Velocity of detonation measurement and fragmentation analysis to evaluate blasting efficacy

Eugie Kabwe

aSchool of Civil,Environmental and Mining Engineering,The University of Adelaide,Adelaide,5005,Australia

bDepartment of Mining Engineering,School of Mines,University of Zambia,Lusaka,Zambia

1.Introduction

This paper evaluates the performance of bulk emulsion explosives HEF100 through a velocity of detonation(VOD)measurement and fragmentation size distribution analysis.The VOD was measured in five blast holes using a resistance wire continuous VOD measurement system.The steady state VOD measured from the holes was compared with the published values under ideal conditions.It was concluded that the steady state VOD values were consistent with the published VOD values.The post blast fragmentation analysis carried out using empirical fragmentation models and image processing software showed that 90%of the blasted material was within 700 mm passing size.

1.1.Velocity of detonation measurement

Explosives with low VOD will have low impact on rock fragmentation than the ones with high VOD(Chiapetta,1988;Heit,2011).According to Cooper(1996),the explosive VOD is commonly used to approximate the detonation pressure and subsequently the explosive shock energy contained in an ideal explosive.The detonation pressure(Pd)of an explosive from the unreacted explosive density and VOD is given by

wherePdis the detonation pressure(GPa),ρeis the explosive density(g/cm3),Cdis the VOD(m/s)andγis the ratio of speci fi c heats of detonation product gases (γ≈3).According to Cunningham(2002),γmay be approximately 2.6 for Ammonium Nitrate Fuel Oil(ANFO)to 3.2 for emulsion.Reduction in the VOD will produce a decrease in thePdvalue as well as the shock energy of the explosive(Tete et al.,2013).VOD measurements indicate the performance of an explosive in real time.There are two common VOD measurement systems,i.e.the point-to-point system and continuous system.The former has limitation as compared to the latter used in this study(Crosby et al.,1991;Mishra and Sinha,2003;Harsh et al.,2005).Pradhan and Jade(2012)carried out a study to investigate the performance of bulk emulsion explosive in a watery blast hole by measuring its in-hole VOD.The performance was found to be unsatisfactory due to reduction in VOD and failure of explosive column to detonate fully.ˇZganec et al.(2016)conducted a study to understand the influence of three different types of primers on the VOD of ANFO and complex ANFO blends.The VOD was measured in situ by a continuous method.It was concluded that ANFO or complex ANFO blends with the same percentage of added emulsion,density and borehole diameter had different steady VODs due to different primer properties.Mendes et al.(2014)compared the VOD for emulsion explosive sensitized with hollow glass micro-balloons and emulsion explosive sensitized with hollow polymer micro-balloons.They concluded that the nature of the sensitizing agent had no significant impact on the explosives detonation behavior.

Fig.1.Schematic illustration showing formation of crushing zone,fracture zone and fragment formation zone.

1.2.Empirical fragmentation models

Kuznetsov(1973)suggested the following empirical equation to predict the mean fragmentation size resulting from rock blasting:

wherexmis the mean fragment size(cm);Ais the rock factor(between 0.8 and 22,depending on rock hardness and structure and its derivation is given in Eqs.(3)and(4))(Gheibie et al.,2009;Singh et al.,2016);Kis the powder factor(kg/m3);Qis the mass explosive in the hole(kg);andRWSis the explosive weight strength relative to ANFO(%).The relation between rock factor(A)and blastability index(BI),proposed by Lilly(1986),can be obtained from Eq.(3),whereBIis determined from Eq.(4):

whereRMDis the rock mass description,JPSis the joint plane spacing,JPOis the joint plane orientation,SGIis the speci fi c gravity in fl uence(t/m3),andHDis the hardness factor.Inserting the parameters ofBIandA,the model(Eq.(2))is presented as

The Rosin-Rammler(Rosin and Rammler,1933)equation is then used to predict the fragment size distribution resulting from rock blasting.It is given by

whereP（x1）is the proportion of the material larger thanx(sieve size,in m),x=x50(the 50%passing value)is the characteristic size(cm),andnis the uniformity index.The final equation of the Kuz-Ram(Cunningham,1983)is given by

whereBis the burden thickness(m),Sis the spacing,dis the borehole diameter(mm),Lbis the bottom charge length(m),Lcis the column charge length(m),Ltotis the total charge length(m),His the bench height(m),andSDis the standard deviation of drilling accuracy(m).TheSDvalue is determined by

