FRAGM: A BLASTING FRAGMENTATION MODEL OF ROCKS by Sergey Victorovych Zagreba A Thesis submitted to the College of Engineering and Mineral Resources atWest Virginia University in partial fulfillment of the requirements for the degree of Master of Science in Mining Engineering Approved by Syd S. Peng, Ph. D., Committee Chairperson Felicia Peng, Ph. D. Yi Luo, Ph. D Department of Mining Engineering Morgantown, West Virginia 2003 Keywords: rock blasting, fragmentation prediction, burden influence ABSTRACT FRAGM: A BLASTING FRAGMENTATION MODEL OF ROCKS bySergey Victorovych Zagreba Fragmentationisamajorconcernofanyblastingoperation.Informationonthe degreeandsizedistributionoffragmentswithinablastedrockmassisessentialfor efficient rock loading and crushing operations. Detailedliteraturereviewshows that majority of the previous researchers estimated blastfragmentationbyconsideringfourbasicvariables,i.e.rockproperties,explosive properties, drilling pattern and bench geometry. However, when considering the effect of burden on rock fragmentation, simplified assumptions were made and its variability along the bench height was often ignored. Inreality,becauseofthenon-uniformburdenalongthebenchheight,theactual powder factor in the front row of holes could differ significantly from the one estimated assuminguniformburden.Thiswillbemoresoifthebenchishighlyirregularandhas significantly different toe and crest burdens. Ignoring this fact may result in a poor fit of theexistingfragmentationmodelsfortheactualdata.Researchinthisthesis demonstratesthisfactandtheresultsunderscoretheimportanceofconsideringthetrue bench profile for the blast fragmentation analysis. Forthepresentwork,theirregularityofthebenchprofileandtheresultingnon-uniformburdenwasestimatedusingthelaserprofilingtechnique.Anewrock fragmentation model, FRAGM, which considers the variability in burden, was developed andverifiedbycomparingwithactualblastresultsfromaWestVirginianlimestone quarry.Thedevelopedmodelcanbeusedasaquickandreliablemeanstopredictor assess the rock fragmentation before or after a blast. iiiAcknowledgment IwishtoexpressmysinceregratitudetoDr.SydS.Peng,ThesisAdvisorand Chairman of Department of Mining Engineering of the West Virginia University, for his patienceandguidancethroughoutthisstudy.Withouthissupportthisworkwouldnot havebeenpossible.Iwouldliketoconveymythanksandappreciationtotheother committee members, Dr. Felicia Peng and Dr. Yi Luo for their constructive criticisms and concrete suggestions at several stages of this work. A special thanks to Ms. Karen Centofanti for her assistance in the official work. Finally, I am greatly indebted to my wife, Mary Beth, and my entire family whose supportcanneveradequatelybeexpressedinwords.Thankyouforencouragingme throughout my life to meet challenges with determination and to strive for success. ivTable of Contents Abstract ..ii Acknowledgment iii Table of Contents ... iv List of Tables .vi List of Figures vii Chapter 1 Introduction .. 1 Chapter 2 Literature Review 4 2.1 Mechanism of rock breakage by blasting . 4 2.1.1 Radial cracking theory . 62.1.2 Shock wave theory 11 2.1.3 The contribution of the shock wave and gas pressure .13 2.2 Extent of blast damage zones .. 192.3 Effect of controllable blast parameters on fragmentation ..22 2.4 Effect of discontinuities on rock fragmentation by blasting 302.5 Methods of study of rock fragmentation by blasting .. 31 2.5.1 Kuz-Ram model 34 2.5.2 Hole-by-hole analysis 40 Chapter 3 Development of the Proposed Model FRAGM .. 41 Chapter 4 Description of the Rock Fragmentation PredictionEngineering Model FRAGM .55 4.1 Bench and borehole information . 57 4.1.1 Burden 57 4.1.2 Spacing ... 59 4.1.3 Powder factor . 60 4.1.4 Loading density .60 v4.1.5 Diameter of blastholes ...61 4.1.6 Stemming ... 62 4.1.7 Subdrilling .. 63 4.2 Explosive types ..64 4.3 Rock strength ..64 4.4 Delay time ..68 4.5 Geological conditions .. 69 4.6 Output data description ..70 Chapter 5 Verification of the Proposed Engineering Model 71 5.1 Introduction . 71 5.2 Image analysis technique and sampling .. 725.3 Constraints ..74 5.4 Verification of proposed development in the field .75 Chapter 6 Quality Control .. 104 6.1 Introduction.104 6.2 Ammonium nitrate based dry explosives .1046.3 Slurries 105 Chapter 7 Conclusions and Recommendations .106 References 109 Appendix A Verification of the Proposed Methodology by Hand Calculations 120 Appendix B Profiling the Quarry Bench Face .134

