21 DP Blair - Limitations of Electronic Delays for the Control of Blast Vibration and Fragmentation

8/6/2019 21 DP Blair - Limitations of Electronic Delays for the Control of Blast Vibration and Fragmentation

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Rock Fragmentation by Blasting Sanchidrin (ed) 2010 Taylor & Francis Group, London, ISBN 978-0-415-48296-7

Limitations of electronic delays for the control of blast vibrationand fragmentation

D.P. BlairTNL Consultants, Carrine, WA, Australia

ABSTRACT: Delay accuracy and timing are typically not the major variables that govern blast vibrationand fragmentation. The most significant variables are usually the explosive charge weight and the localgeology. It is shown that there is only a restricted distance range over which electronic delays can be usedto control the frequency (spectral) content of ground vibration. Furthermore, spectral control does notimply reduced levels of peak vibration. An analysis of peak vibration levels due to quarry blasting indi-

cates that electronic delay blasts performed no better than pyrotechnic delay blasts in reducing groundvibration. It is often assumed that electronic delays will ensure stress wave superposition (addition) atspecific locations in a rock mass and so promote fragmentation. However, even when using electronicdelays, there remains considerable uncertainty in the stress collision point. Irrespective of this uncertainty,the results from a new analytical model of wave propagation do not support the assumption that stresswave superposition promotes fragmentation. Regarding optimum delay intervals for fragmentation, thereis, unfortunately, a considerable uncertainty in the published experimental data, which makes it difficultto determine the dependence of fragmentation on delay interval. As an associated issue, data from 36electronic delay blasts and 36 pyrotechnic delay blasts show no statistical difference in shovel dig rates. Theelectronic delay timing was designed on the basis of stress wave superposition, with the assumption thatan improvement in muckpile fragmentation would yield an improvement in shovel dig rates.

1 INTRODUCTION

Delay accuracy and timing are just two of themany variables controlling blast vibration andfragmentation, and are typically not the majorvariables, especially in surface mining. In thisregard, the most significant parameters are gen-erally variations in local geology and the explo-sive charge weight. Other significant influenceson vibration include the distance to the monitorand its local conditions (i.e. soil layer over bedrocketc), the detector coupling and the local geometry

(i.e. the top of a highwall, the crest of a berm,etc). Although there might be less variables con-trolling fragmentation, the local geology is a verydominant influence, probably more so than forthe case of vibration. The undoubted significanceof these variables should add a cautionary noteto any claim that controlling the delay sequenceand its accuracy will guarantee reduced vibrationand/or optimum fragmentation. In fact Blair &Armstrong (1999) have already shown that blastvibration is unpredictable in the presence of highlyvariable geology, irrespective of delay accuracy.

Furthermore, they note that simply replacing astandard pyrotechnic delay sequence by the equiv-alent electronic delay sequence will certainly not

guarantee an overall reduction in blast vibration.Nevertheless, vibration, at least, is relatively simpleto measure in-situ, and given a sufficient numberof blasts it would be straightforward to experi-mentally determine the influence of delay sequenceand accuracy for a particular set of circumstances.Fragmentation, on the other hand, is difficult andexpensive to measure in-situ, primarily because thethree-dimensional attributes (such as sieve-passing)of all fragments of the entire muckpile should beassessed for each blast. It is because of such dif-ficulties that small-scale explosive tests are often

conducted on uniform samples, with the addedadvantage of eliminating major influences due togeological variations. However, the stress wave pro-duced by the charge in each small blasthole withinthe sample will reflect off the nearby free faces, andthis mechanism, which plagues most small-scalestudies, could seriously confound the measuredfragmentation. Of course it is possible to confineeach face with energy-absorbing material and thiscould reduce the influence of reflected energy, butthis is a relatively rare situation and further com-plicates the experimental arrangement.

Johansson et al. (2008) used cylindrical samples0.14 m in diameter and 0.28 m in length with a sin-gle explosive source placed in a central hole, and


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claimed that the cylindrical specimen minimisedthe influence of geometry in the testing procedure.However, this claim could be questioned because asurrounding cylindrical surface is expected to be areasonably efficient and coherent reflector of waveenergy back into the central portions of the sample.In realistic field measurements, a significant portionof the stress wave energy propagates away from thefragmented zone, whereas in most small-scale testsmuch of this energy is either trapped within thefinite volume (to promote fragmentation) or trans-formed into kinetic energy of fragments.

As an example of unconfined free faces,Katsabanis et al. (2006) conducted a series ofsmall-scale tests on granodiorite blocks of dimen-sions 0.92 m 0.36 m 0.21 m, with 23 blastholesper block, and with specified uniform delay inter-vals ranging from 0 s to 1000 s. However, each

of the 23 outgoing compressive stress waves sepa-rated by the specified primary delay interval willalso have a sequence of 6 secondary reflected ten-sile stress waves, one off each face. Unfortunately,this secondary sequence will have a highly non-uniform delay interval dependent on the locationof each blasthole to each free face. According totheir measured p-wave velocity of 3900 m/s for theintact material, the time delay between the primaryand reflected wave could lie within the approxi-mate range of 15 s to 225 s. Thus fragmenta-tion within the block is unavoidably influenced

by events at non-uniform delay intervals, and thisreflection mechanism, alone, suggests that theresulting fragmentation could be insensitive to thedelay interval between blasthole initiations. Hencecaution should be exercised when inferring opti-mum delay sequences for full-scale fragmentationbased on such tests.

Irrespective of any concerns regarding wavereflections, the experimental data from small-scaletests that purport to show a trend in fragmentationwith delay interval are often scant (due to the dif-ficulty of conducting such experiments), and also

have a significant scatter with regard to the trendbeing inferred. This is certainly the case for mostof the results shown in Tidman (1991), who sum-marised data from 10 major studies for which itwould seem imperative that acceptable statisticalmethods be used to make any inferences. Unfor-tunately, it appears that no such analysis has beenconducted. Although the total data set was rela-tively large (some 50 data points), the overall scat-ter was significant, and the number of data pointsfrom individual tests was small. A small numberof these tests showed an increase in fragmenta-tion with decreasing delay interval, however themajority did not. Consequently, when taken as awhole, it is difficult to be convinced that there isany realistic and consistent trend in the data. As an

example in this regard, it is worthwhile conductinga statistical assessment of some more recent datagiven in Figure 6 of Katsabanis et al. (2006). Thisfigure shows only 7 data points for each of twogiven sieve passing sizes (80%, 50%) as a functionof delay interval, and the authors claimed thatthe results showed a meaningful trend (i.e. theyimplied a decrease in fragmentation with increas-ing delay interval). This data for the 80% passingsize is reproduced in Figure 1, and shows that thedatum at zero delay interval lies significantly aboveall other data points. If this single point is removedthen an approximate insight to the remaining (butvery scant) data can be obtained using standardstatistical methods (see for example, Davies &Goldsmith 1972). Firstly, very conservative (70%)upper and lower bounds can be placed on the mean(regression) as illustrated, and implies that a per-

