its size was reduced since “Split Desktop” cannot process images lager than the above size. Most of the images range in dimensions between 1450 – 1580 pixels width and 800 – 900 pixels height. The images downsized, were reduced to 1580⋅812 pixels size.
The images were then scaled and delineated by the “Split Desktop” software.
For the delineation, the “Split Desktop” auto-parameters function was used to determine the noise size, the watershed ratio and the gradient size. The options to remove noise and de-interlace the image were also used at this step.
After the delineation was done, the image with the delineation mask was manually edited. The time required for editing the image ranged from 30 to 35 minutes depending on the quality of the delineation performed by the software. An effort was made to spend an equal amount of time on each image.
The basic steps of the editing process include breaking false delineations separating large fragments into smaller ones, drawing new delineations between individual fragments which were assumed united by the software, outline and characterize patches of fine material, and, outline areas which are not to be taken into consideration in the fragment size distribution analysis, such as the edges of the truck tray used for scaling.
After editing was done the image was transformed into a binary image and the size of the individual fragments was computed. A fines adjustment factor of 20 % was used to compensate for the fine material which would be concealed by larger particles and a Rosin – Rammler distribution was chosen to construct the fines part of the distribution curve. The parameters governing image analysis process such as the value for the fines adjustment factor and the time spent editing images were chosen on the basis that they were deemed optimum by previous research (Nyberg et al., 2006) for the mine conditions.
The last stage of the image analysis process was the acquisition of the fragment size distribution curve. An example of a delineated image and of the fragment size distribution curve constructed by “Split Desktop” can be seen in figures 5.7 – 5.8
Figure 5.7: Example of original cropped image (left) and delineated binary image (right)
Figure 5.8: Fragment size distribution curve constructed by “Split Desktop”
5.3 Results
For each image analyzed with “Split Desktop” the fragment size distribution curve was acquired for that particular truck load along with size values for X10 to X90 and the top size (X100). During the analysis these values were averaged per domain in order to produce what is considered to be an approximate representation of the size distribution of the material fragments within that particular domain.
5.3.1 Low Specific charge domain
For the low specific charge domain, 30 images of truck loads were analyzed. In table 5.2 the average fragment size data are presented along with the standard deviation. In Graph 5.1, the sieving curve, plotted in a semi-log space can be seen.
% Passing Particle
Size (mm) Domain average value
Standard Deviation
4000.0 100.0 0.0
2000.0 100.0 0.0
1000.0 99.4 1.5
750.0 96.1 5.1
500.0 84.6 9.6
250.0 54.7 7.7
125.0 32.4 4.7
88.0 24.6 4.4
63.0 18.9 4.2
44.0 14.3 4.0
31.0 10.8 3.7
22.0 8.3 3.4
16.0 6.6 3.1
11.0 5.0 2.7
7.8 3.9 2.4
5.5 3.1 2.2
4.0 2.3 1.7
Table 5.2: Low specific charge domain mean fragment size data
Low specific charge domain mean fragment size distribution curve
0.0 20.0 40.0 60.0 80.0 100.0 120.0
1.0 10.0 100.0 1000.0 10000.0
Fragm ent size (mm )
% Passing
Graph 5.1: Low specific charge domain mean fragment size distribution curve
The mean values for x20, x50, x80 and top-size is presented in the following table with range and the standard deviation. The sample size is n=30.
x20 x50 x80 Topsize
Mean value (mm) 70 233 463 838
Standard deviation 19 47 108 190
Minimum value (mm) 37 161 293 527
Maximum value (mm) 98 369 735 1235
A total of 30 images were analyzed using “Split Desktop” for the high specific charge domain. Mean values for the fragment size distribution are presented in the following table (table 5.4). The results are plotted in semi-log space in graph 5.2
% Passing Particle
Size (mm) Domain average value
Standard Deviation
4000.0 100.0 0.0
2000.0 100.0 0.0
1000.0 99.5 1.01
750.0 96.1 4.6
500.0 86.7 9.7
250.0 61.6 12.1
125.0 37.0 7.4
88.0 27.9 5.3
63.0 21.2 4.2
44.0 15.8 3.5
31.0 11.9 3.0
22.0 9.1 2.6
16.0 7.1 2.3
11.0 5.3 1.9
7.8 4.1 1.7
5.5 3.2 1.4
4.0 2.4 1.1
Table 5.4: High specific charge domain mean fragment size data
High specific charge domain mean fragment size distribution curve
0.0 20.0 40.0 60.0 80.0 100.0 120.0
1.0 10.0 100.0 1000.0 10000.0
Fragment size (mm)
% Passing
Graph 5.2: High specific charge domain mean fragment size distribution curve