Appendix C Using an Image-Processing Program ..162 Split-Desktop viList of Tables Table 2.1 Spalling-related values by Petkof et al. (1961) 18Table 4.1 Explosive strength based on composition 65 Table 4.2 Rock properties by Mohanty (1987) 66 Table 4.3 Rock properties presented by Cook (1976) . 67 Table 5.1 Predicted and actual size distribution for the blast # 1 79 Table 5.2 Predicted and actual size distribution for the blast # 2 85 Table 5.3 Predicted and actual size distribution for the blast # 3 91 Table 5.4 Predicted and actual size distribution for the blast # 4 96 Table 5.5 Predicted and actual size distribution for the blast # 5 .. 102 Table B.1.1 Results of the bench face profiling (Blast # 1) .. 137 Table B.1.1.1 Results of the estimation of rock volume in the first row of blastholes (Blast # 1) ..140

Table B.1.2 Results of the bench face profiling (Blast # 2) ... 141 Table B.1.2.1 Results of the estimation of rock volume in the first row of blastholes (Blast # 2) ..145 Table B.1.3 Results of the bench face profiling (Blast # 3) . 146 Table B.1.3.1 Results of the estimation of rock volume in the first row of blastholes (Blast # 3) ..149 Table B.1.4 Results of the bench face profiling (Blast # 4) ... 150 Table B.1.4.1 Results of the estimation of rock volume in the firstrow of blastholes (Blast # 4) .155 Table B.1.5 Results of the bench face profiling (Blast # 5) ... 156 Table B.1.5.1 Results of the estimation of rock volume in the first row of blastholes (Blast # 5) ..161

viiList of Figures Figure 2.1 Diagrammatic representation of the interaction of a spherical wave with theradial crack systemmodified by Roberts and Wells (1954) . 7 Figure 2.2 Favorable reflection geometry for extending cracks towards the free face by Roberts and Wells (1954) 7 Figure 2.3 a)incidence of the reflected wave at the crack tip b) region influenced by the reflected waves c) theoretical crater development a single hole; presented byRoberts and Wells (1954) 10 Figure 2.4 Typical distance-time plot for granite by Petkof et al. (1961) . 15 Figure 2.5 Typical distance-time plot for marble by Petkof et al. (1961) . 16 Figure 2.6 Typical distance-time plot for limestone by Petkof et al. (1961) . 17Figure 2.7 The damage zones surrounding an explosive charge 20 Figure 2.8 Crack system for the square pattern with 80 mm holes and0 mm standard deviation in drilling by Lownds (1976) .24 Figure 2.9a Crack system for the square pattern with 80 mm holes and 200 mm standard deviation in drilling by Lownds (1976) 25 Figure 2.9b Crack system for the square pattern with 80 mm holes and300 mm standard deviation in drilling by Lownds (1976) 26 Figure 2.10a, b Effective circles around holes for a square pattern: a) no deviation in drilling; b) 30 %of the burden deviation indrilling; by Lownds (1976) 28 Figure 2.11 a, b Increased radius of effective circles: a) no deviation in drilling; b) 30 % of the burden deviation in drilling; by Lownds (1976) 29 Figure 3.1 Diagram of a blasting pattern and the geometry of charged blastholes 42 Figure 3.2 Typical representation of the drillhole inclination versusthe bench face angle presented by Oloffson (1990) . 43

viiiFigure 3.3 Variation of burden in case of vertical holes by Bhandari (1997) ..45Figure 3.4 Parts of a bench presented by Hustrulid and Kuchta (1998) 46Figure 3.5 Two areas of breakage .. 48 Figure 3.6 Three cases in main breakage area...51 Figure 4.1 Procedures of blast round design and evaluation of blastingperformance.56 Figure 4.2 X-Y-Z coordinates data of the bench boreholes 58 Figure 5.1.1 The quarry highwall before actual shot (blast # 1) .76 Figure 5.1.2 Muckpile immediately after the shot (blast # 1) .77 Figure 5.1.3 Cumulative size distribution (blast # 1) ..80Figure 5.2.1 The quarry highwall before actual blast (blast # 2) . 82 Figure 5.2.2 Muckpile a few days after the shot (blast # 2) . 83 Figure 5.2.3 Cumulative size distribution (blast # 2) ..86 Figure 5.3.1 Quarry highwall and muckpile approximately week after the shot (blast # 3) ... 