fectly horizontal line (i.e. no dependence of frag-mentation on delay interval) is also consistent withthese bounds. Secondly, Hypothesis testing understandard linear regression analysis can be appliedin which a probability, P, is calculated based on theF-statistic. In this case the Null Hypothesis is thatthere is no meaningful relationship between delayinterval and fragmentation, and current wisdom isto reject the Null Hypothesis only if P < 0.05. Theset of those 6 data points for a non-zero delay inter-val yields P = 0.85 for the 80% sieve passing fractionand P = 0.56 for the 50% passing fraction (data not

shown) and thus there is no evidence whatsoeverto reject the Null Hypothesis. Of course, in reach-ing these statistical conclusions the data point atzero-delay was discarded from each set. There arethree comments to make in this regard. Firstly, anargument could be made that these points oughtto be rejected anyway because they represent thecase of instantaneous initiation, which is physicallydifferent to all other cases. Secondly, the inclusionof a single extra point, lying well above all others,makes it quite difficult (if not impossible) to selectan underlying model of the data. In this regard, lin-

ear regression is probably not a reasonable modelfor all the data shown in Figure 1. Thirdly, andmost importantly, even if some underlying modelcould be found, it would be difficult to accept thatthe inclusion of a single extra point at the zero-delay interval could significantly alter the previousstatistical assessment of the 6-member set. Basedon this statistical evidence, one would be perfectlyentitled to claim that the data shown in Figure 6(and Figure 1, for that matter) of Katsabanis et al.(2006) does not support the assumption that frag-mentation is a function of delay interval. TheirFigure 1 also shows a curve fit that is quite uncon-vincing in view of the scatter in the data.

The scant data of Katsabanis et al. (2006) sug-gests that fragmentation is coarsest for a zero delay


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interval, however this is not verified by all the

data sets presented in Tidman (1991). Althoughit seems reasonable to assume poor fragmentationfor zero delay interval, this assumption should alsobe tested by further experimental data and appro-priate statistical analysis.

The modelling of fragmentation is probably evenmore difficult than its in-situ measurement. In thisregard there are two important requirements for anymodel. Firstly, the model must incorporate mecha-nisms such as cracking and extension of cracks bygas loading. Although there are two-dimensionalmodels that meet this requirement (see, for exam-

ple, Minchinton & Lynch 1996), there are, as yet,no satisfactory three-dimensional models.

Secondly, the model must be able to resolvethe high-frequency stress waves propagated fromthe blasthole. The explosive pressure load can beclassified by PVN(the von Neumann borehole pres-sure at the detonation front), tCJ and PCJ, where tCJis the time taken for the pressure to decay to theCJ (Chapman-Jouguet) value, PCJ. As an exam-ple, for ANFO in an 89 mm diameter blasthole,PVN= 14.2 GPa, tCJ= 4.2 s and PCJ= 5.7 GPa.Using the explosive source function given by Blair

(2007) it can be shown that the rise time of thispressure load is 2.9 s, and its total duration is21 s. Current models of wave radiation from ablasthole simply do not use source functions withsuch short rise times and durations. For example,Rossmanith & Kouzniak (2004) used an unrealistictriangular pulse shape with a rise time of 83 s andduration of 913 s. Although the models of Blair &Minchinton (1996, 2006) used a more acceptablepulse shape, its rise time and duration were unre-alistically large at 280 s, and 2028 s, respectively.Hence all these models will grossly overestimatethe regions of wave overlap/superposition near anexplosive charge. This is a significant limitationespecially if wave superposition is assumed topromote fragmentation.

Unfortunately, in the marketing of electronicdelays for the control of fragmentation, in particu-lar, science is too often replaced by claims basedon anecdotal evidence, unrealistic modelling, insuf-ficient data or questionable inferences drawn fromdata that has significant scatter. In light of all previ-ous discussion, there are some very sound reasonsto suggest that electronic delays might only have alimited role, at best, in controlling blast vibrationand fragmentation. The main aim of the presentwork is to investigate these limitations. As a partof this aim, results will be presented from a newanalytical model that has a realistic pressure load,and these results will be discussed with regard toelectronic delays and fragmentation.

2 BLAST VIBRATION CONTROL

There are two quite distinct aspects to controllingblast vibration. The first aspect is spectral control,i.e. the control of the frequency content, and is rel-evant to vibrations in (resonant) structures. The sec-ond aspect is peak level control, i.e. the control ofthe peak level of vibration (usually the vector peakparticle velocity, vppv), and is more relevant to therequirements of regulatory compliance. In this casethe monitoring region could be either non-resonant(such as flat open ground in uniform geology) orresonant (such as an urban dwelling or a soil layer

over base rock). Unfortunately, there can be no sim-ple relationship between spectral control and peaklevel control. In other words there can be no simplerelationship between frequency content of a vibra-tion waveform and its vppv (Blair 2004). Neverthe-less, when monitoring vibrations in resonant regions,it is reasonable to expect that if the spectral output ofblast vibration excites a particular resonance, then themeasured vppv could increase. In this case, spectralcontrol could imply a degree of peak level control.However, compliance monitoring is often conductedwell away from structures, and in such cases spectral

control would not imply peak level control. Boththese aspects are now considered in detail.

2.1 Spectral control

Although Blair (1993) and Blair & Armstrong(1999) have discussed the spectral control ofground vibration in much detail, they did notemphasise the inherent (ideal geology) limita-tions of spectral control to any great extent. Theseinherent limitations are now considered, and areprobably best introduced by considering a popularmisconception, which can be loosely paraphrasedas: Use accurate delays and reduce the delay inter-vals; as the delay intervals become smaller, the fre-quencies become higher and will be more readily

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RegressionUpper 70% for meanLower 70% for meanKatsabanis et al

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Figure 1. Statistical analysis of the data from Katsabaniset al. (2006).


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attenuated in the ground, thus reducing vibrations.Another version of this misconception is listed ona product website which claims that the use of elec-tronic delays will allow vibrations to be typicallyshifted to higher, less damaging frequencies.

It is interesting to note that the ultimate in fastfiring is to have a zero delay between blastholes,which, according to the misconception, wouldimply infinite frequencies. Although this simpleexample is quite sufficient to expose the miscon-ception, it is worthwhile examining the physics insome detail. In this regard Figure 2 shows the totalvibration waveform from 10 blastholes, uniformlydelayed by 50, 20, 10, 5 and 2 ms.

All blastholes are charged identically andassumed to be equidistant from the monitor andlocated in uniform, non-attenuating geology. Fur-thermore, each blasthole is assumed to produce

a single vibration waveform given by the impulseresponse of a Butterworth filter that is band-limitedover the range 4 Hz to 100 Hz. The lower responseis selected because it mimics the typical response ofmost geophones and the upper response is selectedbecause it approximates the upper frequency limitof amplitudes generally observed in compliancemonitoring (repeats of the first 50 ms of this fil-ter response are shown in the lower plot). Figure 2clearly shows that there can be a significantincrease in the low-frequency content for smalldelay intervals, which, in fact, is precisely opposite

to the claim implied by the misconception.Figure 3 shows the amplitude spectra for the

delayed blasts, in which a larger range of delayintervals has been modelled. There are 9 spectralamplitude plots, all offset, and for uniform delayblasting of 100 ms down to 0.2 ms. The dashedline on the lower plot shows N times the ampli-tude of the single hole response, where N is thenumber of blastholes. In other words, the dashedspectrum is that expected if all N holes were initi-ated simultaneously. The spectral banding for thelarger delay intervals is quite obvious, with domi-

nant contributions spaced according to the delayinterval between blastholes. A detailed analysis ofthis banding for a given delay interval has beenpreviously given (for example, see Blair 1993) andwill not be repeated here.

