tionur

n M

erialapenue de

Received 8 March 2006; received in revised form 16 May 2006; accepted 23 May 2006

control. Understandably, research literature on rockexcavation by blasting is spread amongst the miningand rockmechanics journals. This paper is thus a response

Engineering Geology 87 (20 Corresponding author. Tel.: +44 2 7594 7327.1. Engineering context

Efficient production of construction materials and thequest for improved quarrying techniques have a stronglink with civil engineering, engineering geology androck mechanics as explained in a companion paper(Latham et al., 2006). The CIRIA/CUR (1991) rockmanual on coastal and shoreline engineering includedbrief references to some possible methods for armour-stone production and yield curve prediction. In its second

edition (CIRIA, CUR, CETMEF, 2007) it has sought toupdate and expand on the special problems faced bypracticing engineers wishing to plan on the basis ofpredicted armourstone yields, but such a publicationcannot include a satisfactory discussion of the relatedresearch, much of which is very recent. Engineersworking for the first time on an armourstone project,face many potential pitfalls. Most will therefore wish toobtain maximum assistance from geologists for thoseaspects of blasting that the production engineer cannotArmourstone production involves aspects of blast design and yield prediction. How they differ from methods drawn fromexperience in mining and aggregates blasting operations is examined. A number of possible blast fragmentation models andassociated prediction methods are described, several being outlined in full. Their applicability to armourstone production and yieldcurve prediction is discussed by comparing model results based on a hypothetical armourstone blast design in a rock mass withrealistic properties for an armourstone quarry. It is suggested that appropriate models for armourstone yield prediction will requiresome form of an in-situ block size distribution assessment. Such approaches rule out the standard application of the KuzRammodel. The recently reported Swebrec function and associated prediction model, developed by the Swedish Blasting ResearchCentre, provides a promising replacement for the RosinRammler based models for representing armourstone blast yield curves. 2006 Elsevier B.V. All rights reserved.

Keywords: Armourstone; Yield curve; Blasting; Fragmentation; Model; QuarryAbstractAvailable online 1 August 2006Prediction of fragmentareference to armo

John-Paul Latham a,, Jan Vaa Department of Earth Science and Engineering, Imp

b Boskalis, PO Box 43, 3350 AA Pc CETE de Lyon, LRPC, Groupe McaniqE-mail addresses: j.p.latham@imperial.ac.uk (J.-P. Latham),j.a.vanmeulen@boskalis.nl (J. Van Meulen),sebastien.dupray@equipement.gouv.fr (S. Dupray).

0013-7952/$ - see front matter 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.enggeo.2006.05.005and yield curves withstone production

eulen b, Sebastien Dupray c

College London, London SW7 2AZ, United Kingdomdrecht, Holland, The Netherlandss roches, 69674 Bron Cedex 01, France

06) 6074www.elsevier.com/locate/enggeoto the need to describe and compare the most promisingprediction techniques often applied to higher energy

aggregates and mine production methods and see howthey fare when applied to the low energy fragmentationblasts associated with armourstone production as is theconcern of civil engineers.

The quantification of the percentages of blocksbounded by joints or bedding planes within a rock massand of sufficient size to be useful in breakwater armourlayers was addressed in a recent companion paper(Latham et al., 2006). The prediction of the in-situ blocksize distribution (IBSD) was presented as a vital firststep towards better prediction of the blasted block sizedistribution (BBSD), commonly termed the yield curveor fragmentation curve in quarrying and mining. Themotivation for this study of the factors governing theyield curves of armourstone quarries supplying break-water projects comes from two sources. First, theproduction engineer needs tools (i.e. BBSD models) tohelp achieve the blasting objectives and there are notmany of these in existence that were designed for low

armourstone blasting techniques were developed withlow benches of 10 m, 4.5 m burden and 3.0 m spacing.Based on a BondRam analysis (described later), thepredicted yield was greater than 50% exceeding 1 tassuming a specific charge of 0.23 kg/m3. The actualaverage production over several weeks of armourstoneblasts generated the following: 10 t, 83% passing; 5 t,60% passing, 3 t, 49% passing; 1 t 40% passing an evenhigher percentage of armourstone than predicted.

In this paper, we introduce the subject of rock blastingin sufficient detail to present themain differences betweenvarious BBSD prediction models potentially suited to therange of low energy blasts associated with armourstoneproduction. We begin with a brief introduction to thoseblasting factors that concern armourstone and aggregatesproduction. The fragmentation process is briefly de-scribed to better understand the basic differences betweenaggregates and armourstone blast design and practicalmeasures often found useful to maximise the yield of

61J.-P. Latham et al. / Engineering Geology 87 (2006) 6074fragmentation blasting. Second, the breakwater design-er is fully aware that a much more cost effective designcan be specified given an accurate prediction of thequarry yield.

The Espevik quarry shown in Fig. 1 excavates aslightly metamorphosed granite gneiss. It was originallyopened with the intention of fully exploiting its armour-stone potential while having the option of selling theundersize as aggregates. The type of IBSD and BBSDanalysis methods discussed later in this paper and itscompanion were vital elements in winning the case forthe investment to go ahead and open the quarry. SpecialFig. 1. The Espevik Quarry in Norway, as seen during loaarmourstone are listed. Starting with the widely employedKuzRammodel and endingwith amodel based on a newthree-parameter function, the Swebrec function, for theyield curve which replaces the RosinRammler equation,various models are presented. Practical methods for theassessment of blastpiles (muckpiles) to check and feed-back for further calibration of predictions are also given.The differences between various models predicting theBBSD curves for a given hypothetical armourstone blastdesign and a given IBSD assessment provide the basis of adiscussion on suitability of approaches for armourstoneblast yield prediction.ding of a 20,000 t barge in January 1992, see text.

ering2. Factors affecting blasting for armourstone andaggregates

Certain aspects of armourstone production requireattention to details that are not usually emphasised inthe extensive literature on blasting, e.g. Persson et al.(1993), JKMRC (1996), Jimeno et al. (1997). Thefocus of armourstone production is on larger blocksthan for normal fragmentation blasting. The aim ofany blast is to produce rock of the size and form thatwill facilitate subsequent operations such as crushingand lead to minimum overall costs. The blast design isa significant process in securing desired fragmentationbut there are many difficulties to overcome, not leastbecause there are many factors affecting fragmentationbeyond the control of the blast engineer. These factorswere investigated by Lilly (1986) and Lizotte andScoble (1994) and considered in the formulation of ablastability index by Latham and Lu (1999).