88 Figure 5.3.2 Muckpile after the shot (blast # 3) ... 89 Figure 5.3.3 Cumulative size distribution (blast # 3) ... 92 Figure 5.4.1 Muckpile immediately after the shot (blast # 4) .. 94 Figure 5.4.2 Cumulative size distribution (blast # 4) ..97 Figure 5.5.1 The quarry highwall before actual shot (blast # 5) .99 Figure 5.5.2 Muckpile immediately after the shot (blast # 5) .. 100 Figure 5.5.3 Cumulative size distribution (blast # 5) 103 Figure A-1 Typical bench face profile of borehole in the first row ..123 Figure B-1 Laser surveying equipment used for profiling the face (courtesy Measurement Devices Ltd.) 135

Figure C-1 Typical JPEG image is taken in the field for the calculation of size distribution ..164 Figure C-2 Typical grayscale image .. 165 Figure C-3 Typical binary image ... 166 1Chapter 1 Introduction Adequaterockfragmentationisthemajorobjectiveofanyblastingoperations. Fragmentationisthebasicconcerninrockblastingandservesasthemainmeasureof blasting effectiveness. Good fragmentation is the key to successful mining operation and equipmentmaintenance.Itisdesirabletohaveauniformfragmentsizedistribution, avoidingbothfinesandoversizes.Itisveryimportantthatblastpatterncanbequickly andaccuratelyanalyzedbeforeactualblast.Anyminingoperatorscanminimizetotal productioncostspertonofrockblasted.Thisrequiresanevaluationofthecomponent costs, which include drilling, blasting, loading, hauling and crushing costs. The drilling and blasting are the first unit operations in the mining process and have a major impact on the performance and cost of subsequent unit operations. An increase in the degree of fragmentation will give the loading equipment a higher rate of productivity. This will result in lower costs per ton or cubic yard moved. The effect of wear and tear will also decrease, giving lower operating cost per hour. Undersimilarconditionsofhaul,lift,sizeandtypeoftruck,andhaulroad condition,truckproductionperhourwillincreasewithgreaterdegreeoffragmentation duetofastershovelorloaderloadingratesandadecreaseinbridgingatthecrusher. There will be a consequent decrease in cycle time. At a standard operating cost per hour, this increase in truck speed or productivity will result in lower unit operating costs.Anincreaseinthedegreeoffragmentationgiveslowercrushingcostsasmore materialpassesthroughasundersize.Linercosts,repairandmaintenance,andbridging timewilldecreaseandthecrushingrateperhourwillincrease.Thedecreasedbridging time also cuts down on truck delay time at the crusher, which, in turn, gives higher truck 2and shovel (loader) productivity. Any increase in the degree of fragmentation means less work for the crusher.Thesehavebeentheeasiesttoexplainsincetheunitcostsalwaysdecreasewith increasingfragmentation.Thesameisnottrueforthedrillingandblastingcosts.There are many possible combinations, which can occur depending upon the particular design. For a given rock type, geologic structure, and firing sequence, an increase in the degree offragmentationmaybeachievedby(a)increasingtheconsumedquantityofagiven explosive,(b)changingtoanexplosivehavinggreaterenergycontentperunithole volume (higher energy content/ density), or (c) combinations of both.Forblastingcase(a)theassociateddrillingcostwouldincreaseiftheexplosive quantityweretobeincreasedbysimplydrillingthesamediameterdrillholesbutona tighter pattern. Thus there would be more drill holes required to blast a given volume. If larger diameter drill were substituted and the increased hole volume achieved in this way then the rate of increase or decrease would depend upon the comparative drilling cost per foot of hole.For case (b), assuming that the same hole diameter and pattern are used, the drilling cost would remain constant independent of the fragmentation. For case (c) the drilling cost could remain constant, increase or decreasedepending upon the situation.Theobjectiveofthisresearchworkare:1)toestablishamethodologyforblast fragmentationprediction;2)todevelopanengineeringmodelforfragmentationsize predictionbasedonthemethodologyestablishedinthefirststep,andtoprovidean 3algorithm for prediction; and 3) to compare field data with predicted values to verify the model.Theengineeringmodelconsidersfourmainfactors:explosiveproperties,rock properties, drilling pattern and actual bench geometry. Field data would be used to verify the theoretical development. 