The important insight to gain from Figure 3 isthat as the delay interval decreases, all frequencies(including the very low frequencies) are stretchedout along the horizontal axis, whilst all amplitudesare constrained to remain under the dashed outline.It is also clear that as the delay interval approacheszero, the amplitude response approaches the case forinstantaneous initiation (dashed line), as expected.This spectral plot clearly shows that there is a signifi-cant increase in low-frequency content as the delayinterval decreases, which is consistent with the time

waveforms shown in Figure 2. The spectral plot ofFigure 3 also explains some of the apparent anoma-lies seen on vibration records of electronic short-delay blasts in which there can be a significant levelof low frequency energy that seems to appear fromnowhere. This is due to the limited frequency responseof geophones in particular, which are incapable ofdetecting amplitudes accurately below about 4 Hz or

so in a slow-fired blast. However, when firing fast,the amplitudes at ultra-low (un-detected) frequenciesare now shifted higher into the low-frequency range,which can be measured by the detectors. Figure 3shows that this low-frequency intrusion begins tooccur for delay intervals of 10 ms or lower.

Siskind et al. (1980) measured the vibrationresponse a large variety of residential structures anddetermined resonant frequencies in the range 4 Hzto 28 Hz. According to the simple model illustratedby the spectral response in Figure 3, delay intervalswould need to be less than 50 ms and somewhatgreater than 10 ms in order to avoid exciting thesestructural resonances. This limitation on delay inter-vals implies a degradation of the spectral controlavailable even when using ideal (no scatter) delays.

Figure 3. Amplitude spectra of the synthetic vibrationwaveforms.

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FREQUENCY (Hz)

Delay Interval = 0.2 ms

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50 ms

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Figure 2. A synthetic vibration waveform for 10 blast-holes uniformly delayed.


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The models discussed so far have involvedblastholes of equal charge weights, and equal dis-tances from the monitor. It is now shown that thespectral control is further degraded if the distances orcharge weights are unequal (i.e. the scaled distancesare unequal), as is typical in many blasts, especiallyfor measurements in the near-field. In order to illus-trate this point, Figure 4 shows 10 blastholes, eachseparated by 5 m, charged identically, initiated fromwest to east and detected by 5 monitors placed onthe circumference of a semicircle of radius 27.5 m.Each monitor location is specified by a rotationangle, , defined positive anticlockwise from East.The figure also shows the modelled vibration enve-lope function recorded by each monitor assumingideal (no-scatter) delays and uniform geology. Theseenvelope functions are constructed from the meas-ured triaxial components of velocity from a single

blasthole (seed) firing in massive sandstone. It isclear that each station receives varying responsesfrom each blasthole, and that monitors located at= 0 or 180 degrees have the largest non-uniformityin responses and the monitor at = 90 degrees hasthe most uniform responses.

At this stage it is instructive to introduce thenotion of a space-frequency plot, which showshow the amplitude spectrum changes as a functionof rotation angle, , i.e. as a function of monitorlocation with respect to the blast. In this case themonitoring space traversed is the circumference of

a semicircle, and is specified by the circle radiusand the rotation angle. Figure 5a shows the space-frequency results for a monitoring radius of 27.5 m(as illustrated in Figure 3) and Figure 5b shows theresults for a monitoring radius of 100 m.

It is obvious from Figure 5a that the spectralbanding is least smeared for = 90 degrees, i.e. at thatmonitoring station for which each blasthole vibra-tion is most uniform. Clear spectral banding impliesgood spectral control. Thus there is poor spectralcontrol (i.e. a significant smearing of spectral com-ponents) for = 0 or 180 degrees and this is due

to the non-uniform responses from each blastholerecorded at these monitors. As expected, this spectralsmearing is significantly reduced when monitors areplaced at a much greater radius (Figure 5b), becauseeach hole-monitor distance is then approximatelyequal and so the vibration response from each holeis similar for all rotation angles.

The single row blast shown in Figure 4 is use-ful in highlighting the influence due to varyingblasthole distances to a given monitor, however,it is hardly a practical design. Figure 6 shows asmall blast of 96 holes, with a 20 ms delay betweeneach row (on the vertical zip line) and 100 msbetween each hole within a (horizontal) row. Themonitors are spaced along the circumference ofa circle of prescribed radius. Figure 7a shows the

space-frequency diagram for monitors placed ona radius of 60 m and Figure 7b shows the resultswhen the monitoring radius is increased to 200 m.Figure 7c shows the results for a monitoring radiusof 200 m in variable geology that is modelled byintroducing a 20% random fluctuation on eachwaveform signature, and even this mild degree ofvariability smears out the spectral control. Forinterest, Figure 7d shows the results for blastingwith pyrotechnic delays (scatter assumed to be1%) in uniform geology. Thus reduced accuracy ofdelays will also degrade the spectral control.

Assuming uniform geology and accurate delays,the present results imply that the spectral controlimproves as the blast-monitor distance increases.However, if the distance is too great, the vibra-tion waveform from each blasthole broadens sig-nificantly due to ground attenuation, and this,

itself, also reduces the spectral control that can

Figure 4. Vibration from10 blastholes detected at5 locations on a semicircle.

Figure 5. Space-frequency plots, ideal delays, idealgeology; (a) monitoring radius 27.5 m; (b) monitoringradius 100 m.

(a)

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be achieved with the delay initiation sequence.In order to illustrate this effect, Figure 8a showsthe normalised envelope of vibration from a sin-gle blasthole fired in coal overburden materialand monitored at various distances. The wave-form broadening with distance is quite apparent.The spectral content of these waveforms is shownin Figure 8b as the mean of the triaxial (L, T, V)components, and it is obvious that the waveformbroadening is equivalent to a decrease in frequencycontent as is expected. In fact for distances 500 m,there is little contribution from each blasthole forfrequencies above 10 Hz. Thus any productionblast that is comprised of such blastholes willalso not produce energy above 10 Hz, irrespectiveof the delay sequence and its accuracy. In other

words, there is no possibility of channelling energyinto higher frequencies using smaller delay inter-vals. Thus vibration monitoring at large distancesplaces a severe restriction on the degree of spectralcontrol available. It is worthwhile to recollect atthis stage that vibration monitoring at small dis-tances was also shown to place a severe restrictionon spectral control, even in ideal geology, and isdue to the non-uniform response of each blasthole(Figure 4). Thus there is only a restricted distancerange, somewhere in the medium-field, for whichaccurate delays will be an aid in controlling the

spectral output of vibration.