The highnvalue indicates uniform sizing while lower value indicates larger proportion of fines and coarse material(Gheibie et al.,2009;Singh et al.,2016).The Kuz-Ram model can predict the coarse fragments reasonably accurate,but it can also significantly underestimate the amount of fines generated(Ouchterlony,2005).Spathis(2004)observed that the uniformity indices in the Kuz-Ram model ranged between 0.8 and 2.2,and the characteristic sizes of the model were in errors of 105%and 179%,respectively.This leads to model extensions which involve one Rosin-Rammler function for the coarse material and another to improve the prediction of fines.Ouchterlony(2005)proposed the Kuznetsov-Cunningham-Ouchterlony(KCO)model to predict the fragment size distribution by replacing the original Rosin-Rammler equation with the Swebrec function(Eq.(9)).The fines part of the fragment size distribution received a more satisfactory prediction when the Swebrec function was introduced(Ouchterlony,2016).Like the Rosin-Rammler,KCO model uses the 50%passing valuex50as the central parameter but it also introduces an upper limit to fragment sizexmaxand a curve undulating parameterbsimilar tonin the Kuz-Ram model(Gheibie et al.,2009).Expression for thex50remains the same,and the expression forband Swebrec function is given by

Fig.2.Overview of the blast block.

Table 1Rock parameters of the trial site determined on the gneiss rock type using RocData(Rocscience,2013).

Table 2Rock mass rating of the trial site(Bieniawski,1989).

Table 3Blast design parameters and initiation system used.

whereP(x)is the percentage of material passing sieve sizex(%),andxmaxis the maximum in situ block size(cm).

Spathis(2004)argued that Cunningham(1983)had misinterpreted the Kuznetsov(1973)formula for the mean fragment size used as a mean,but later treated it as a median.Spathis(2004)suggested the addition of a prefactor to the Rosin-Rammler equation and proposed thatx50should be

Fig.3.Illustration of the conventional charged hole.

Table 4Explosive properties.

Fig.4.Blast timing design(unit in ms).

whereΓis the gamma function.

Eq.(12)represents the KCO model as an improved extension of Kuz-Ram model to overcome the failure of predicting the fine range and the upper limit of particle size:

Kanchibotla et al.(1999)proposed the crush zone model(CZM)to improve the Kuz-Ram’s inability to predict the fragment size distribution.Based on the assumption that fragmentation is caused separately by two different mechanisms,the finer material is generated mainly in the crushed zone while the coarser material is generated by tensile fracturing and pre-existing fractures in the rock mass,as shown in Fig.1.

The CZM model applies two different Rosin-Rammler functions to estimate the fragment size distribution curve.One function is used to predict the fines part of the curve and the other function describes the coarse part of the curve(Gheibie et al.,2009).The two curves join at a fragment size(xc)dependingon the rock properties.The coarse part of the curve is represented by

Table 5Monitored blast holes parameters.

Fig.5.Blasted muck pile and rock fragmentation.

whereP（xc）is the percentage of material passing characteristic sizexc(%),xcis the characteristic size(m),andncoarseis the uniformity index for the coarse part of the curve.Thencoarsevalue can be determined from

The fine material is considered to come from a cylindrical crushed zone around the blast hole in which particles are generated by crushing of the rock due to compressive shear failure(Kanchibotla et al.,1999;Kanchibotla,2003).The crushed zone radius is assumed to be the distance from the blast hole tothe point where radial stresses exceed the uniaxial compressive strength(UCS)of the rock mass.It is represented by

wherercis the crushed zone radius(m),ris the blast hole radius(m),σcis the compressive strength of the rock(Pa).Detonation pressure is calculated by

Fig.7.Time-depth graph for blast hole 2.

whereρcis the density of explosive material(kg/m3).The mass of the rock that fails due to tensile failure is represented by

whereFcis the fraction of rock mass that fails in tension,Mois the mass of rock failed in compression(kg),andMis the total mass of rock per blast hole(kg).The fines part of the size distribution curve is predicted by

wherenfineis the uniformity index for the fines part of the curve,which can be determined from

Fig.8.Time-depth graph for blast hole 3.