Uncontrollable factors: geological characteristics ofthe rock mass or effects of rainfall

discontinuity spacings and orientation (bedding,joints, faults, cohesion across planes). In-situ blocksize distributions can be assessed using the techniquesdescribed elsewhere (e.g. Latham et al., 2006)

strength and elasticity (rock type, weatheringcharacteristics)

density, porosity, permeability presence of water in blastholes, fractures and joints spatial variations of geology and rock types in general

Controllable factors:

properties and detonation methods of the explosivesused, including delay timings

blast design (configuration and drilling pattern).

Successful blasting engineers work to clearly definedobjectives such as: the required size distribution results,ease of blastpile digging, minimum disruption to nextblast, etc. They apply theoretical understanding of therock fragmentation process and rock characteristics,knowledge of the effects of using different explosivesand detonation techniques, the environmental constraintsand lastly, experience and expertise in combining thesewhich may include the assistance of blasting software.

The most important fragmentation objectives forarmourstone blasts are:

blasting for improved yields of heavy blocks in spe-

62 J.-P. Latham et al. / Enginecially set aside faces of aggregates quarries blasting for improved or reduced yields of heavyblocks in dedicated quarries.

The economics of the second case are constrained by aneed to produce, as far as is possible, only the materialdemanded by the design. This may require that secondarybreakage is embraced fully as a means of production whensetting the blasting objectives. (This is the theme of thefinal section of the companion paper, Latham et al., 2006).

2.1. Fragmentation processes

The way in which in-situ bedding, jointing and otherdiscontinuities slice up the natural rock mass into blocksof predefined shape distributions and size distributionsprior to blasting is illustrated in virtually every exposureof rock. The concentrated release of energy from ex-plosives detonated in confined blastholes, transforms theIBSD to a BBSD of finer material (Fig. 2). To summarisethe consensus of blasting research based on referencessuch as those mentioned above; the sudden very highphase transformation pressures in the blast detonationcauses shock wave transmission, compressive crushingnear the borehole walls, radial tensile fracturing andslabbing tensile cracking at free faces. Fracturing andfragmentation is accompanied by detonation gas flowinto cracks, extending them further. The explosive gas,assisted by gravity, heaves the blocks away from theface and into the blastpile. The ability to achieve a desiredBBSD depends on knowledge of the IBSD, the strengthand persistence of the natural geological flaws and:

other uncontrollable factors such as strength, elastic-ity and density that contribute to the inherent ease ofbreakage or blastability of the rock,

blast energy mobilised through the blast design.

2.2. Comparison of armourstone and aggregates blastdesign

Design of an aggregates blast aims to minimiseexcess oversize (and expensive secondary breakage)keeping the average BBSD to

an armourstone blast applied to the same rock mass. IBSD and BBSD are

63ering Geology 87 (2006) 6074Fig. 2 is a schematic diagram showing the essentialdifferences in yield curves. RosinRammler coeffi-cients were used to illustrate blast curves correspondingwith typical results from the aggregates industry andbreakwater contractors. The theoretical curves aredefined later in the text. In terms of practical blastdesign, many simple steps to improve armourstoneproduction are discussed below. The most fundamentalfor an armourstone blast, is a low specific charge:0.2 kg/m3 is often used and even lower values may helpachieve the objectives. For a rapid insight into thepractical and technical factors governing production inan armourstone quarry dedicated to producing break-water materials, see Van Meulen (1998).

2.3. Suggestions for improving the yieldsof armourstone

Fig. 2. Illustration of theoretical scenarios for an aggregates blast andrepresented by RosinRammler curves.

J.-P. Latham et al. / EngineGenerally, the proportion of armour-sized blocks inthe blast increases with increasing intact tensile strength,increasing Young's Modulus and increasing disconti-nuity spacing. Normal blasting practice (e.g. for aggre-gates and ores) aims to achieve high fragmentationblasts. By contrast, greater percentages of armourstonecan be achieved by adjusting common practice throughconsideration of the following list based on the originalresearch by Wang et al. (1991). Note, blast terminologyis provided in Fig. 3.

1. A low specific charge. Generally, a specific charge aslow as 0.11 to 0.25 kg/m3 can be used. If possible, theexplosive used should have lower velocity of deto-nation, (VOD). For such low specific charges, main-taining high drilling accuracy is more critical to avoidinsufficient rock break out.2. The spacing to burden ratio should generally be lessthan or equal to 1 with burden larger than the dis-continuity spacing in a jointed rockmass. Ratios as lowas 0.5,more typically associatedwith pre-splitting, havebeen successfully applied to armourstone operations.

3. If the bench is either too high or too low, armourstoneproduction will be poor. For an initial estimate, benchheight could be selected as two to three times theburden. In planning bench levels, the rock mass fromwhich most armourstones might be produced, such asthickly bedded layers, should be located nearly at the topof the bench alongside the stemming section of theholes.

4. A large stemming length, larger than the burden, isusually recommended.

5. A small blasthole diameter of less than 100 mm isrecommended.Fig. 3. Geometric blast design parameters.

ering6. One row of holes is found to be better than multi-rows.If permitted, holes should be fired instantaneouslyrather than using inter-hole delaying, but may causehigh undesired ground vibration.

7. A bottom charge of high energy concentration isneeded for the bottom to cleanly break away.

8. A decoupled column charge of ANFO packed inplastic cartridges (sausages) is often effective when a3003000 kg mass range is the main product sizerequired, the explosives are then evenly distributedgiving quite even fragmentation.

9. A decked charge, to break up the continuity of ex-plosives, will be necessary in most situations whenarmourstone greater than 3 t is required. The materialfor decking can be either air or aggregates.

The most common objective of an armourstone benchblast is to achieve a BBSD with the maximum percentageof the largest blocks possible. Such a blast is to cause theminimum of new fractures while having sufficient energyconcentration to fully loosen the in-situ blocks and bringthe rock face down cleanly. The best achievable BBSDcurve will lie close to and just to the left of the upper partof the IBSD curve, spreading out considerably at lowersizes. Where the mean discontinuity spacing gives vastin-situ blocks, blast design must ensure sufficientbreakage to limit the proportion of blocks above 20 t,which is about the limit for practical handling.

It is interesting to note that a lower percentage ofarmourstone recovery can often be more economical,even though more rock is eventually excavated andtherefore more is left behind as over-production be-cause of poorer rates of production. Excavation of theblastpile and keeping good faces and toes becomes moredifficult the greater the yields of heavy armourstone andthe lower the specific charge. The rate of output fromexcavators, loaders and selection plant also becomesslower.

3. Prediction of yield curves

It is not uncommon for disputes to develop overliability for unforeseen materials production costs wherecontracts are based upon dedicated armourstone quarries.Average yield curves derived from back analysis thatrepresent results of materials tonnages supplied to abreakwater project as different classes of stone (e.g. core,underlayer, various armour classes etc.), often reveal thatin practice, the final percentage of armourstone blocks(e.g. >3 t) was less than the predicted curves suggested.