2.2 Peak level control

As noted previously, spectral control does not implypeak level control. However, a lack of spectralcontrol (i.e. for blasts comprised of broad wave-forms) could well imply a lack of peak level control.In this regard it is instructive to analyse a 10-holeblast having 100 ms delay between holes (simi-lar to the design shown in Figure 4) and havingthose seed functions used to construct Figure 8a.Figure 9 shows the normalised vibration envelopeassuming ideal delays, and it is obvious that theindividual holes can be detected only for a moni-toring distance of 200 m; for distances of 500 m or

leadin

100 m

Figure 6. 96-hole blast, monitors on circle.

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Figure 7. Space frequency plots. (a) ideal delays, idealgeology, monitoring radius 60 m; (b) ideal delays, idealgeology, monitoring radius 200 m; (c) variable geology,ideal delays, monitoring radius 200 m; (d) uniform geol-ogy, pyrotechnic delays, monitoring radius 200 m.

greater the individual holes are smeared throughoutthe broad nature of the waveforms which should beinsensitive to any scatter in delay time intervals. Thisviewpoint is entirely consistent with the previousviewpoint regarding the lack of spectral control.

In order to demonstrate the insensitivity offar-field vibration to delay scatter, a Monte Carlo


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wave superposition model was constructed forthe 10 blastholes with a nominal delay interval of100 ms. Figure 10 shows the normalised envelopeof vibration for monitoring distances of 500 m and4000 m, predicted using electronic delays and pyro-technic delays. These envelope functions representthe peak amplitude predicted during 100 simula-tions of each delay type, i.e. they are peak-detec-tion envelopes, which show the maximum vibrationamplitude at any particular time. These resultsclearly demonstrate that the peak vibration levelis very insensitive to delay accuracy for this simpleblast. However, it is worthwhile considering a morerealistic blast having 96 blastholes in the drill patternshown in Figure 6, and monitored at 500 m. How-ever, the zip line now goes North up the centre ofthe pattern, and two different delay sequences were

modelled. Sequence 1 consisted of a 42 ms delaybetween rows and 17 ms between holes in each rowinitiating to the East. For holes in each row initiat-ing to the West there was one offset delay of 25 msfollowed by the remainder at 17 ms. Sequence 2 wasa time-expanded version of Sequence 1 and con-sisted of an inter-row delay of 100 ms, an inter-holedelay of 42 ms and an offset delay of 65 ms. Thesetypes of blast designs are quite realistic for quarryand even open pit operations.

Figure 11 shows the peak envelope results, allnormalised by the same factor in order to comparethe amplitudes for both sequences and both delaytypes (pyrotechnic, electronic). As expected, thetime-expanded Sequence 2 gives lower amplitudessimply because it reduces the crowding of blast-hole waveforms.

Again, it is quite obvious that the peak vibra-

tion level is very insensitive to delay accuracy forthese realistic blast designs. It is also very perti-nent to note here that expanded pyrotechnic delaysequences can be just as effective as equivalent elec-tronic delay sequences in reducing wave crowding,which, in turn, reduces vibration. Yet again, forthese large enough monitoring distances (500 m),electronic delays provide no clear advantage overpyrotechnic delays for the control of peak levels ofground vibration. Furthermore, in highly attenuat-ing geology the vibration waveforms will be broad-ened at even moderate distances, which implies

that pyrotechnic delays will also compete well withelectronic delays for these distances

0 2 4 6Time (s)

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Figure 8. (a) vibration envelopes from single blastholes;(b) the mean amplitude spectra.

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Figure 9. Normalised vibration envelopes, 10 holeblast, 100 ms uniform delay interval.

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Figure 10. Peak vibration envelopes.

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Figure 11. Peak vibration envelopes for the twosequences.


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In a practical sense it is expected that influencesdue to geology, blast-monitor distance and rotationangle, , will most likely be present to some extentin any blast. In this regard, Figure 12 shows a plotof log(vppv) versus log(scaled distance) obtainedfrom 446 pyrotechnic delay blasts and 258 elec-tronic delay blasts fired in the same set of quarries;the solid curves are linear regression fits to the data.Figure 13 shows a probit plot of the residuals andthe non-linearity of this plot, especially the devia-tion in the tails, visually indicates that the scatterdoes not obey a normal distribution (Miller 1998).The degree of normality can be formally quantifiedby evaluating the Shapiro-Wilk Wstatistic and itsassociated probability, PW, for the data set in ques-tion (see for example, Royston 1982). For bothdata sets it was found that PW< 0.005 and so theassumption of normality must be rejected (Miller

1998). Thus the standard statistical tests, based onleast squares regression (Davies & Goldsmith 1972),cannot be used to make inferences on vibration dif-ferences between the pyrotechnic and electronicdelay blasts. In this case, nonparametric (distribu-tion free) statistics should be applied. The slopeand intercept of each plot were estimated usingTheil-Sen statistics (Sprent 1989), and bootstraptechniques (Efron & Tibshirani 1993) were usedto determine confidence intervals and associatedprobabilities, PB, for these statistics. It was foundthat PB< 0.005 for the differences in slope as well as

intercept, and so the assumption of statistical simi-larity between electronic and pyrotechnic data setsmust be rejected. However, although the differencesare statistically significant they are not practicallysignificant. There is certainly nothing to suggestthat the electronic delay blasts produced a lowervibration than that of the pyrotechnic delay blasts,especially for high vibration levels, which are perti-nent to both compliance and structural damage.

The significant scatter in the results of Figure 12is due to one or more of the major influences dis-cussed previously, and strongly suggests that a large

number of blasts would generally be required inorder to detect statistically meaningful differencesin vibration between pyrotechnic and electronicdelays at any specific site. In view of all previousanalysis and discussion it is not surprising that delayaccuracy plays only a very minor role in control-ling blast vibration. In fact, the vibration screen-ing effect due to damage from prior blastholes ina sequence (Blair 2008) has a far greater influencethan delay accuracy or flexibility on the reduc-tion of ground vibration. Furthermore, sequencesdesigned to take advantage of this screening effectcan be implemented using either electronic orpyrotechnic delay sequences.

Naturally there are situations (not necessarilyrelated to vibration or fragmentation) where elec-tronic delays can be superior to pyrotechnic delays,

such as in underground mass blasts and large castshots in surface coalmines. However, in most othercases, pyrotechnic delays perform as satisfactorilyas electronic delays with regard to vibration pro-vided reasonable initiation sequences are employed.Of course there are some delay sequences thatcould be considered unreasonable with regard tovibration. For example, in underground develop-ment blasts, long-period (LP) electric detonatorsare sometimes used. These are pyrotechnic delaydevices with a rather restricted range in selectabletimes, which invariably means that there can be

a set of blastholes (sometimes >5) close in spaceand initiating at the same nominal delay time.Although the pyrotechnic delay scatter ensures thatnear-instantaneous initiation within a set would behighly improbable, the vibration waves from theseholes could still crowd in time to produce an exces-sive vibration. In this situation a carefully delayedsequence of electronic detonators would signifi-cantly reduce the average vibration, not becauseof the delay accuracyper se, but rather because ofthe flexibility to choose a sequence with a reason-able delay time between all blastholes. However, itis also pertinent to note that there are alternativepyrotechnic delay systems for development blaststhat have an improved flexibility over the LP series.In a practical sense, these alternative systems shouldperform just as well as electronic delay systems for

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Figure 12. Peak vibration for pyrotechnic and elec-tronic delay sequences fired in the same set of quarries.