4Chapter 2. Literature Review 2.1 Mechanism of rock breakage by blasting Blasting theory is one of the most interesting, challenging, and controversial areas of theexplosivesengineering.Itencompassesmanyareasinthescienceofchemistry, physics, thermodynamics, shock wave interactions, and rock mechanics. In broad terms, rock breakage by explosives involves the action of an explosive and the response on the surrounding rock mass within the realms of energy, time and mass. This chapter content willemphasizetheconceptassociatedwithblastingtheories,ratherthanarigorous mathematical,physical,orchemicaltreatmentthroughformulae.Whereformulaeare used, they are merely to enhance the concept presented. In spite of the tremendous amount of research conducted in the last few decades, no singleblastingtheoryhasbeendevelopedandacceptedthatadequatelyexplainsthe mechanisms of rock breakage in all blasting conditions and material types. There is as yet noconsistentandwidelyapplicabletheoryofblasting,butonlyanumberoflimited theories,manyofwhichareempiricalinnatureandbasedonidealsituations.The reflected theory has been chosen in this thesis for its simplicity and ease of applications. Rockfractureresultingfromexplosionprocessofexplosivesloadindrillholes dependonthenumberoffreefaces,theburden,theholeplacementandrockgeometry, thephysicalpropertiesandloadingdensityoftheexplosive,thetypeofstemming,the rock structure and mechanical strength, and other factors. Final fragmentation in a bench blasting operation can be attributed to a combination of:1.crushing of the rock immediately around the explosive cavity; 52.initial radial fracturing due to tensile tangential stress component in the outgoing stress wave; 3.secondaryradialfracturesformedatthesurface,propagatinginward,dueto enhanced tangential stress accompanying free surface displacement; 4.extension of the initial radial fractures by reflected radial tensile strain at oblique angles to the surface; 5.joining of inward propagating radial fractures with initially created outward radial fractures; 6.tangential fractures formed at the surface, propagating parallel to the free surface; 7.tensile separation and shear of rock at places of weakness in the rock mass;8.separation of the rock due to reflected radial tensile strain; 9.fracture andacceleration of fragments by strain energy release; 10. further fracture and acceleration of broken rock by late expanding gases; and11. pre- existingdiscontinuities in the rock mass. Whilenoneofthesemechanismscanbeignored,explosive-generatedradial fracturesarecrucialindeterminingtheoverallfragmentationasHarriesandHengst (1977)andLownds(1983)showedusingsimulationmodels.Thosestudiesdescribe computersimulationmodels,whichcalculateblastresultsprovidinginformationonthe fragmentation.ThemodelsarebasedonHarrieshypothesis(1977)thatradialfractures are primarily responsible for fragmentation in rock. 62.1.1 Radial cracking theory ThepracticalimplicationsforblastingaredescribedbyRobertsandWells(1954). They explained that the cracks grew outward away from the hole under the action of the gas pressure. The authors pointed out that the cracks would have extended a distance of only 0.38 times the burden width (0.38B) when that portion of the incident wave directly in front of the charge meets the free surface (Fig 2.1a). The crack tip and the front of the reflected wave will meet at the distance (X). cXcX B38 . 02=;(2.1.1.1) X = 0.55B(2.1.1.2) whereB- the burden, ftc- the crack velocity, ft/ sec. Asindicated,thecrackgrowinginthisdirectionshouldstoporberetardedatthis point.Cracksgrowingatanangle tothesurfacewillalsobeinfluencedbythe reflected wave. If this wave meets the tip of the static crack it can accelerate the increase of the crack growth (Roberts and Wells, 1954). The length e will depend upon the crack orientation and crack velocity. As can be seen (Fig. 2.2) tan 2 =he (2.1.1.3) 7

Figure 2.1Diagrammatic representation of the interaction of a spherical wave with the radial crack system modified from Roberts and Wells (1954).