Prediction of blasted block size distributions, BBSDs

64 J.-P. Latham et al. / Engine(fragmentation curves, yield curves) is the subject ofsignificant research effort as the possible error in pre-diction remains very high. Accuracy is limited becausethe geological conditions cannot easily be determined forevery blast and the implementation of the blast designmay suffer from practical constraints. For dedicatedarmourstone quarries, early prediction of quarry yieldcurves, whether by trial blasts, or by scanline and boreholediscontinuity surveys together with blast modelling, playsa vital part in breakwater design optimization. Describedbelow are four approaches to fragmentation prediction:

KuzRam model, implemented in many softwareapplications

BondRam models EBT model KuznetsovCunninghamOuchterlony (KCO)models

3.1. KuzRam model

Cunningham brought Kuznetsov's (1973) work up todate, introducing the KuzRam Model in 1983. Laterrevisions to KuzRam, Cunningham (1987), includedimproved estimation of the rock mass factor A based onLilly's (1986) blastability index. There are four im-portant equations that by simple substitution of para-meters, give the BBSD curve. The use of the KuzRam,or similar models, requires caution. Factors of recog-nised importance such as detonation delay timing arenot included in KuzRam (a large literature on timingeffects exists, some indications are given by Chung andKatsabanis (2000)) while the effect of rock massstructure, and the burden to spacing ratio needs carefulconsideration (Konya and Walter, 1990).

(i) RosinRammler Equation: is the cumulative formof the Weibull distribution and provides the basic shapeof the BBSD to be expected, in terms of the 50% passingsieve size in the blastpile, Db50 and RosinRammleruniformity index for sizes, nRRD, giving the fractionpassing, y, corresponding to a certain sieve size Dy(Rosin and Rammler, 1933).

y 1expf0:693Dy=Db50nRRDg 1After Db50 and nRRD have been determined from

Eqs. (2) and (3) below, substitution of Dy values willreturn fraction passing values from which the completeBBSD curve can be deduced. For a BBSD predictionfocused on armourstone sizes of say, 0.1 m to between 1and 2 m, the RosinRammler equation is considered themost attractive simple choice. It should be noted thatwhere data from sieved or photo-analysed blastpiles

Geology 87 (2006) 6074deviate surprisingly from the RosinRammler fitting

eringfunction near the maximum sizes, this could be due tothe inherently poor sampling of the coarsest fractionwhich can throw the measured results out from theaverage production in question. Shortcomings of theRosinRammler equation include:

It has been reported to sometimes give a poor fit toblastpiles with high yields of armourstone sizes(Lizotte and Scoble, 1994).

It fails to give a clear maximum size because thefunction is asymptotic to the 100% passing value.

It is commonly unable to describe with reasonableaccuracy the fines content below sizes of about50 mm in a blast (Ouchterlony, 2005a); of particularconcern for predicting the detailed nature of thequarry run and the resultant behaviour of corematerials derived from the quarry.

(ii) Kuznetsov Equation: gives Db50 (in m not cm) asa function of (A, V, Q, E), which locates the position ofone point on the BBSD curve. Essentially, this suggeststhat average size is controlled by specific charge

Db50 0:01d AV=Q0:8d Q0:167d E=1150:633 2

where:

A = rock factor; = 1 for extremely weak rock, A=7for medium rock,A=10 for hard, highly fissuredrock; A=13 for hard, weakly fissured rock.Several schemes similar to rock mass ratingsystems now exist for improved estimation of A.For example, Lilly's (1986) original blastabilityalgorithm was adopted by Cunningham (1987).

Q = charge concentration per blast hole (kg); tocalculate, consider borehole volume filled anddensity of explosive.

V volume of rock broken per blast hole (m3)E relative weight strength of explosive (ANFO=

100, TNT=115);Q /V Specific Charge (kg/m3), a general measure of

explosive power in the blast

Spathis (2004) pointed out an implicit assumption inCunningham's KuzRam application of Kuznetsov'soriginal equation. The assumption is increasingly invalidfor lower nRRD values typical of armourstone blastsbecause the mean size differs more significantly from themedian size as nRRD decreases. Spathis plotted thecorrection needed as a function of nRRD which indicatesthat for n as low as 0.8, the characteristic size would be

J.-P. Latham et al. / EngineRRD

1.8 times too large if Eq. (2) is used without the correction.(iii) Cunningham's uniformity index algorithm:Cunningham (1987) developed an empirical equationthat determines nRRD i.e. the steepness of the BBSDcurve, as a function of blast design geometry withterms independent of those in Eqs. (1) and (2). Note,there is no significant body of evidence fromphysically measured sieved distributions to supportthis equation, although it remains widely used as atool. The first term typically takes a value of 1.5 andis a base term about which the other terms for holepatterns, drill deviation, different column and basecharges and charged proportion of bench, are allcorrection terms.

nRRD 2:214B=dd f0:51 S=Bg0:5d 1W=Bd absBCLCCL=L 0:10:1d L=H

3where

d = borehole diameter (mm)B = burden (m),S = spacing (m),BCL = bottom charge length (m),abs = absolute value ofCCL = column charge length (m),L = total charge length above grade (m),H = bench height or hole depth (m).W = standard deviation of drilling error (m),

(iv) Rock factor A: This section provides a guide tosetting parameters of the rock mass from which the rockmass factor A, needed for the KuzRam and KCOmodels, can be estimated. It would be a very rare rockmass that could achieve A-values above 14 and for rockto be considered for armourstone, it is considered likelythat A would fall in the range of 914.

A 0:06RMD JF RDI HF 4where

RMD = Rock mass description=10 if powdery orfriable, = JF if vertically jointed, = 50 if massive rock

JF = Joint Factor = Joint Plane Spacing term (JPS)+Joint Plane Angle term (JPA)

JPS = 10 if average Principal Mean Spacing, PMS(e.g. cube root of product of three principal meanspacings) 1 m.

JPA = 20 if dipping out of face, 30 if strikingperpendicular to face, 40 if dipping into face

65Geology 87 (2006) 6074 RDI = Rock Density Influence=0.025r(kg/m3)50

ering HF = Hardness factor=E / 3 if E50, depending on uniaxial compressive strengthUCS (MPa) or Young's Modulus E (GPa).

3.2. BondRam models

Da Gama (1983) applied Bond's Third Theory ofcomminution to blasting using Bond's relation, (Eq.(5) below) to fix the 80% passing size in the blast.Bond's relation was applied together with the RosinRammler Eq. (1), and Cunningham's uniformitycoefficient in Eq. (3), by Wang et al. (1992a,b). Theycalled this combined approach the BondRam model.It is termed BRM(A) in this paper while another morerecent approach by Chung and Katsabanis (2000) istermed BRM(B).