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Figure 13. A probit plot of the residuals in log(vppv).


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the control of vibration due to development blasts,especially at distant monitoring stations.

3 FRAGMENTATION CONTROL

There are at least three major assumptions impliedin most arguments to support the use of electronicdelays to optimise fragmentation. Firstly, thereis some known delay interval, or range of delayintervals, that will produce optimum fragmenta-tion. Secondly, the scatter in electronic delay timesis negligible. Thirdly, superposition of stress wavesfrom individual blastholes will promote overallfragmentation within an extended volume of rock.

The first assumption was discussed in detail inthe Introduction where evidence was presented todemonstrate that this assumption is unsound, and

much more experimental work and appropriatestatistical analysis is required in order to obtaindefinitive conclusions. With regard to the secondassumption it should be noted that it is impossiblefor any timing device to have perfect accuracy. Elec-tronic delays are clock-based systems and so theymust have a scatter in times that is proportionalto the desired delay time; thus it makes no senseto claim an absolute accuracy, such as 1 ms, forthese devices, as is often done. Furthermore, accu-racies quoted in this form are statistically impre-cise. The scatter in delay times for any detonator

within a batch is properly classified by a coeffi-cient of variation, which is defined as /, where is the standard deviation in initiation times and is the mean (or nominal) initiation time of thebatch. In this regard / for pyrotechnic delaysgenerally lies in the range of 1% to 4%, whereas/for electronic delays generally lies in the rangeof 0.02% to 0.05%. Laboratory tests on either typeof delay would probably yield values closer to thelower limit whereas field implementations prob-ably yield values closer to the upper limit, espe-cially in high-temperature environments. Thus if

/= 0.04% for an electronic delay of nominaltime = 3 s (as might be required during a moder-ate-sized blast) then its standard deviation wouldbe 1.2 ms. Assuming that the scatter in delay timesis given by a normal distribution, then there is a31% chance that a 3 s detonator will fire 1.2 mseither above or below its nominal value. This sim-ple example shows that even electronic delays arenot accurate enough to maintain a uniform delayinterval of the order of milliseconds throughoutmany blasts. Clearly, this has implications for fastfiring in any attempt to optimise fragmentation.This issue is discussed later in more detail.

With regard to the third assumption (superpo-sition of stress waves) there are further points toconsider. For example, in modelling and concep-tual ideas, it is often assumed that all blastholes

produce the same stress waveshape and superposein an ideal manner to create a zone of high stressvia constructive interference. However, it is wellknown that even identically charged blastholes inuniform geology can produce waveforms of mark-edly different shape, and that these waveformswill also suffer significant changes as they travelbetween interacting blastholes in ground dynami-cally altering as the blast progresses (Blair 1993).Thus it is difficult to accept that ideal stress wavesuperposition will occur to any great degree. How-ever, even if ideal stress wave superposition didoccur, significant problems still remain with theidea that such superposition promotes fragmenta-tion in an extended volume of rock. These prob-lems are now discussed with reference to the resultsfrom a new analytical model of ideal stress wavepropagation from a blasthole. This model is based

on the method described in Blair (2007) that hasbeen altered to include solutions to the full stresstensor under the influence of an extended chargewith a finite velocity of detonation (VoD) within aviscoelastic rock mass. The dynamic stresses can becalculated by evaluating the appropriate displace-ment derivatives in the (r, z) directions of a cylin-drical coordinate system for which ur and uz arethe only displacements of interest. In particular,the maximum shear stress,m, in a rock of shearmodulus, , is defined as:

m r z t A A( , , ) = +2 12

22

(1)

where

Au r z t

z

u r z t

rr z

1 = +

( , , ) ( , , )

(2)

Au r z t

r

u r z t

zr z

2 =

( , , ) ( , , )

(3)

The maximum shear stress is chosen as the waveattribute of interest because it is a stress invariant(i.e. it does not depend upon the rotation angleat any particular point in the rock mass), and,furthermore, can be associated with the strengthof materials (Timoshenko & Goodier 1971).Figure 14 shows contour plots of the dimension-less maximum shear stress, m(r, z, t)/2, due to abase primer located at (x,y) coordinates (0, 3) ina 6 m vertical blasthole. Figure 15 shows the resultsfor the simultaneous initiation of a base and topprimer. The elastic properties of the rock mass are= 16.9 GPa and Poissons ratio, , is 0.25; thisgives a p-wave velocity, VP, of 4.5 km/s. The rockis also assumed to have a seismic Q of 100, typicalof the viscoelastic response for a competent mate-rial. In each figure, the stress wave propagation


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is shown at the four time instants when the head(leading) wave is at 2 m, 4 m, 6 m and 7 m fromthe base of the blasthole. These results are calcu-lated for an ANFO explosive in an 89 mm diam-eter blasthole for which the VoD, VD, is assumedto be 4.5 km/s =VP; all other explosive propertieshave been given previously. The wave contours areplotted over a space of 4 m 8 m using 161 321grid points. All contours are plotted from 0.005to 1.0 in increments of 0.005, and thus the stresslevel is proportional to the darkness shown in thecontours. A contour value of 1.0 occurs wherethe stress wave amplitude in the medium equalsthe material shear modulus.

The fastest moving (head) wave in this exam-ple is a spherically spreading p-wave, and thisproduces a Mach cone due to the slower shear-vertical (SV) wave in the surrounding medium.

The half-angle of this S-wave Mach cone isgiven by = arcsin(VS/VD). For the Machcones in Figures 14 and 15, = arcsin(VS/VP) =arcsin( / )1 3 = 35.3 degrees.

The travelling ring load ceases when it has con-sumed the explosive and from then onwards thewavefronts weaken with distance due to geometricspreading. Figure 14 shows that the single primerproduces the dominant stress because it is able togenerate the SV-Mach wave over a 6 m columnlength. However, for the dual-priming case shownin Figure 15, each oppositely directed ring load

travels only 3 m before exhausting all the explosiveat the point of wave collision (y= 0). From thenonwards the propagating stress waves reduce rap-idly in strength primarily due to geometric spread-ing, thus the SV Mach cone is much weaker abovethe original charge than it was for the case of singlebase priming. Hence such dual priming will pro-duce reduced fragmentation in regions above thecentral plane of the blasthole. Although the stresswave propagation downwards might give improvedfragmentation for those regions below the chargecentre, it is reasonable to suspect that the overall

volume fragmentation will be worse than it wouldhave been for the case of base priming alone, wherea high amplitude SV wave propagates upwards andaway from the blasthole. Any surface reflection ofthis wave would also promote further fragmenta-tion in travelling back down through the medium.