Figure 2.2Favorable reflection geometry for extending cracks towards the freesurface byRoberts and Wells (1954). 8and sin 2 =ge (2.1.1.4) hence h = 2 tane (2.1.1.5) and g = 2 sine(2.1.1.6) Thetimerequiredforthewavetotraveladistanceh=gatvelocitycmustbethe same as that needed by the crack traveling at a velocity V crack to travel distance e. Thus t crack = crackV e= c h g += t wave (2.1.1.7) Assuming that V crack = K c(2.1.1.8) where K is a constant, then

e h g + = K1(2.1.1.9) Substituting the values for h and g into equation (2.1.1.9) one finds that 9 K12 sin12 tan1=||.|

\|+ (2.1.1.10) Simplifying yields tan= K (2.1.1.11) or = tan 1 K(2.1.1.12) Ifthecrackvelocityisknownthentheorientationofcrackswhichwillbeeffected can be calculated. For the case (Robert and Wells, 1954) when V crack = 0.38c (2.1.1.13) The most favorable crack orientation would be = tan 1 0.38 = 20.8 0 (2.1.1.14) Thelengthetowhichthecrackwouldhavegrowntoitsencounterwiththe reflected wave is e = 2B sin(2.1.1.15) and the distance, which the wave would have traveled isg + h = | | 2 cos 1cos+B(2.1.1.16) 10 Figure 2.3a)incidence of the reflected wave at the crack tip; b) region influenced by the reflected waves; and c) theoretical crater developmentof a single hole; presented by Roberts and Wells (1954). (a) (b) (c) 11Ascanbeseenintheexpandedviewofthecracktip(Figure2.3a),itistheradial (tensile)componentofthereflectedwave,whichactstoextendthecracktip.The tangential component is compressive and acts in the direction of crack propagation. Other cracksintheburdenregionwillalsobeaffectedbythereflectedradialcomponentand encouraged to extend. Crack oriented behind the line of blastholes (Figure 2.3b) will not be affected.Forasingleholeshotincloseproximitytoafreeface(Figure2.3c),theexpected included angle (B) for the broken rock is expected to be B = 180 0 2= 138.4 0 (2.1.1.17) AssumingthatV crack=0.38c,itagreesquitewellwithwhathasbeenobservedin practice (Roberts and Wells, 1954). 2.1.2 Shock wave theory Shock wave theory of rock breakage has been proposed in many forms by different researchers.Thismodelstatesthatmostoftherockbreakageinablastoccursatafree face as a result of spalling, which occurs when a compressive wave is reflected at a free boundary. The slabs, which are spalled from the rock edge, are formed in a succession of increasing thickness, where the number of slabs depends on the amplitude and duration of the stress wave. 12 TheUnitedStatesBureauofMinesconductedaseriesofexperimentstostudythe explosioncratertoconfirmtheshockwavetheory.AtchisonandDuvall(1957)studied the relationship between the radial strain and explosive energy for a concentrated charge. Their results may be expressed by the equation below = nmWDCP

3 / 1 2(2.1.2.1) whereD/W1/3 isthescaleddistance;Pmistheexplosionpressure; istheexplosive density; c is the wave velocity; andis the strain wave. They found n was 1.56 for the transition zone and 1.24 for the seismic zone in Greenstone granite using 60% ammonia gelatin at a density 1.41 g/cc. This relationship should apply quite generally since it does not depend on any specific type of wave form. Therefore, the factor n will vary from one set of conditions to another. For cylindrical charges, the empirical formula to determine the relationship between theradialstrainandtheexplosivepropertieswasstudiedbytheSovietresearchers. Adushkin et al. (1987) published the following equation: C EUrm /=6.62 * 10-3 2 . 1

qeR (2.1.2.2) 13where: Urm - the radial component of the maximum particle velocity, m/sec; R - the distance between observation points, m; qe-thelineardensityoftheexplosiveforaTrotylchargeequivalentinenergy,kg/m, - the material density, kg/m3; c - the elastic lontitudinal wave velocity in the material, m/sec;E - the concentration of explosive energy in the charge, J/m3. One argument against the shock wave theory proposed by Langefors and Kihlstrom (1963) is the fact that fragmentation could occur in the absence of a high intensity stress pulse, which cannot be explained by the shock wave theory. However, there is no doubt thatstrainmagnitudeinblastwavesisaveryimportantfactorinrockbreaking mechanism and must therefore be included in any useful model. 