Prediction of Rock Fragmentation Using a Gamma-Based Blast Fragmentation Distribution Model

Transcription

1 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 1

2 Table of contents 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 2 2

3 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). 3 3

4 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) 4 4

5 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 X 50 and n f 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. 5 5

6 Fragmentation measurement by image analysis A semi-automatic method was selected to find muck pile distribution curves for all the blasts. 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. In average, for each blast 30 photos were taken systematically by a high quality digital camera from muck pile in different steps of loading. 6 6

7 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. 7 7

8 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! 8 8

9 Rock fragmentation models (Kuz-Ram Model) n x P Spathis ( xc ) = Highly 1 e(2004) popular addressed and proposed a common by Cunningham, mistake in application of Kuzntsov s x c : characteristic size original expression which is essentially for the mean size and not the 0.8 This model V is based on the Kuznetsove x: screen and size Rosin-Rammler equations. O X median m = A size. QT Q Therefore the correct expression for the characteristic size (x c ): T X S ANFO m = AK Qe x C S 1 + B W n = B X 1 D 2 B P: percent passing n: index of uniformity X m : mean fragment size (cm) X 50 : median fragment size (cm) A: rock factor VX m = O : rock volume fragmented per blast hole (m 3 ) Q Γ( 1+ T : mass of TNT containing the energy equivalent of the explosive 1/ charge n) in each blast hole (kg) K: powder factor (kg /m 3 ) L S 1/ n x 50 = H C (0.693 ANFO : weight strength of the explosive relative to ANFO ) Q e : mass explosive being used in each drill-hole (kg) H: bench height (m) L: total charge length (m) The A = Kuz-Ram 0.06 ( RMD model + JF under + RDI estimates + HF) the W: contribution standard deviation of fines of drilling in accuracy the ROM (m) size distribution (Kojovic et al., 1995; Comeau, 1996). RMD: rock mass description JF: joint factor RDI: rock density index HF: hardness factor 9 9

10 Rock fragmentation models (Swebrec) { 1 [ ln( x x) ln( x X )] b } The Swebrec function is a cumulative fragment size distribution presented by P( x) = 1 + max max 50 Ouchterlony, The Rosin-Rammler 0.8 curve is replaced by the Swebrec function and the model is X 50 S 115 ANFO = g( n) AK Qe known as KCO (Kuznetsov-Cunningham-Ouchterlony). Benefits from a smart and powerful function and it covers a wide range of measured b = 2ln 2.ln( x X )] n [ max 50 fragmentation data b = 0.4( Bref B). X 50.ln( xmax X 50 )] According to Ouchterlony (2005), the Swebrec function can be used in the Kuz-Ram b: model a curve-undulation and removes parameter two of its drawbacks; the poor predictive capacity in the fines x range max : minimum of in situ block size,, Spacing or Burden and the upper limit cut-off to block sizes. x: screen size B ref : reference burden (m) b: a curve-undulation parameter 10 10

11 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 x max (Spathis., 2012)

12 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: F ( x; k, θ ) = x γ k, θ Γ( k) k: shape parameter Ө : scale parameter x: screen size Fine-to-central part equation Central-to-coarse part equation 12 12

13 The gamma-based KC-KUM model F ( x; k, θ ) x γ k, θ = Γ( k) KC-KUM n f X 50 k k > 0 2 θ 4X 50 θ > 0 P KC KUM Fine-to-central part equation Central-to-coarse part equation 0.3 k nf S X θ B k > 0 θ > 0 P KC KUM ( X 40% ) ( X 40% ) X 50 n f γ, = 2 4 X 50 n Γ f 2 γ n = f 0.3, Γ 0.3 ( n ) f x S X B x X

14 Results and performance assessment e L = log X X d m 14 14

15 Results and performance assessment Overall absolute Log errors of the models in illustration of blast fragmentation distribution Overal absolute Log errors Blast No. Kuz-Ram Swebrec KC-KUM J J J J J J J J

16 Rock fragmentation prediction by gamma-based model P KC KUM ( X 40% ) γ n = f 0.3, Γ 0.3 ( n ) f x S X B

17 Conclusions It is a simple blast fragmentation model, but not too simple! A blast fragmentation model based on gamma CDF developed with promising results. In terms of rock blasting engineering, in particular fragmentation; The proposed KC-KUM model, provides blast engineers another option for the prediction of rock I fragmentation. would like to Prediction remain sceptical of X 80 can be done just by the central to coarse part equation. So I PREFER TO RUN VARIOUS MODELS As the first step, SIMULTANEOUSLY KC-KUM showed to have IN ANALYSIS. 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! 17 17

18 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 18 18

19 Thank You! Questions? 19 19

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21 Run the Model in Microsoft EXCEL 21

22 Run the Model in Microsoft EXCEL 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. 22