3.2.1. BRM(A)Bond equation: based on Bond's third theory of

Comminution, the reduction in the 80% passing sizeduring blasting is expressed in terms of the blast energyqei and a material property, Wi as follows:

qei 10dWid f1=MDb801=MDi80g 5To apply BRM(A), qei and Wi values together with

Di80 from IBSD information are substituted in Eq. (5) andDb80 is determined. Substituting y=0.8 and Dy=Db80,together with nRRD, determined from Eq. (3), in Eq. (1),then gives Db50, from which the complete BBSD curveof RosinRammler form can be deduced where:

Db80 and Di80 are the 80% passing sieve sizes, afterblasting and in-situ respectively (in microns)

qei is the energy required for fragmentation and is afunction of (E, V, Q, r). It can be estimated from

qei 0:00365EQ=V =qr 6where E=weight strength of explosive (%) relativeto ANFO and r = rock density in t/m

3

Wi (in kW h/t) is analogous to Bond's Work Index forgrinding but is here calibrated for blasting (Da Gama,1983) as follows:

Wi 15:42 27:35Di50=B 7

where B = burden (m), Di50=50% passing in-situblock size (m) and the empirical fit coefficients havethe appropriate units.

Note: in grinding, work index values are known from

66 J.-P. Latham et al. / Enginetables for grinding of different ores, or they are deter-mined by grinding experiments. Such index values maybe misleading if used directly in blast models without acorrection factor.

3.2.2. BRM(B)Chung and Katsabanis (2000) demonstrated that Eq.

(3) gave nRRD values consistently too high compared toresults they studied from sieved blastpiles of small scaleblasts. They suggested linking Db50 determined fromKuznetsov's Eq. (2) with Db80 determined from Bond'stheory, as a means to obtain nRRD in the RosRam equa-tion, Eq. (1), thus providing an alternative to Cunning-ham's Eq. (3). In so doing, nRRD, as given analytically by0.842/ (lnDb80 lnDb50) together with Db50 given fromKuznetsov's equation, were found to provide RosRamcoefficients in Eq. (1) that generated final BBSDprediction curves fitting closer to field data. This BondRam approach was proposed by Chung and Katsabanis(2000). However, they assumed the 80% passing in-situsize to be infinite which is an unnecessary restrictionwhen an estimated IBSD curve, suggesting Di80 perhapsof 1 to 2m, has been derived. Here, the use of realistic (notinfinite) Di80 in Eq. (5) is suggested. The consequentincrease in nRRD values obtained from using realistic in-situ sizes comparedwith applying their assumption can bequite significant. This may provide a partial explanationfor the low nRRD values of the two sieve-measured full-scale quarry examples quoted by Chung and Katsabaniswhich gave predicted nRRD of 0.77 and 0.73 when themeasured values were 0.81 and 0.85 respectively. It isworth noting that when using this approach, the uni-formity index is no longer given as a function of blastdesign geometry as implied by Eq. (3). It would appear tobe a promising yield prediction approach for armourstoneproduction and is termed BRM(B) in this paper.

It should be pointed out that to produce more accurateBondRam predictions, further calibration of an appro-priate value for Wi is recommended for quarry benchblasting of armourstone. Da Gama (1983) suggested theuse of Eqs. (6) and (7), a relation from empirical studies ona small data set of blasts in a basalt quarry. From a backanalysis of case histories, results presented in Lu andLatham (1998) suggested a somewhat lower range ofvalues e.g. Wi=6.71.1 kW h/t for one particular Car-boniferous limestone quarry and Wi=104 kW h/t forhost rock from various ore mining blasts. Lower values ofWi imply greater ease of blasting into small pieces. Blasti-ng engineers wishing to adopt the Bond equation forblasting are advised to consult recent research, e.g.Kariman et al. (2001) to constrain the wide choice fromthe high values suggested by Da Gama for basalt

Geology 87 (2006) 6074(25 kW h/t) and the significantly lower value of

emon

ering10 kW h/t as suggested above and recently by Chung andKatsabanis (2000), or calibrate their own case-specificWithat provides a consistently good fit to observed frag-mentation in the quarry.

3.3. EBT Model

Lu and Latham (1998) developed an energy-block-transition (EBT) model for BBSD prediction based onrelating the area between the IBSD and BBSD curves tothe energy consumed in transforming bigger blocks tosmaller ones. First, the IBSD curve is predicted (seemethods suggested in Latham et al., 2006) giving themean in-situ block size, kai. A measure of the intrinsicblastability of the rock mass, known as the EBT-coefficient, Bi must then be obtained, together with theenergy input, qei, see Eq. (6). Procedures for doing soare described in Latham and Lu (1999) where ablastability designation BD10 /Bi was proposed forobtaining Bi. Alternatively, they recommended thatwhen procedures for deriving BD needed to be made

Fig. 4. Use of a three point method to characterise fragmentation and dquarry analysis by J Van Meulen.

J.-P. Latham et al. / Enginemuch simpler, the schemes for calculating rock factor Acould be used, where Bi =10A / 13. The mean blastedblock size, kab can then be obtained from the EBTmodel, Eq. (8) as follows:

qei kaikabBi

kaikab2

0:5 8

A predicted BBSD curve can then be obtained.Further to the discussion by Spathis, 2004, it should benoted that ka is the mean and as such will not be wellapproximated by the median for low uniformity indices.The reader can find relations relating median and meanfor different distributions in statistics texts but theSpathis paper is an ideal starting point.3.4. KCO model

In recognition of the poorer fit in the fines region ofthe two-coefficient RosRam and power law equa-tions, more complex equations with four or five curvefitting coefficients have been introduced. These curveshapes can overcome the underestimate of fines oftenfound with RosinRammler curves and are designedto account for more complex combinations ofbreakage mechanisms such as fine-scale crushingnear the borehole, fines development occurring alongpropagating branching cracks, and the coarser frag-mentation by tensile cracking (Djordjevic, 1999;Kanchitbotla et al., 1999). More recently, and withno reduction in curve fitting accuracy compared withthe four- and five-coefficient equations, Ouchterlony(2005b) proposed a 3-parameter cumulative sizedistribution function, termed the Swebrec function,given here as Eq. (9)

y 1=f1 lnDbmax=Dy=lnDbmax=Db50bg 9

strate the decrease in D50 with increasing specific charge data from

67Geology 87 (2006) 6074where Db50 is given from Eq. (2), (where the rock massfactor A found from Eq. (4) is required), and b is calledthe curve undulation parameter. Ouchterlony suggestsDbmax which is the upper limit to the blasted fragmentsizes can be taken as equal to the largest in-situ blocksize,Di100 or either the burden or spacing if smaller thanDi100. When introducing the correct blast parametersinto Eq. (9), the equation becomes a BBSD predictionmodel. The KCO (KuznetsovCunninghamOuchterl-ony) model was proposed as a suitable name for themodel. Ouchterlony has proposed two methods forpredicting the value for b.