2.1.3 The contribution of the shock wave and gas pressure Some of the earliest photographic studies regarding bench blasting were reported by theUnitedStatesBureauofMinesinthelate1950s(AtchisonandDuvall,1956;Blair, 1960).Atthattimetheemphasiswasonstudyingtheshockwaveaspectofblasting action.Withthisconcept,theshockwavegeneratedbytheblasttravelstothefree surface from which it reflects. If the tensile strength is low, compared to the amplitude of the tensile portion of the wave, the rock face will spall. The spalled rock then travel away 14fromtheremainingrockwithacertainvelocity.Thisisobviouslyacontributiontothe overall heave of burden rock. TheUnitedStatesBureauofMinesconductedacomprehensiveblastingresearch program in the 1960s, which has resulted in findings of great interest. The test performed andreportedbyPetkofetal.,(1961)wastostudythemotionofbenchfacesduring blasting.Thetechniquesusedinthesestudieswere(1)high-speed(1,000framesper second) photography of the quarry face in front ofone charge hole of a quarry blasting round and (2) measurement of the radial strain wave generated in the rock by the charge at a distance equal to the burden. Thehigh-speedcameraprovideddataintheformofamotionpictureoftheblast. Frame-by-frame projection of the film permits the measurement of the rock movement as afunctionoftime.Thetimeofchargedetonationcouldbeobtainedbyobservingthe flashoflightfromthedetonationcord.In caseswherethedetonatingcordcouldnotbe usedasatimer,theoriginofthetimeaxiswasthefirstobservablemotionoftherock. The slope of the line drawn through the points of the distance- time plot is the horizontal velocityofthebrokenrockorthefly-rockvelocity.Typicalresultsforthethreerock typesaregiveninFigure2.4,2.5,and2.6.Thepointindicatedascalculatedonthe figures is that corresponds to the shock wave at the face.Ingeneral,theoverallcurveconsistsoftwostraightlinesegments.Thesecondof thesesegmentshasasignificantlygreaterslopethanthefirstindicatingastepwise increase in the velocity at the inflection point. 15 Figure 2.4Typical distance-time plot for granite by Petkof et al., (1961). 16 Figure 2.5Typical distance-time plot for marble by Petkof et al., (1961). 17 Figure 2.6Typical distance-time plot for limestone by Petkof et al., ( 1961). 18 Table 2.1. Spalling-related values (Petkof et al., 1961) Rock type Shot MeasuredStrain, m SpallingVelocity, ft/sec Time,msec L - 1 1150 43 0.065 L - 2 1000 37 0.44 L - 3 750 28 0.46 Granite L - 4 1350 50

0.52 T - 1 270 11 0.67

T 2A 700 29 0.78 Marble T 2B 510 22 1.02 Limestone L - 1 650 18 0.92 19Themeasuredinitialvelocityoftheblockcomingofftherockfacehasthesame orderofmagnitudeasexpectedaccordingtothereflectiontheoryofrockbreakage (Petkof et al., 1961). The increasing curve slopes suggest thatafter some period of time the rock at the rear of the blasted burden is moving faster than the spalled blocks. This is consistentwiththeaccelerationofthemainportionoftheburdenbythegaspressure. Because of its higher velocity but delayed starting time, the bulk of the blast catches up to thespalledblocksandacceleratesthem.Intheimpact,whichoccursbetweenthesetwo parts of the burden some additional breaking is possible.Theconclusionfromthisseriesoftestsisthatundernormalbenchblasting conditionsspallingisaminorcontributortotheheavingprocess.Thisprocessis dominated by the action of the gas pressure. 2.2 Extent of blast damage zone Thepredictionandobservationofthenatureandextentofthedamageproducedin thesurroundingrockwhenanexplosivechargedetonatesinaboreholeisofmajor practical significance for engineered rock excavation.The radius of the damage zone formed when a cylindrical charge detonates in a rock massisoneofthemostimportantparametersrequiredinthedevelopmentofa scientificallybasedmethodfordesigningblastpatterns.Theprocesstakingplaceinthe rocksurroundingachargearesocomplexthatanexactmathematicaldescriptionis presentlyimpossible(Hustrulid,1999).Thedamagemechanismschangeasthedistance from the explosion increases, and many investigators therefore distinguish a number of 20 Figure 2.7The damage zones surrounding an explosive charge.

