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Prediction of Rock Fragmentation Using a Gamma-Based Blast Fragmentation

Distribution Model

Authors: F.Faramarzi, M.A.Ebrahimi Farsangi and H.Mansouri

Presenter:

Farhad Faramarzi

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Table of contents

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• Introduction

• Fragmentation measurement by image analysis

• Rock fragmentation models

• The gamma-based “KC-KUM” model

• Results and performance assessment

• Rock fragmentation prediction by gamma-based model

• Conclusions

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Introduction

• Rock fragmentation is considered as the most important aspect of production blasting, which affects the costs of drilling, blasting, and also downstream processes such as loading, hauling, crushing and grinding (Mojtabai et al., 1990; Latham et al., 1999; Faramarzi et al., 2013).

• The economics of many operations in the minerals industry depend on the particle size distribution and blasting is usually the first step in creating that size distribution (Kanchibotla et al., 1998).

• Muck pile fragment size refers to the size of the fragments within it after

rock blasting (Sanchidrián et al., 2010).

• Blast fragmentation prediction is the first step toward optimization of blast design parameters to produce required fragment size (Mackenzie., 1967).

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Introduction

Rock fragmentation by blasting is a complicated but it is also an attractive field of study to many rock blasting researchers: • Kuznetsove VM (1973) • Cunningham CVB (1983,1987) • Djordjevic N (1999) • Kanchibotla S et al. (1999) • Chung SH and Katsabanis PD (2000) • Esen S et al. (2003) • Onederra I et al. (2004) • Ouchterlony F (2005) • Gheibie H (2009) • Faramarzi et al. (2013)

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Introduction

Briefly about the new model: • A blast fragmentation distribution model is developed based on the

cumulative distribution function (CDF) of gamma function. • The model is consisted of two similar gamma-based equations, covering

various fragment sizes in muck pile.

• Familiar parameters of median size ‘X50’ and ‘nf’ which is considerably similar to the uniformity index ‘n’ are just required to run the model.

• The 40% grafting point is chosen to connect the generated values of the

two equations.

• Prediction of 80% passing size can be done by this model as well.

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Fragmentation measurement by image analysis

• A semi-automatic method was selected to find muck pile distribution curves for all the blasts.

• In average, for each blast 30 photos were taken systematically by a high quality digital camera from muck pile in different steps of loading.

• Split Desktop software was used to carry out image analysis in which delineating of fragments was done manually and the 100% fines correction option was used.

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Fragmentation measurement by image analysis

Why not sieved data?

• This method is feasible for measuring fragment size in the crusher product and mill feed, but it is too expensive, time consuming and labour intensive process for measuring muck-pile fragment size. Either, it is not possible to pass all the muck-pile material through screens; nevertheless the amount of samples can be effective on distribution results by covering a wider range of fragments size (Drebenstedt and Ortuta, 2012).

Even, if it was practical to sieve whole the muck pile, due to further impacts and abrasion of fragments during the sieving operation; production of more fines is unavoidable and the destructive identity of sieving can be considered as a drawback.

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Fragmentation measurement by image analysis

Therefore, due to numerous practical limitations and lack of trust to this method for modeling blast fragmentation plus fundamentally lack of access to preform such tests, it was preferred to use image analysis method!

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Rock fragmentation models (Kuz-Ram Model)

• Highly popular and proposed by Cunningham, 1983.

• This model is based on the Kuznetsove and Rosin-Rammler equations.

ncxxeP )(1 −−=

167.08.0

TT

Om Q

QVAX ×

×=

633.0167.08.0

115

−−

= ANFO

emSQAKX

−

+

−=

HL

BWB

S

DBn 1

2

1142.2

5.0

)(06.0 HFRDIJFRMDA +++×=

nCxX /1

50 )693.0(=

)/11( nXx m

C +Γ=

P: percent passing n: index of uniformity xc: characteristic size x: screen size Xm: mean fragment size (cm) X50: median fragment size (cm) A: rock factor VO: rock volume fragmented per blast hole (m3) QT: mass of TNT containing the energy equivalent of the explosive charge in each blast hole (kg) K: powder factor (kg /m3) SANFO : weight strength of the explosive relative to ANFO Qe: mass explosive being used in each drill-hole (kg) H: bench height (m) L: total charge length (m) W: standard deviation of drilling accuracy (m) RMD: rock mass description JF: joint factor RDI: rock density index HF: hardness factor

Spathis (2004) addressed a common mistake in application of Kuzntsov’s original expression which is essentially for the mean size and not the median size. Therefore the correct expression for the characteristic size (xc):

The Kuz-Ram model under estimates the contribution of fines in the ROM size distribution (Kojovic et al., 1995; Comeau, 1996).

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• The Swebrec function is a cumulative fragment size distribution presented by

Ouchterlony, 2005.

• The Rosin-Rammler curve is replaced by the Swebrec function and the model is

known as KCO (Kuznetsov-Cunningham-Ouchterlony).