The first is to adopt Cunningham's nRRD from Eq. (3)but to also introduce an effect recognised by Ouchterl-ony, that the size distribution's slope at the Db50 point is

eringalso dependent on Db50 itself. A good approximation forb was found to be:

b nRRDd 2d ln2d lnDbmax=Db50 10The second is to use an empirical equation derived

from sieved results from several full-scale blasts whereDb50 is in mm, (Ouchterlony, 2005a):

b 0:5D0:25b50 d lnDbmax=Db50 11

Ouchterlony (2005b) shows how the function pre-sented in Eq. (9) fits BBSD sieving results from a widerange of rock types and blast conditions remarkably welland plugs into the KuzRam model with ease,improving predictive capability in the fines range andthe cut-off at the upper limit, especially if a good Di100estimate can be substituted for Dbmax. Ouchterlony sug-gests that Dbmax could be set at the minimum of burden,spacing or in-situ maximum size.

It is suggested that the KCO model offers greatpotential to improve on the KuzRam model in mostbench blasting operations. Its suitability for armourstoneblasts also looks quite promising. For armourstone blastprediction, as with all prediction models, it should beapplied with caution, especially as it has been developedfor blasts with relatively higher specific charges and bur-den to spacing ratios than is common for armourstoneblasts. It should also be noted that many unconventionalblasting methods such as decoupling and simultaneousdetonation are used for armourstone blasts. Accuracy ofthe KCO model and the function given by Eq. (9) has notbeen examined as thoroughly in the 80100% passing sizerange (where it is most critical for armourstone prediction),as it has for the medium and smaller sizes consideredmoreimportant for productivity in high fragmentation blasts.

4. Assessment of mass distributions

4.1. Direct screening and block measurement methods

It may sometimes be practical to count the number ofblocks N in the entire potential armourstone oversizematerial in a blast, and to performmeasurements of blockdimensions from a representative sample of say N / 5blocks. The sizes can be converted to masses using shapefactors based on blockiness concepts (e.g. see Gauss andLatham, 1995). Knowing the total rock mass in the blastand estimating the total mass in the oversize, the upperpart of the BBSD can be plotted, andmay bemergedwithphoto-scanline or image analysis results.

In a productionwith no crushing, it is possible to assess

68 J.-P. Latham et al. / Enginethe proportions in a blast if it is all processed. The sortedmaterial volumes are logged during production throughthe selection plant (e.g. trommel screen). Provided thecoarsest proportion from the blast can be estimated, forexample by counting blocks in heavy grading classes or asdescribed above, a curve based on assessment at threepoints can be drawn. In Fig. 4, three important points onthe yield curve were used to chart the change in BBSDwhile reducing specific charge. Screen analysis of full-scale production blasts, clearly more reliable than imageanalysis for assessments, were reported in Stagg andOtterness (1995) and in Ouchterlony (2005a,b).

4.2. Image analysis

A discussion on predicted fragmentation would beincomplete without some mention of assessment methodsto examine actual fragmentation. Automated image anal-ysis methods are becoming more widespread for deter-mining blastpile size distributions inmining and quarryingoperations. Digital photos taken while piles are beingloaded, (so as to represent the full depth of the pile) andtaken from above loaded trucks, provide input that readilyavailable image analysis software will convert into sizedistributions using sophisticated correction algorithms. Ablind trial of various commercial image analysis softwarepackages (Latham et al., 2003) gives a snapshot of theirperformance. Fig. 5 shows images with known size dis-tributions of the type often used to calibrate image analysissoftware. Franklin and Katsabanis (1996) compiled amonograph of papers and references to such methods.

At least half a dozen commercial automated sizingsystems are now in widespread use, not only for blastyield assessment, but also for production control ofprocessed minerals. There is potential for wider use ofsuch systems in quality control of gradings, e.g. bargedeliveries of light gradings.

4.3. Photo-scanline methods

An alternative manual photographic method (Lu andLatham, 1996) that is simple and can be undertakenwithout software is to superimpose scanlines directly onthe scaled photographs. The method was employed byMcKibbins (1996) to assess the armourstone blast(4000 t) shown in Fig. 6. Many scanlines are drawnon each photo with directions chosen to minimise bias.Care is needed to correct for perspective distortion. Asingle length distribution from measurements of seg-ment lengths defined by intersections between the par-ticle edges is created from all the photos making up arepresentative sample. It is invariably found that the

Geology 87 (2006) 6074cumulative form of this length distribution has a Rosin

Fig. 5. Typical size distributions with similar appearance (representative of gradations in blastpiles if scale divisions=1 m). P44: nRRD=0.7,D63.2=800 mm, D50460 mm, P41: nRRD=0.9, D63.2=350 mm, D50240 mm. The same distributions are shown in Fig. 2 Note, for highfragmentation blast geometry in Eq. (3), the KuzRam model often predicts nRRD>1.0. With low nRRD laboratory piles it is very difficult to make up

erfect

69J.-P. Latham et al. / Engineering Geology 87 (2006) 6074Rammler form. The best fit photo-scanline RosinRammler parameters nRRDp, D63.2p, for uniformity andcharacteristic length can be obtained from a linearizedplot. To convert the RosinRammler to a linear form,substitute the left hand side of Eq. (12) as the variable Yand logDp as the variable X and apply linear regressionof Yon X to obtain the gradient and intercept which givenRRDp and D63.2p.

logln1=1y nRRDpd logDpnRRDpd logD63:2p 12

The calibration equations to convert from segmentlength distribution coefficients to nRRD and D63.2 are:

D63:2 1:119D63:2p 13

nRRD 1:096nRRDp0:175 14As for any assessment of blastpiles that only sample

a sample big enough to properly represent the larger sizes present in a ppiles have a partly bimodal distribution due to large size censoring.the surface-visible blocks, the results are likely to givecoarser BBSD predictions than is representative of the

Fig. 6. Photographic image of a blastpile in the Hulands Quarry, Co Durhacontains many blocks from the stemming section and is somewhat coarser tentire pile. Taking many sample photographs duringblastpile loading is preferable.