21zoneswithinwhichthestressedstateandthefracturepatterndiffer.Thepaper Calculationoffracturezonescreatedbyexplodingcylindricalchargesinledgerocks byDrukovanyietal.,(1976)isintheauthorsopinionofspecialimportanceinthis regard.In this paper the investigators distinguish a number of zones within the stressed state and their fracture patterns differ: Inzone1immediatelyadjoiningthecharge(Figure2.7)thecompressivestresses exceedthecompressivestrengthoftherock.Inthiszoneconsiderabledeformations occursandfractureisofovercrushingtype,i.e.,finecrushingisobserved.Current assessmentsofthesizeofthiszoneareconflicting,butmostforeigninvestigatorshold the view that the size of the zone of plastic flow does not exceed 3-5 charge radii.Zone2,thezoneofradialfissures,hasarathercomplexstructure.Theintensityof crushingoftherockinthiszoneasaresultoftheintersectionof(a)thenaturalradial fissuresbytheradialones,and(b)possiblecircularrupturesformingaroundthecharge cavity, decreases with increasing distance from the explosion center. The outer boundary of this zone is located outside the region of individual radial fissures. Zone3isthezoneofelasticdeformation.Forpracticalpurposes,itisofmaximum interesttoestablishtheboundariesoftheregionwithaspecificcrushingintensity (fragment characteristics) or the zone of so-called controllable crushing. The theoretical solution of this problem is extremely complex because one of the governing factors of the processofcrushingisthejointingpatternoftherockmass.Thismeansthattheuseof the theory of mechanics, which is applicable to a continuous medium, cannot provide an exact solution. 22Experimental assessment of fracture zone extent obtained by different methods vary quitewidely.However,toafirstapproximationonecanassumethatwhenhigh explosives are fired in direct contact with the hole wall the boundary of the zone of radial fissuresislocatedatadistanceof40-50chargeradiifromtheexplosioncenter (Azarkovich, 1965, 1981; Anonymous, 1971; Vovk et al., 1973). 2.3 Effect of Controllable Blast Parameters on Fragmentation Thisresearchstudyisfocusedonthepredictionoftherockfragmentation distributionresultingfromagivenbenchblastoperation.Thisisnotaneasytask,since theoreticaldevelopmentsofrockbreakagearehinderedbythenumerousvariables influencing the phenomenon. More than twenty factors appear to affect fragmentation in a blast (Da Gama, 1983). The effect of interaction between several blast design variables onfragmentationresultshadbeenstudiedbymanyresearchers.Thesevariablesare powder factor, drilling pattern, borehole diameter, delay timing, and drilling inaccuracy.Fragmentation results described by the mean fragment size alone are inadequate and afulldescriptionoftheentiresizerangeisneeded.Itwasrealizedthatthedistribution curve (the Rosin-Rammler Curve) had been generally recognized as giving a reasonable descriptionoffragmentationinblastedrock(Faddeenkov,1975;Cunningham,1983, 1987; Harries and Hengst, 1977). To define the Rosin-Rammler curve two parameters are needed,namely,thecharacteristicfragmentsize(Xc)andtheexponentnwhich characterizestheroot-mean-squaredeviationfromthemeanorinotherwordsthe 23uniformity of crushing. If n>1 then the characteristic fragment size (Xc) is approximately equal to the mean fragment size (50% passing).The behavior ofn with inaccuracy in drilling had been studied by Lownds (1976, 1983).Hestatedthatincreasinginaccuracyinholepositionresultsinasignificant decrease of degree of uniformity of the blasted material. From Figures 2.8 and 2.9 it can be seen that greater borehole diameters or, in other words, higher specific consumption of explosives gives better and more uniform fragmentation (lower Xc and higher n). On the other hand, as can be seen from Figure 2.9 that increasing inaccuracy in hole position had little effect on the characteristic fragment size, except for the case of square patternwith50mmholes.Itseemsthatwhentheamountofexplosiveperholeissuch thattheradiusofaffectedrockmassfromtheexplosionissmall,drillingmisalignment not only gives non- uniform fragments but also bad fragmentation. This statement will be demonstrated by the following simple example.Whenholesarefiredindependently,therewilleffectivelybeacylinderofbroken rock mass around each hole after firing (Lownds, 1976). In a horizontal section through thebench,eachcylindercanberepresentedasacircle.Forfractureofthewholerock massduringblastingeverypointinthesectionmustbewithinatleastoneofthese circles.Forexample,inFigure2.10a,asquaredrillingpatternwitheffectivecircles aroundtheholesisshown.A30%oftheburdendeviationindrillingresultedinthe pattern shown in Figure 2.10b. It can be seen from this figure that a large proportion of the area intended to be fractured remained unaffected from radial cracks emanating from the holes. This resulted in a larger characteristic fragment size compared to the case with 24 Figure 2.8Crack system for the square pattern with 80mm holes and 0mm standard deviation in drilling by Lownds (1976). 