• Benefits from a smart and powerful function and it covers a wide range of measured

fragmentation data.

• According to Ouchterlony (2005), the Swebrec function can be used in the Kuz-Ram

model and removes two of its drawbacks; the poor predictive capacity in the fines

range and the upper limit cut-off to block sizes.

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Rock fragmentation models (Swebrec)

( ) ( )[ ]{ }bXxxxxP 50maxmax lnln11)( +=

633.0167.08.0

50 115)(

−−

×= ANFO

eSQAKngX

nXxb ×= )]ln(.2ln2[ 50max

)]ln(..)(4.0 50max25.0

5025.0 XxXBBb ref=

b: a curve-undulation parameter xmax : minimum of in situ block size,, Spacing or Burden x: screen size Bref : reference burden (m) b: a curve-undulation parameter

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Rock fragmentation models (Swebrec)

According to Spathis (2012), error in the characteristic size is less than 5% for n>2, but highly increases for n<2.

Swebrec Probability Density Function (PDF) has a singularity at x=0 for its function’s form. Based on the PDF, the influence of singularity emerges for smaller sizes less than approximately 0.05 of xmax (Spathis., 2012).

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The gamma-based KC-KUM model

The gamma-based blast fragmentation model: • Gamma is a two-parameter family of continuous probability distributions and can be used

as a useful distribution for random variables with range in the positive real line. • Kuznetsov-Cunningham-Kerman University Model (KC-KUM) or (KCF) • A grafting point of 40% was chosen. • The new model is comprised of two similar gamma-based equations for fragment passing

sizes X≤40% and X≥40%. • The cumulative distribution function (CDF) is the regularised gamma function:

( ))(

,,;

k

xkkxF

Γ

= θγ

θk: shape parameter Ө : scale parameter x: screen size

Fine-to-central part equation

Central-to-coarse part equation

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The gamma-based KC-KUM model

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( ))(

,,;

k

xkkxF

Γ

= θγ

θ

KC-K

UM

Fine-to-central part

equation

Central-to-coarse part equation

2

50Xfn

k ≅

504X≅θ 0>θ

0>k( )

Γ

=≤−

2

4,

2%40

50

50

50

Xf

Xf

KUMKCn

Xxn

XP

γ

3.0fnk ≅

1.150

×

≅BXSθ

0>k

0>θ( ) ( )3.0

1.150

3.0 ,

%40f

f

KUMKC nBXSxn

XPΓ

×

=≥−

γ

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Results and performance assessment

=

m

dL X

Xe log

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Results and performance assessment

Overall absolute Log errors of the models in illustration of blast fragmentation distribution

Blast No. Overal absolute Log errors Kuz-Ram Swebrec KC-KUM

J-1 1.03 0.83 0. 30 J-2 0.99 0.49 0.61 J-3 1.70 0.92 0.16 J-4 2.11 1.27 0.61 J-5 0.94 0.78 0.50 J-6 1.81 1.16 0.78 J-7 1.27 0.42 0.42 J-8 0.89 0.44 0.78

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Rock fragmentation prediction by gamma-based model

( ) ( )3.0

1.150

3.0 ,

%40f

f

KUMKC nBXSxn

XPΓ

×

=≥−

γ

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Conclusions

• It is a simple blast fragmentation model, but not too simple! • A blast fragmentation model based on gamma CDF developed with promising

results. • The proposed ‘KC-KUM’ model, provides blast engineers another option for the

prediction of rock fragmentation. Prediction of X80 can be done just by the central to coarse part equation.

• As the first step, KC-KUM showed to have the potential to become a good model!

• Studies are open; more experiments are needed to enhance KC-KUM/ KCF and

obviously developments would be expected. Still a long way ahead!

In terms of rock blasting engineering, in particular fragmentation;

I would like to remain sceptical So

I PREFER TO RUN VARIOUS MODELS SIMULTANEOUSLY IN ANALYSIS.

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Acknowledgements

• Rock Blasting Pioneers for their Valuable Efforts

• Mobin Mining and Constructions Co.

• Gol-e-Gohar Research and Development Centre

• Mr. Mohammad Reza Dehghan

• Mr. Amin Hakami

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Thank You! Questions?

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Run the Model in Microsoft EXCEL

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In fact, some reasons that make blast induced fines estimation highly complicated in full-scale blasts are:

• Crushed zone along the blast hole is not constant and production of fines along the blast

hole varies due to uneven distribution of explosive energy especially where high energy explosives and boosters are utilized. • Variety in geo-mechanical properties of in-situ rock mass along the blast hole, which provides various potentials for fines production.

• Difference in rock structure, density of discontinuities and micro fractures as potential routes for explosive gases flow.

• Difference in velocity of burden movement along the bench height which has effect on the severity of fragments’ impacts and throw.

• Massive movement of thousands of tons of rock which is associated with severe impacts, abrasion and compression of lower fragments by the upper ones, which are essentially comprised of the coarser rocks.

Run the Model in Microsoft EXCEL