1.3.Image processing

There are several digital image processing software packages,e.g.Split,WipFrag,FragScan,and WIEP that are commercially available to analyze the fragment size distribution(Ozkahraman,2006).The Split-desktop(Split Engineering,2001)image processing software is used in this study.Split-desktop was designed to calculate the size distribution of rock fragments through analyzing digital grayscale images acquired through the use of a digital camera(Siddiqui et al.,2009).Image processing can be completely automated to eliminate several process-related expenses,and thus a larger number of measurements can be made by increasing the overall reliability and can be used on a continuous basis without affecting the production cycle(Sanchidrián et al.,2009).However,errors are associated with image processing software;these can be minimized by established sampling methods,employing proper sampling environment and site-specific calibration of the image processing software(Maerz,1999;Maerz and Zhou,2000).The most reliable way for fragmentation to be assessed is through sieving the entire muck pile which is almost impossible.

1.4.Trial site

The blasting was conducted at an open pit,which is part of the project hosted on the Mwombezhi basement dome in the western arm of the Neoproterozoic Lufilian Arc thrust fold belt(Stroud,2010).

2.Materials and methods

2.1.Blast design and parameters

The blast block was approximately 104 m long and 75 m wide with a total of about 299 blast holes(Fig.2).Trial site conditions and rock mass rating were determined(Tables 1 and 2).The planned burden and spacing are 4.7 m×5.2 m with one free face available.The measured burden and spacing on the block did not vary significantly from the plan(Table 3).

The blast holes were primed with AXXIS electronic delay detonators,400 g Viper RDX boosters and charged with HEF100.The average final cup density measured on the trial block was 1.2 g/cm3.Explosive samples were taken at regular intervals and were measured to ensure that the explosives had gassed to the required density.Adequate time was allowed for the explosives to gas before blast holes were stemmed with crushed aggregates.In the blast holes where the final stemming length was measured,the explosives gassed sufficiently before the blast holes were stemmed.Fig.3 shows the conventional charged hole.

2.2.Explosive properties

HEF100 is a booster sensitive bulk emulsion explosive designed for open pit mines.It is a low viscosity black emulsion specially formulated using recycled oil/alternative fuel.Its VOD can reach up to 5500 m/s depending on density,diameter size,and confinement.The product has a critical minimum diameter of 75 mm which yields proper confinement in order to deliver higher VOD results.HEF100 is pumpable and water-resistant,and is known for its high shock energy delivery to shatter the rock and provide properly fragmented rock particles.The technical specifications of the product are illustrated in Table 4.

2.3.Blast timing

The block was divided in northern and southern portions to optimize the results of the blasting.The northern section was timed with 17 ms between blast holes with partly 25 ms between rows in the eastern direction.Timing was increased to 65 ms in the last rows towards the position of the new high wall to protect the high wall and reduce back-break.The southern portion of the block was timed at 42 ms between the blast holes and 25 ms between rows,as illustrated in Fig.4.

Fig.9.Time-depth graph for blast hole 4.

Fig.10.Time-depth graph for blast hole 5.

Five blast holes were selected to measure the VOD for HEF100.The five monitored blast holes were located on the north side of the block from the initiation point.The aim of this study was to monitor the in-hole blast performances of the explosives.The blasting design parameters and the time recorded during the VOD measurement are illustrated in Table 5.Post blast assessment and fragmentation analysis were conducted(Fig.5).

Table 6Steady state VOD recorded in five blast holes.

Table 8Kuz-Ram fragmentation model results.

Table 9KCO fragmentation model results.

Table 10CZM fragmentation model results.

Table 11Fragmentation results.

Table 12Different fragment sizes according to different fragmentation models.

3.Analysis and results

3.1.VOD analysis and results

Depth of blast hole 1 was 13.2 m and full column detonation was recorded at 10.7 m.The recorded VOD was 5234 m/s for the full column length and 597 m/s around the stemming zone indicating contamination of the explosive at 0.2 m.The VOD inceased to 6505m/sat0.3m before attaining steady state,as illustrated in Fig.6.

Depth of blast hole 2 was 12.7 m and stemming length was 3.3 m.Full detonation VOD was recorded at 9.8 m.The recorded VOD was 5478 m/s at 0.5 m at 0.095 ms.Due to low run-up,the explosive took time to attain a steady state of VOD.Initial VOD recorded was 4872 m/s at 1.7 m,and it attained steady state of 5387 m/s at 7.2 m and decreased to 788 m/s around the stemming area(Fig.7).