5. Comparison of BBSD prediction models

The purpose here is not to explore the range of validityof eachmodel, and compare it with well documented casehistories. (With the equations given above, the reader cansimply implement the model formulae and compare yieldcurve results for various local quarry and blasting con-ditions using a spreadsheet). Instead, a hypothetical caseof one potentially reasonable armourstone blast design,applied to a hypothetical rock mass viable for armour-stone is considered to illustrate some of the models dis-cussed above. The chosen hypothetical rock mass isequivalent to a widely jointed but not especially massiverock mass typical of a competent limestone of density2.7 t/m3. It is given a rock factor A of 10 with an IBSDanalysis as given in Table 1. A somewhat less steep IBSD

RosinRammler distribution in effect, even the artificially made upmight be appropriate for a more massive rock mass withlocally disturbed fractured areas.

m UK, used for photo-scanline analysis. The surface of the blast pilehan the material beneath.

Example applications of the KuzRam model areshown for a suggested armourstone blast design withparameters as shown in Table 2 and the results of the

Table 1Assumed IBSD for illustration

Fraction passing Mass (kg) D sieve (m)

0.1 710 0.7630.3 1795 1.0390.5 3423 1.2880.7 5902 1.5450.8 7933 1.7050.9 10,892 1.8950.95 14,105 2.0661 23,242 2.440

70 J.-P. Latham et al. / Engineeringmodel in terms of RosRam yield parameters are asshown in Table 3. Interestingly, for these chosen chargelength to borehole length ratios, burden and spacing val-ues, it appears that Cunningham's Eq. (3) is in this casesuccessful in the sense that it gives a reasonably lowuniformity index in the same range commonly observedfor armourstone blasts. In applying KuzRam to uncon-ventional blasts, it is often difficult to judge how best toconvert the subtleties of special armourstone techniquessuch as air-decking, decoupling, delay timings into modelparameters. In selecting the values given in Table 3, theblast assumes a fully coupled long base charge with nocolumn charge as such, but a long stemming length. Toaddress the idea that the upper rock mass blocks aresimply liberated in armourstone blasts, McKibbins (1996)attempted a BBSD prediction by summing block sizesgiven by the IBSD of the upper stemmed part of the blast(assumed to be liberated and untransformed in the blast),with those block sizes transformed by a blastmodel for thelower charged part of the hole. This composite modelapproach gave less satisfactory results than the BondRam approach.

Table 2Suggested armourstone blast parametersKuzRam model input parameters Suggested armourstone blast

Rock factor A () 10Specific charge Q /V (kg/m3) 0.266Spacing /burden () 0.61Borehole diameter (m) 0.082Burden (m) 4.1Spacing (m) 2.5Charged column length (m) 9Bench height (m) 15No. of holes 10Volume of rock blasted (m3) 1538Explosive weight strength 100Charged explosive (kg) 404St. dev. of drill error (m) 0.1Avery important observation is that because of the lowvalue of nRRM for many armourstone blasts used onbreakwater projects (nRRD typically from 0.7 to 0.9, seeLatham et al., 2006), a significant shift in sizes is predictedwith the Spathis correction.Within this range of nRRM, theroutine application of KuzRam gives yield sizes that area factor of about 1.8 too large because of significantdifferences between mean and median for such widedistributions (see Spathis, 2004). The shift is shown inFig. 7, however both yield prediction curves appearunrealistic when compared with the reasonable IBSDcurve we have assumed for the rock mass.

To apply the standard BondRammodel BRM(A), theblast in Table 1 uses the same uniformity index as in theKuzRammodel. The Bond equation requires input fromIBSD at 80% passing together with the blast input energyand importantly, the Work Index. Two example values,Wi =24 and Wi =10 kW h/t are examined in Fig. 8, theformer derived from Da Gama's calibration, the latterbeing closer to expected values for a blast in competentlimestone, see Table 4.

When adopting the BondRam model, sBRM(B),the blast geometry approach to finding nRRM via Eq. (3)is discarded. In our hypothetical example, both of thesBRM(B) slopes shown in Fig. 8 have higheruniformity than were found using BRM(A) and Eq.(3), which is opposite to the original finding of Chungand Katsabanis (2000) where higher specific chargeblasts (0.8 kg/m3) were considered. Substituting alower Work Index shifts the 80% passing valuefractionally more. Because in both cases the M is

Table 3Parameters for KuzRam models

RosRamcoefficients

KuzRam SFB(KR)

Shifted KuzRam SFB(sKR)

Vb50 (m3) 0.386 0.0763

Mb50 (kg) 1013 206Db50 (m) 0.859 0.505nRRM () 0.265 0.265nRRD () 0.795 0.795

Geology 87 (2006) 6074b50

pinned by Eq. (2) it therefore gives a slightly steeperyield curve. Note, to obtain Mb50 the Spathis correctionhas been applied. Without it, the results for BRM(B)would appear impossibly steep for this example. It isinteresting to note that although the Mi80 value has beenused in the analysis, there is an unsatisfactory lack ofconvergence of the initial top mass Mi100 and the finaltop mass Mb100 for all but the sBRM(A) Wi10 curve.This effect would be less pronounced and the BBSDresults more generally acceptable had the chosen IBSDbeen given a less steep curve.

Fig. 7. Application of the KuzRam model to the hypothetical blast and rock mass parameters (Table 2), showing how the correction identified bySpathis (2004) results in a major shift in the final predicted yield curve (sKR). Neither result appears compatible with the suggested IBSD curve.

71J.-P. Latham et al. / Engineering Geology 87 (2006) 6074The Swebrec function and KCO model removes thisproblem by setting the before and after top massesequal but the uncertainty at the 100% value is alwaysquite large. The KCO methodology takes no furthernotice of the predicted IBSD curve's actual form exceptin a rather subjective manner through the JPS score forthe rock factor A. The two Swebrec function curvestake two quite different paths between Mb50 and Mb100depending upon whether the new empirical KCO or thefirst KCO model is used to obtain the undulationparameter b (see Fig. 9 and Table 5). Note that in bothcases the Spathis correction has been applied to obtainMb50. The data set used by Ouchterlony (2005b) tocalibrate the empirical relation Eq. (11) may not besufficient to represent low energy blasts typical ofarmourstone with the same level of confidence as foraggregates and mine blasts. Speculating, an undulation

parameter giving a yield curve about half way between

Fig. 8. Application of two different BondRammodels showing results broadlvalue (Wi) assumed, see text.the two shown would seem more reasonable for suchan armourstone blast.

The wide variation between prediction model resultsshown in Figs. 79, for one set of blast design data, istestimony to the difficulty of BBSD prediction, espe-cially for the case of armourstone production.