The model used by Rossmanith & Kouzniak(2004) is only valid for infinite charge lengthsfor which the p- and SV-Mach waves are alwaysfully developed, radiating out through the entiremedium and maintaining constant amplitude asthey progress in space along any one blasthole.However, the present model shows the morerealistic situation in which there is a build-up ofthese waves as the detonation progresses awayfrom the primer, producing a maximum volumeinfluence at the instant all the charge is consumed.

From then onwards all stress waves decrease due togeometric spreading. The model of Rossmanith &Kouzniak (2004) cannot account for these effectsand so it significantly overestimates the influence

of stress wave interaction in this regard.The stages of stress wave progression in Figure 14

can also be used to investigate stress wave interac-tion between neighbouring holes. For example,neighbouring holes space-delayed by 2 m (i.e. time-delayed by 0.44 ms in this case) would not havetheir SV-Mach cones intersecting in the first twoframes of Figure 14 simply because the waves in thefirst frame have not had time to radiate far from theblasthole. However, in the Rossmanith-Kouzniakmodel the SV-Mach waves from two neighbour-ing holes will always intersect somewhere, and this,

again, shows how this model overestimates thedegree of stress wave interaction.The wavefront contours in Figures 14 and 15

also show that each stress wave is highly localisedin space (approximately 0.2 m in width) and thisimplies a time width of 44 s at any particular loca-tion due to the p-wave velocity of 4500 m/s. Thuseven the best of the electronic delays are not accu-rate enough to guarantee waveform collision at pre-cise locations. In fact, as shown previously, there isa 31% chance that a dual-primed electronic delayblasthole in moderate-sized blasts will fire with atime difference greater than 1.2 ms between topand base primers that are planned to fire simulta-neously. During this time difference the stress wavefrom the first initiated primer will have travelled atleast 5.4 m and so the stress wave collision point can

Figure 14. Four stages of wavefront progression due toa single base primer.

Figure 15. Wavefront progression due to a top and baseprimer simultaneously initiated.


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never be guaranteed, even in an approximate sense.This same argument applies equally well to stresswave interaction between neighbouring holes.

The upshot of all this detail is that the stresswaves are not similar in shape (due to variations inlocal geology and dynamic alteration of the groundas the blast proceeds) and even if they were simi-lar, the collision region will be varying by randomand significant amounts as the blast progresses.This occurs even using electronic delays, for eithertop/base initiation in a single blasthole or planneddelays between neighbouring holes. As anotherpoint, even under ideal conditions the amplitude ofthe interacting stress waves will vary significantly,depending on the consumed charge lengths at thetime and place of collision. Finally, even if theregions of wave collision could be predicted, theywould be highly localised and so comprise only a

small fraction of the total volume of rock to befragmented. All this evidence shows that stress wavecollision certainly plays no predictable role in rockfragmentation by blasting, and most likely playsno significant role either. Furthermore, amongstall the complexities and variables involved, there isno evidence to suggest that replacing pyrotechnicdelays with electronic delays will provide any con-sistent improvement in fragmentation.

From a viewpoint of mine productivity, it isoften assumed that an improvement in fragmenta-tion will yield an improvement in shovel dig rates.

In this regard, a large open pit mine kindly sup-plied their data from a trial of 72 blasts, 36 firedwith pyrotechnic standard delay sequences, and 36fired with electronic delay sequences designed onthe basis of stress wave superposition. Each blastpair (pyrotechnic, electronic) was fired in the samepit region, however they were not necessarily side-by-side and so cannot be considered as matchedpairs. The blasts were dug with 4 shovels, two thatwere old and two that were new. Furthermore, eachblast was entirely dug with either a new shovel or anold shovel in order to reduce shovel bias. A prelimi-

nary analysis showed that the dig rate of each oldshovel was essentially the same and significantlyless than the dig rate of each new shovel (whichwas also essentially the same). Thus the total datawas divided into 4 sets: Pyrotechnic 1pyrotechnicdelay blast, dug with old shovels; Pyrotechnic 2pyrotechnic delay blast, dug with new shovels;Electronic 1electronic delay blast, dug with oldshovels; Electronic 2electronic delay blast, dugwith new shovels. Figure 16 shows the probit plotsfor these four sets of dig rate data, in bench cubicmetres per hour (BCM/hr).

The large vertical offset of the upper plots dem-onstrates the significantly higher dig rate of thenew shovels. However, the parameter of interesthere is the difference in dig rates between the pyro-technic and electronic delay blasts for the same

type of shovels. All these probit plots are morelinear, over their entire range, than those shown inFigure 13 for the vibration. Thus, visually at least,the variations within each separate set appear to benormally distributed. However, to be more defini-tive, Table 1 shows the probability, PW, associatedwith the Shapiro-Wilk statistic for each set, and isa measure of the strength of the Null Hypothesis(i.e. the variations within each set follow a randomnormal distribution). Accepted statistical wis-dom decrees if PW> 0.1, then there is no evidenceagainst the Null Hypothesis. In fact PW is muchlarger than 0.1 in all cases, and thus the statisti-cal evidence strongly suggests that the variationsare normally distributed. Inferences based on thet-test can then be made regarding differences inthe average dig rates for each set. This is formallydone using a two-sample t-test assuming unpaired

data with unequal variance (it is quite clear fromFigure 16 that Pyrotechnic 1 has a larger variancethan Electronic 1). In this case the Null Hypoth-esis is that there is no difference in the averagedig rates between the pairs of sets considered,and Pt is a measure of the strength of this NullHypothesis. The results are listed in Table 2, andshow that there is no statistical difference (Pt> 0.1)in the average dig rates between blasts fired withelectronic delays and those fired with pyrotechnicdelays when both blast types are dug with the sametype of shovels. When different types of shovels dig

each blast then there is a significant difference inall dig rates (Pt< 0.005), which is due solely to thedifference in dig rates between shovel types.

All these results show that electronic delaysequences, based on waveform superposition the-ory, did not alter muckpile dig rates, and hence, byassociation, did not alter fragmentation. As a fur-ther disadvantage, blasts designed on the basis ofstress wave collision also generally involve abnor-mally short delay intervals (1 ms or so) between cer-tain blastholes. Such a design will certainly increasevibration due to wave crowding (see Figure 11 and

associated discussion) and so is a poor design withregard to wall stability in open pits.

800

1000

1200

1400

1600

1800

.01 .1 1 5 10 2030 50 7080 90 95 99 99.999.99

Pyrotechnic 1Pyrotechnic 2Electronic 1Electronic 2

BCM/hr

Percent

Figure 16. Probit plots of dig rates; 4 data sets from72 blasts.