Blast hole 3 with depth of 12 m was positioned in the second row with a planned timing of 59 ms after blast hole 1.The recorded rise in VOD was 4232 m/s at 0.7 m caused by mud around the primer restricting the detonation energy transfer from booster to the explosive.The hole recorded a low VOD of 947 m/s at 3.2 m from the bottom of the column due to reduced confinement.The steady state VOD of 5140 m/s at 4.3 m from the top was recorded.The last part of the blast hole showed a decline in VOD to 1533 m/s recorded at 0.5 m closer to the stemming zone due to reduced confinement around that part(Fig.8).

Blast hole 4 with 12.2 m depth and stemming length of 3.6 m recorded a full column VOD at 8.6 m.The hole had a planned timing of 59 ms after the initial hole detonated.The run-up VOD from the booster was 6384 m/s,and it attained a steady state of VOD of 5169 m/s at the 7 m depth.The detonation slowed down to 620 m/s at 0.2 m around the stemming area(Fig.9).

Fig.11.Fragmentation distribution curve.

Fig.12.Comparison of fragmentation distribution curves.

Blast hole 5 was positioned on the third row initiated at 67 ms after blast hole 1.The blasthole hada depth of 13.3 mwith a column length of 10.3 m and recorded a steady state VOD of 4981 m/s at 10.2 m.The run-up VOD recorded was 6420 m/s from the booster positioned at depth of0.4m from the bottom.The booster was pulled up 0.2 m from the bottom of the blast hole and the VOD of 756 m/s was recorded at the stemming region at a length of 0.3 m.VOD recorded was lower compared to the others,as a result of reduced confinement caused by movement of the burden on the block(Fig.10).The measured VODs for the five holes are listed in Table 6.

3.2.Fragmentation analysis and results

3.2.1.Fragmentation model analysis

The allowable size classification for the crushers at the site is illustrated in Table 7.In the Kuz-Ram model,the predicted averagex50size was 220 mm and the uniformity factor was 1.42.Proportion of material below 900 mmP（x90）was about 99%for the conventional blast(Table 8).

In the KCO model,the average fragment size is 100 mm and the curvewith varied parameter isb=1.59 for the conventional blasted muck pile(Table 9).

In the CZM model,the predicted average value ofx50is 348 mm for the conventional blast.The uniformity factor for the fines part of the size distribution is 0.081 for the conventional blasts while for the coarse part of the distribution,it is 1.253(see Table 10).

3.2.2.Digital imaging analysis

Thirty pictures were taken on the muck piles analyzed and processed with Split-desktop(Split Engineering,2001)to estimate size distribution results.Size distribution results and fragment size distribution curves show that 70%of the muck pile passes through the 418.62 mm sieve,and an average top size measured was 1164.38 mm for 0.05%of the entire muck pile,as illustrated in Table 11 and Fig.11.The top size material is equivalent to 46 m3of blasted materials.These coarse fragmentations were resultant from the large toe burden as well as the back end of the muck pile.A total of 82,620 m3of blasted materials from the block were within 700 mm size.The values of the mean fragmentation from the empirical models were in range with those obtained from Splitdesktop image analysis(see Table 12 and Fig.12).

4.Conclusions

In this context,it is observed that the VOD recorded in blast hole 5 is lower as compared to other blast holes.This is a result of reduced confinement caused by movement of the burden on the block.The VOD is specified by explosive manufacturers in their product catalogue.Usually,these VOD values are based on the laboratory measurement.However,the laboratory values are usually different from those measured in the field.The following conclusions are drawn in this work:

(1)The published VOD under ideal conditions for HEF 100 varies from 3500 m/s to 5500 m/s.The steady state VOD for the holes selected varies from 4981 m/s to 5387 m/s.The VOD recorded is consistent and within product specification.

(2)The fragmentation size distribution analysis shows that more than 82,620 m3representing 90%of the blasted muck pile are within 700 mm passing rate and 46 m3of muck pile representing 0.05%are above 1100 mm.

(3)The fragmentation size distribution analysis using Split Desktop shows that the 20%(x20),50%(x50),and 80%(x80)passing fractions are in close range with the predicted values from the empirical fragmentation models,which presents the data consistency.

Conflicts of interest

The author wishes to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

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