6. Discussion

Experience to date does not point to a single bestprediction method for armourstone. The best practice issomewhat clearer for prediction in higher fragmenta-tion blasts for mines and aggregates quarries. This isbecause the number of documented studies with highaccuracy in the blastpile assessment (accuraciesassociated with sieving a sample of the full-scaleblast or a well controlled image analysis campaign

using several magnifications), together with detailed

y compatible with the IBSD, and a large dependence on theWork Index

methods and conclusions of (Latham et al., 2006), theweighted joint density method of Palmstrm (2001)using drill core data appears to be a suitable first

Table 4Parameters for BondRam models

BondRammodel parametersand results

SFB BRM(A) Wi10

SFB BRM(A) Wi24

SFBa BRM(B) Wi10

SFBa

BRM(B)Wi24

Work index(kW h/t)

10 24 10 24

Specific charge(kg/m3)

0.266 0.266 0.266 0.266

Vi80 (m) 2.938 2.938 2.938 2.938Mi80 (kg) 7933 7933 7933 7933Di80 (m) 1.705 1.705 1.705 1.705Vb50 (m

3) 0.0424 0.0123 0.0764 0.0764Mb50 (kg) 114.463 33.21 206.2 206.2Db50 (m) 0.4134 0.2737 0.5051 0.5051nRRM () 0.265 0.265 0.353 0.327

Table 5Parameters for KCO models

Swebrec function inputs KCO Eq. (10) New KCO Eq. (11)

Vb50 (m3) 0.0763 0.0763

Mb50 (kg) 206 206Db50 (m) 0.505 0.505nRRM () 0.265 nRRD () 0.795 b () 1.88 3.73Dbmax (m) 2.44 2.44

72 J.-P. Latham et al. / Engineering Geology 87 (2006) 6074IBSD and rock mass analysis, has been growing.However, even the large amount of case studiesreported remains a relatively small database if all theblast design variables are to be investigated. Field datain the literature from low energy blasts, where theobjective is often simply to liberate in-situ blocks foruse as armourstone, are much scarcer.

If a reasonably confident estimate of rock mass factorA can be made, but discontinuity spacing is poorlyknown, the KuzRam model will provide a completeprediction curve but with a value for nRRD that has areputation in general blast designs for being too high,thus generally under-predicting the amount of finesproduced.

To take advantage of the known importance of the in-

nRRD () 0.795 0.795 1.058 0.980a Note, the Spathis (2004) correction has been applied.situ discontinuities, it is invariably worth the investmentin IBSD data and at least, to estimate the maximum andtypical in-situ block volumes. Drawing upon the IBSD

Fig. 9. Swebrec function and application of two forms of the KCO model (Oapproach in poorly exposed green field sites whenscanline surveys and photographic face mapping areimpossible.

If a thorough site investigation can reveal the essentialvariations of the in-situ rock mass properties, the IBSDcurve giving 100, 80 and 50% passing values will help theblast prediction considerably. The BondRam and EBTmodels make good use of the whole IBSD and if the workindex Wi or Bi is well calibrated for the rock mass inquestion, these approaches look promising as they do notrely on an accurate determination of maximum in-situ size.The BondRam model focuses on the 80% passing sizes,which in practice, have great significance for armourstoneproduction. Also,Mb80 can potentially be determined withmore accuracy than Mb100 during early assessment stagesof the actual production, fromwhich further calibration andrefinement of models can take place.

The KCO model approach appears to be suitable forpredicting the smaller sizes (below 50 mm) of any blastwhich has great implications for quarry waste in break-water projects as discussed in Latham et al. (2006). Italso appears that if IBSD analysis methods are used touchterlony, 2005a,b) showing compatibility with the IBSD, see text.

eringprovide a reasonably confident estimate of Di100=D-

b100=Dbmax it may work well for armourstone blasts. Itis suggested that there may be advantages to resettingthe Swebrec function so that it operates with a Db90 orDb95 for the input parameter, because of the increasinglack of confidence with the determination of the IBSDand thus BBSD as they approach the 100% value.However, this raises the further problem of how to relateDi95 to Db95.

At present, with the KCO model one must chose fromtwo approaches offered for setting the undulationparameter b. It has been seen how each one can givevery different proportions of large blocks for the part ofthe curve betweenDb100 andDb50. Future research resultsto test the simpler empirical Eq. (11) and the successfulsetting of objective values for rock mass factor A andDbmax will help evaluate the use of the three parameters inthe Swebrec function and whether the new KCOmodel isindeed the best on offer for armourstone blast prediction.

8. Concluding remarks

The KuzRam model is not appropriate for predic-tion of BBSD for armourstone blasts because no refer-ence to the IBSD is given to constrain the location of theRosinRammler curve. Typical armourstone blasts havelower uniformity coefficients than high fragmentationblasts and therefore it is vital that the correction iden-tified by Spathis (2004) is applied to all uses of theKusnetsov equation in BBSD models for armourstoneproduction.

Blastability approaches such as the BondRam andEBT models have the advantage of using IBSD infor-mation in the relationship that governs the location ofthe BBSD curve, however, the intrinsic blastability co-efficients suggested for use with different rock massesremain poorly calibrated for these blastability models.

The introduction of the Swebrec function, and theKCO model by Ouchterlony (2005a) has advancedconsiderably our ability to predict the fines content inroutine blasts. In allowing the slope of the curve at Db50to be a function of Db50 the curve takes a more realisticpath. For armourstone blasts, yield curve prediction withthe KCO model looks promising but now requiresfurther validation with case histories.

We are a step closer to making predictions for ar-mourstone blast yield curves with the confidence neededby practitioners. A summary of experience (see Table 3,Latham et al., 2006) learned by breakwater contractorsworking with production engineers when openingarmourstone quarries, will continue for some years to

J.-P. Latham et al. / Enginebe a primary source from which to predict yield curves.Acknowledgements

This paper extends the content of work presented inthe Rock Manual (CIRIA/CUR/CETMEF, 2007) and isprinted with kind permission of CIRIA/CUR/CETMEF.The authors are grateful for comments provided duringreview and the motivation provided by the Rock Manualteam.

References

CIRIA/CUR. 1991. Manual on the use of rock in coastal andshoreline engineering. CIRIA special publication 83, CUR report154, 607p.

CIRIA, CUR, CETMEF, 2007. The Rock Manual. The Use of Rock inHydraulic Engineering (Second Edition). C683. CIRIA, London.

Chung, S.H., Katsabanis, P.D., 2000. Fragmentation prediction usingimproved fragmentation formulae. FRAGBLAST The Interna-tional Journal for Blasting and Fragmentation 4 (2), 198207.

Cunningham, C.V.B., 1987. Fragmentation estimations and the KuzRam model four years on. In: Fourney, W.L., Dick, R.D. (Eds.),Proc. Second Int. Symp. on Rock Fragmentation by Blasting.SEM, Bethel CT, pp. 475487.