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4 DISCUSSION AND CONCLUSIONS

4.1 Vibration control

It has been shown that there are natural limits tocontrolling blast vibration at any monitoring sta-

tion. These limits are independent of the delayaccuracy and arise due to geologic influences aswell as the relative distance between the monitor-ing station and the blast. However, if the geol-ogy is relatively uniform and the blast-monitordistance lies in the medium-field then there ispotential, at least, to control the spectral outputof blast vibration using electronic delays. Forexample, if a structure in the medium-field hasa dominant resonant frequency at fR (Hz) then asufficiently accurate delay interval, t (s), given bytR= 1/fR will excite resonances at nfR, where n is

a +ve integer (see the spectral banding in Figure 3,for example). So it might seem reasonable to set adelay interval t < 1/fR to avoid exciting the fun-damental resonance. However, most blast designsinvolve more than a single delay element and thiscould produce extra delay intervals related to bothsums and differences of these elemental delaytimes. Furthermore, many structures have multi-ple resonant frequencies. The upshot of this com-plexity is that when using accurate delays with anumber of delay elements it could be difficult toavoid exciting one or more structural resonances.Even when using pyrotechnic delays it is possibleto get a degree of spectral banding, especially atlow frequencies, where delay accuracy plays alesser role. Thus it might be advantageous to pur-posely randomise the delay sequence in a precisemanner to guarantee no spectral banding over thefrequency range of interest. Clearly, this techniquecannot be implemented using pyrotechnic delaysbecause it requires the flexibility and accuracy ofelectronic delays. The randomised sequence should

be based on sub-random numbers that maximallyavoid each other, rather than the usual pseudo-random numbers, which are known to cluster. Itmay also be desirable that the sequence maintainsthe same average delay intervals as the standard(un-randomised) sequence. The optimum sequencecan be implemented using a gated function whosemark-space ratio is varied in order to control thestrength of the randomness and act as a further aidto avoid clustering. These types of delay sequenceshave been used for some time now at a particularmine site and demonstrate a significant reductionin the vibration spectral peaks recorded at surfacemonitoring stations. Nevertheless, whilst such arandomising technique might prove beneficial tocontrolling peak vibration levels in resonant struc-tures, it does not imply a reduction in peak vibra-tion levels at non-resonant monitoring stations.

Most stations are probably non-resonant,especially for compliance monitoring. For suchstations it has been shown that reasonable pyro-technic delay sequences can control vibrations justas well as electronic delay sequences, especially formonitoring stations at typical distances 500 m(Figure 10). One dominant cause of excessivevibration at non-resonant stations is due to wavecrowding, whereby there are too many blastholesinitiating within a certain time interval. Wavecrowding depends mainly on the delay interval andnot its scatter, and for reasonable blast designs it

has been demonstrated (Figure 11) that pyrotech-nic delays can work just as well as electronic delaysin reducing this crowding effect.

However, in certain cases the flexibility ofelectronic delays could provide superior designs,especially for large blasts with numerous holes.Nevertheless, if a vibration problem exists witha particular pyrotechnic delay sequence, then thepresent work suggests that a first attempt shouldbe made to solve the problem with alternativepyrotechnic sequences before considering elec-tronic sequences with their associated high cost.

In view of the natural limitations to vibra-tion control as well as the fact that pyrotechnicsequences can compete with electronic sequences inmany cases, it is not surprising that field measure-ments of a large number of quarry blasts showedno significant difference in performance betweenthese types of sequences (Figure 12).

4.2 Fragmentation control

The measurement and modelling of fragmentationare both undoubtedly very difficult problems. Mostarguments raised in support of fragmentation con-trol assume that there is some known dependence offragmentation on delay interval and that stress waveinteraction promotes fragmentation. Unfortunately,

Table 1. Shapiro-Wilk probabilities for each dig rate set.

Set Arrangement PW

Pyrotechnic 1 Pyrotechnic, old shovel 0.92Pyrotechnic 2 Pyrotechnic, new shovel 0.63Electronic 1 Electronic, old shovel 0.67Electronic 2 Electronic, new shovel 0.47

Table 2. Pair-wise comparisons of the 4 data sets.

Pair-wise comparisons Pt

Pyrotechnic 1 vs Electronic 1 0.86Pyrotechnic 2 vs Electronic 2 0.56Pyrotechnic 1 vs Pyrotechnic 2


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there is little evidence from experiments or modellingthat gives support to either argument.

Fragmentation measurements in small-scale testsare significantly influenced by nearby free faces, andmeasurements for full-scale blasts are inordinatelytime-consuming and thus expensive. These arethe main reasons why there is scant data availableworldwide, and much of that data has significantscatter, making it difficult to draw any convincingconclusions. Although it is conceivable that therecould be a measurable dependence of fragmenta-tion on delay interval for a particular site, it wouldbe difficult to predict. It is even more difficult topredict exactly what role, if any, the delay accuracyplays in fragmentation. In fact many detailed trials,coupled with sound statistical analysis, would berequired to establish any dependence of fragmen-tation on delay interval and its scatter.

It could be assumed from past data that frag-mentation is most coarse for a zero delay interval.However, this assumption would also need to beverified more soundly in a statistical sense. If thisassumption can be verified, then it is quite possiblethat most of the variation for in-situ fragmentationmight well occur for extremely short delay inter-vals. For example, the data of Katsabanis et al.(2006), reproduced in Figure 1, is consistent withthe assumption that this interval is less than 10 sfor their test sample with a burden of approxi-mately 0.09 m. This delay interval would scale up

to be approximately 0.1 ms per metre of burden forin-situ blasting. It has already been demonstratedthat even electronic delays will not be accurateenough to ensure consistency of such a fine inter-val throughout a blast.

A new analytical model that considers ideal stresswave propagation shows that any superpositionof stress waves from single-primed neighbouringblastholes or from dual-primed single blastholesplays little or no role in promoting fragmentation,especially throughout an extended volume of rock.Furthermore, the model predicts that dual priming

within a single blasthole sends out two relativelyweak stress waves whereas single priming sendsout a single dominant stress wave. This, alone,suggests that dual priming will probably have anadverse influence on fragmentation. In this regardthere is an associated point that appears to havebeen overlooked by proponents of the stress wavecollision theory of fragmentation. If stress wavesuperposition does occur to any meaningful degreewithin a localised region of rock, then the inter-acting stress waves must have similar amplitudesand be in phase over that particular region. On theother hand, probability alone dictates that therewould also be many other regions where the stresswaves would never have similar amplitudes and/orthe desired phase relations. This reasoning is also

supported by results from the new analytical modelas previously discussed. Furthermore, if stresswave interaction was a dominant influence then theoverall fragmentation ought to be highly variable,even in uniform geology. There is no experimentalevidence to support such an outcome.

In view of these natural limitations to fragmen-tation control, it is not surprising that dig ratemeasurements of a large number of open pit blastsshowed no difference between blasts fired withpyrotechnic delays and those fired with electronicdelays (Table 2). Furthermore, the probit plots ofFigure 16 show that even when digging with thesame shovel types (eg. Pyrotechnic 1 vs Electronic 1)there can be large differences (over 20%) in dig ratesbetween delay types when comparing individualblasts. Thus it requires many blasts to get a mean-ingful comparison. Unfortunately, typical trials are

conducted using a small number of blasts, and theresults of such can be completely misleading.

Although the dig rate results are site-specific,they are consistent with the notion expressed ear-lier that stress wave collision probably plays nosignificant role in rock fragmentation by blasting.Nevertheless, experimental results for other sitescan only help resolve this complex issue, provided astatistically meaningful number of controlled meas-urement trials are conducted, and this is not a sim-ple task. However, even if other measurements doshow a dependence of fragmentation on the delay

sequence/type for a given site, then it might provedifficult to isolate a particular mechanism that isresponsible for such dependence. Nevertheless, insome circumstances it could be reasonable to sus-pect certain mechanisms. For example, in geologywith dominant fracture planes, the fragmentationmight be influenced by a ratio such as t/tf, wheret is the delay time interval and tf is some averagetravel time for stress waves to propagate betweenthe fracture planes. As noted previously, if therequired t is of the order of milliseconds theneven electronic delays would not be able to main-

tain this value accurately throughout most blasts.It is generally accepted that fragmentation isfundamentally influenced by stress wave propaga-tion from a blasthole and the subsequent inter-action of explosive gasses with the stressed rock.Thus there are two requirements for any model offragmentation. Firstly it must be able to correctlydescribe the stress wave propagation and secondlyit must be able to describe the subsequent influenceof explosive gasses on the altered rock. It has beenshown that current models are lacking on bothaccounts when considering the volume (i.e. 3D)assessment of fragmentation.

If an ultimate model of fragmentation wasavailable and computable, it would be possible todirectly demonstrate what role, if any, is played by


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stress wave superposition. Such an ultimate modelwould need to be numerical rather than analytical,and would probably use a dynamic finite elementmethod (DFEM) or a dynamic finite differencemethod (DFDM) to describe the stress wave andcrack propagation component, coupled with a gas-flow model to describe overall fragmentation. Thusit would be a code similar to the two-dimensionalcoupled DFEM-gas flow approach reported byMinchinton & Lynch (1996), but made fully three-dimensional and capable of resolving the high fre-quency stress wave produced by a realistic pressureload. It is instructive to estimate the computingtask for such a code. The number of finite ele-ments required can be estimated from the previ-ous low-resolution DFEM component reported inBlair & Minchinton (2006). In order to resolve thehigh-frequency stress waves shown in Figures 14

and 15, the DFEM would require a minimum of1000 2000 elements to cover the 4 m 8 m zone.In three-dimensions the solution would require atleast 1000 elements along the third direction, givinga total of 2 billion 3D elements. Calculations forinteracting blastholes would require a larger vol-ume with even more elements. Clearly, the requiredDFEM calculations, alone, are not yet feasible,even using the fastest supercomputers available.

Of course there are alternative (and perhapsfaster) numerical codes, such as the Hybrid StressBlast Model (based on the work of Cundall et al.

1996), that are being used to predict fragmentation.However these alternative codes use small rigidspheres as basic elements and so, unlike DFEM/DFDM codes, they do not have realistic elasticityor viscoelasticity built in at the fundamental level.Because of this significant limitation, as far asI am aware, such numerical codes are not capableof correctly predicting the stress wave propagationcharacteristics in a viscoelastic material, such asthose shown in Figures 14 and 15; the dominantSV-Mach propagation, in particular, has a majorinfluence on fragmentation. Thus, irrespective of

any mechanisms that these alternative codes mayhave to account for cracking and gas flow, it is rea-sonable to question their capability to realisticallymodel fragmentation.

ACKNOWLEDGEMENTS

The results shown in Figure 12 were extractedfrom the vibration databases of particular quarryoperations. In this regard I am primarily indebtedto Neil Patterson. Professor Patrick Royston of theNational Institute of Medical Research, London,

kindly supplied me with his Fortran code to evaluatethe Shapiro-Wilk statistics. I also appreciate somevaluable discussion with Patrick in this regard.

REFERENCES

Blair, D.P. 1993. Blast vibration control in the presenceof delay scatter and random fluctuations betweenblastholes. Int. J. Numer. Anal. Methods Geomech.17: 95118.

Blair, D.P. & Armstrong, L.W. 1999. The spectral controlof ground vibration using electronic delay detonators.Int. J. Blasting and Fragmentation. 3: 303334.

Blair, D.P. 2004. The frequency content of ground vibra-tion. Int. J. Blasting and Fragmentation. 8: 151176.

Blair, D.P. 2007. A comparison of Heelan and exact solu-tions for seismic radiation from a short cylindricalcharge. Geophysics. 72: E33E41.

Blair, D.P. 2008. Non-linear superposition models of blastvibration. Int. J. Rock Mech. & Min. Sci. 45: 235247.

Blair, D.P. & Minchinton, A. 1996. On the damage zonesurrounding a single blasthole. Proc. 5th Int. Symp. onRock Fragmentation by Blasting, Montreal, Canada,2529 August, pp. 121130.

Blair, D.P. & Minchinton, A. 2006. Near-field blastvibration models. Proc. 8th Int. Symp. on Rock Frag-mentation by Blasting, Santiago, Chile, 711 May,pp. 152159.

Cundall, P.A., Lorig, L.J. & Potyondy, D.O. 1996.Distinct-Element Models of Explosion-Induced Fail-ure of Rock, Including Fragmentation and Gas Inter-action. In: A. Jenssen et al. (eds.), Explosion Effectsin Granular Materials: 369394. Oslo: NorwegianDefense Construction Service.

Davies, O.L. & Goldsmith, P.L. 1972. Statistical Methodsin Research and Production. London: Longman.

Efron, B. & Tibshirani, R.J. 1993. An introduction to the

bootstrap. Monographs on Statistics and Applied Prob-ability. New York: Chapman & Hall.Johansson, D., Ouchterlony, F., Edin, J., Martinsson, L. &

Nyberg, U. 2008. Blasting against confinement, frag-mentation and compaction in model scale. Proc. 5thInt. Conf. & Exhib on Mass Mining, Lulea, Sweden,911 June, pp. 681-690.

Katsabanis, P.D., Tawadrous, A., Braun, C. & Kennedy, C.2006. Timing effects on fragmentation. Proc. 32ndConf. on Explosives and Blasting Technique, Dallas,Texas, 29 January1 February, pp. 243254.

Miller, R.G. 1997. Beyond ANOVA. Basics of AppliedStatistics. London/New York: Chapman & Hall.

Minchinton, A. & Lynch, P.M. 1996. Fragmentation and

heave modelling using a coupled discrete element gasflow code. Proc. 5th Int. Symp on Rock Fragmentation byBlasting, Montreal, Canada, 2529 August, pp. 7181.

Royston, J.P. 1982. An extension of Shapiro and WilksWTest for Normality to large samples. Applied Sta-tistics 31: 115124.

Siskind, D.E, Stagg, M.S., Kipp, J.W. & Dowding, C.H.1980. Structure response and damage produced byground vibration from surface mine blasting, USBMRept. of Investigation RI 8507.

Sprent, P. 1989. Applied nonparametric statistical meth-ods. New York: Chapman & Hall.

Tidman, J.P. 1991. Targets for blast fragmentationmodels. Proc. 7th Ann. Conf. on Explosives and Blast-ing Res. Las Vegas, 67 February. ISEE.

Timoshenko, S.P. & Goodier, J.N. 1971. Theory of elasticity.Third Edition. Tokyo: McGraw-Hill.

Documents

21 DP Blair - Limitations of Electronic Delays for the Control of Blast Vibration and Fragmentation