DaGama,D.C., 1983.Use of comminution theory to predict fragmentationof jointed rock mass subjected to blasting. Proc. First Int. Symp. onRock Frag. by Blasting, Lulea, Sweden, August 1, pp. 563579.

Djordjevic, N., 1999. Two-component model of blast fragmentation.Proc 6th Int Symp on Rock Fragmentation by Blasting, Sym-posium series S21. SAIMM, Johannesburg, pp. 213219.

Franklin, J.A., Katsabanis, T. (Eds.), 1996. Measurement of BlastFragmentation. AA Balkema, Rotterdam, p. 315.

Gauss, G.A., Latham, J.-P., 1995. The on-site quality control of the as-produced properties of armourstone during construction of a rockrevetment in South Devon. Geotechnical and Geological Engi-neering 13, 2949.

Jimeno, C.L., Jimeno, E.L., Carcedo, F.J.A., 1997. Drilling andBlasting of Rocks. AA Balkema, Rotterdam.

JKMRC, 1996. Open Pit Blast Design Analysis and Optimisation.Julius Kruttchnitt Mineral Research centre, Indooroopilly, Aus-tralia, p. 338.

Kanchitbotla, S.S., Valery, W., Morell, S., 1999. Modelling fines inblast fragmentation and its impact on crushing and grinding. In:Workman-Davies, C. (Ed.), Proc Explo 1999 Conference.AusIMM, Carlton, VIC, pp. 137144.

Kariman, A., Ozkan, S.G., Sul, O.L., Demirci, A., 2001. Estimation ofthe powder factor in bench blasting from the Bond work index.Transactions of the Institution of Mining and Metallurgy (Sect A:Min. Technol.) 110, A114A118.

Konya, C.J., Walter, E.J., 1990. Surface Blast Design. Prentice hall,Englewood Cliffs, New Jersey, p. 303.

Kuznetsov, V.M., 1973. The mean diameter of fragments formed byblasting rock. Soviet Mining Sciences 9 (2), 144148.

Latham, J.-P., Lu, P., 1999. Development of an assessment system ofblastability for rock masses. International Journal of RockMechanics and Mining Sciences 36, 4155.

Latham, J.-P., Kemeny, J., Maerz, N., Noy, M., Schleifer, J., Tose, S.,2003. A blind comparison between results of four image analysissystems using a photo-library of piles of sieved fragments.

73Geology 87 (2006) 6074FRAGBLAST The International Journal for Blasting andFragmentation 7 (2), 105132.

Latham, J.-P., Van Meulen, J.A., Dupray, S., 2006. Prediction of in-situblock size distributions with reference to armourstone for break-waters. Engineering Geology 86, 1836.

Lilly, P.A., 1986. An empirical method for assessing rock massblastability. In: DAVIDSON (ed.) Proc AusIMM/I.E. Aust. New-man Combined Group Large Open Pit Mining Conference.,Victoria, 4144, 8992.

Lizotte, Y.C., Scoble, M.J., 1994. Geological control over blast frag-mentation. CIM Bulletin 87 (983), 5771.

Lu, P., Latham, J.-P., 1996. Estimation of blasted block size distributionof a blastpile combining photo-scanline technique with RosRamand Schuhmann models. In: Guo, Y., Golosinski, T.S. (Eds.),Proceedings of the '96 Int. Symposium on Mining Science andTechnology, Jiangsu, China. Balkema, Rotterdam, pp. 683688.

Lu, P., Latham, J.-P., 1998. A model for the transition of block sizesduring blasting. FRAGBLAST The International Journal forFragmentation and Blasting 2, 341368.

McKibbins, L.D. 1996. An assessment of armourstone potential atHulands Quarry. MSc Thesis, London University, QueenMary andWestfield College p 222.

Ouchterlony, F., 2005a. What Does the Fragment Size Distribution ofBlasted Rock Look Like? In: Holmberg, R. (Ed.), I Proc 3rd EFEEWorld Conference on Explosives and Blasting. European Feder-ation of Explosives Engineers, UK, pp. 189199.

Ouchterlony, F., 2005b. The Swebrec function: linking fragmentationby blasting and crushing. Mining Technology (Trans. Inst. Min.Metal A) 114, A29A44.

Palmstrm, A., 2001. Measurement and characterization of rock massjointing. In: Sharma, V.K., Saxena, K.R. (Eds.), In-situ Character-

Persson, P.A., Holberg, R., Lee, J., 1993. Rock Blasting and ExplosivesEngineering. CRC Press, Boca Raton, Florida, USA.

Rosin, P., Rammler, E., 1933. The laws governing the fineness ofpowdered coal. Journal of the Institute of Fuel 7, 2936.

Spathis, A.T., 2004. A correction relating to the analysis of the originalKuzRam model. FRAGBLAST The International Journal forBlasting and Fragmentation 8, 201205.

Stagg, M.S., Otterness, R.E., 1995. Screen analysis of full-scale pro-duction blasts. Proc. Eleventh Annual Symposium on Explosivesand Blasting Research. International Society of Explosivesengineers, Nashville Tennessee.

Van Meulen, J.A., 1998. Opening and operation of the Pasir Panjangquarry: a dedicated armourstone quarry in the Malaysian jungle.In: Latham, J.-P. (Ed.), Advances in Aggregates and ArmourstoneEvaluation. Engineering Geology Special Publication, vol. 13.Geological Society, London, pp. 107120.

Wang, H., Latham, J.-P., Poole, A.B., 1991. Blast design for armour-stone production. J. Quarry Management. Part I (July), 1721, PartII (Aug), 1922.

Wang, H., Latham, J.-P., Matheson, G.D., 1992a. Design of fragmen-tation blasting in surface rock excavation. In: Hudson, J.A. (Ed.),Proceedings of the ISRM Symposium: EUROCK '92. Balkema,Rotterdam, pp. 233238. Chapter 41.

Wang, H., Latham, J.-P., Poole, A.B., 1992b. Producing armour-stone within aggregate quarries. In: Magoon, O.T., Baird, W.F.(Eds.), Durability of Stone for Rubble Mound Breakwaters.ASCE, pp. 200210.

74 J.-P. Latham et al. / Engineering Geology 87 (2006) 6074isation of Rocks. AA Balkema, pp. 4997.

Prediction of fragmentation and yield curves with reference to armourstone productionEngineering contextFactors affecting blasting for armourstone and aggregatesFragmentation processesComparison of armourstone and aggregates blast designSuggestions for improving the yields of armourstone

Prediction of yield curvesKuzRam modelBondRam modelsBRM(A)BRM(B)

EBT ModelKCO model

Assessment of mass distributionsDirect screening and block measurement methodsImage analysisPhoto-scanline methods

Comparison of BBSD prediction modelsDiscussionConcluding remarksAcknowledgementsReferences