25 Figure 2.9aCrack system for the square pattern with 80mm holes and 200mm standard deviation in drilling by Lownds (1976). 26 Figure 2.9bCrack system for the square pattern with 80mm holes and 300mm standard deviation in drilling by Lownds (1976). 27no drilling inaccuracy, and also in a non- uniform fragmentation because of the obvious asymmetry of the track system.A 33% increase in the radius of the effective circles around blastholes (by increasing the amount of explosives per hole) and with no faulty drilling is shown in Figure 2.11a, while a 30% of the burden deviation in drilling is shown in Figure 2.11b.From Figure 2.11b, it can be observed that with this radius of effective circles there aresomesmallareasunaffectedbytheexplosivesaction.Thatis,themeanfragmentis expectedtoremainthesame,buttheuniformityoffragmentationwilldecreasebecause of the non-uniform distribution of holes on that section.The analysis of the effect of controllable blast parameters on fragmentation using the literature review lead to the following conclusions:1.For the effect of powder factor on fragmentation, it was found:-thepredictedbehaviorofcharactericticfragmentsize(63.9%passing) withpowderfactormatchwellwiththatpredictedbyKuznetsovs equation (Kuznetsov, 1973; Cunningham, 1983, 1987; Lownds, 1983).-adecreaseoftheuniformityoffragmentationwasfoundwithdecreasing powder factor (Lownds, 1983).2.The drilling pattern has the following effect on fragmentation: -staggered pattern gives lower characteristic fragment size compared to the squarepatternforthesamepowderfactor,becauseofthebetter distribution of explosives in the rock mass in the former case. -staggeredpatterngivesmoreuniformdistribution(highervalueofthe Rosin-Rammler exponent n). 28 Figure 2.10 Effective circles around holes for a square pattern: a) no deviation in drilling; b) 30 % of the burden deviation in drilling; by Lownds (1976). 29 Figure 2.11Increased radius of effective circles: a) no deviation in drilling; b) 30 % of the burden deviation in drilling; by Lownds (1976). 303.Agreaterboreholediameterproducesabetterandmoreuniformfragmentation for a given blast pattern. 4.Inaccuracyindrillinghadanegativeeffectonuniformityoffragmentation. However, no effect on the characteristic fragment size was observed, except in the case of low usage of explosives where the characteristic fragment size was found to increase as the drilling deviation was increased. 2.4 Effect of Discontinuities on Rock Fragmentation By Blasting Rock properties are the uncontrollable variables in blast design. Blast performance is influencedbygeologicstructureandrockstrength.Inalmosteveryminingpractice,the rocksarefarfromhomogeneous.Therearejoints,beddingplanes,mudorsoftseams, whichhaveamajoreffectonblastingperformance.Thesearedefinedasplanesof weaknesswithinarockmassalongwhichtherehasbeennovisiblemovement.There willbeadifferenceintransmissionofthestresswavesthroughthejointsdependingon whether the joint is tight, open or filled (Obert and Duvall, 1950; Goldsmith, 1967). Tight jointsdonotaffectthetransmissionofstresswaveswhereastheopenandfilledjoints introduce an acoustic impendance mismatch and reflect the stress waves. If the reflected waveissufficientlystrong,internalspallingtakesplace.Theradialcracks,whichthe strain wave would have formed in a continuous rock, are prematurely interrupted by the joint.Manyinvestigatorshavestudiedtheeffectofdiscontinuitiesonrockbreakage induced by blasting. A brief review of their results is presented below: 31-Fourneyetal.,(1983)hasfoundinhismodelscaleexperimentsajointinitiated fragmentation mechanism. For a layered medium this mechanism of joint initiated cracking yields a much smaller average fragment size than would be obtained in a homogeneous media. This reduction in fragment size is at least 1.5 times. -DaGama(1983)foundinfull-scalebenchblaststhatlessenergyisrequiredto fragmentadiscontinuousrockthanahomogeneousrockandusedtheBonds third law of comminution to estimate this energy reduction. -Harries(1983)infull-scalebenchblastsfoundthatanyincreaseinthemean spacingbetweenjointsand/orbeddingplanespartingsdemandsthatagreater degree of new breakage is created in a blast. An increase in the degree of fissuring usuallyencouragetheuseofgreaterburdens,blastholespacingsandcollar(or stemming) length and correspondingly lower energy factors. Ash(1973)statedthatbetterfragmentationoccurswhendrillholesareoriented alonglinesperpendiculartothemostprominentjointfaceoftherockmass.Large fragments result from those lines of drill holes parallel to that joint face. 2.5 Methods of Study of Rock Fragmentation by BlastingIngeneraltherearethreemethodsbywhichrockfragmentationbyblastingcanbe studied: 1.Using a full- scale blasting process as a model 2. Using scale models 3.Using numerical models. 32Theactualfull-scaleblastingoperationcanbetoolargeforexperimentation.For mostsmall-scalemodelblasting,sizingof100%oftheblastedmaterialwithsievesfor particle size determination is usually feasible. However, sieving is not possible with full-scaleproductionblastsalthoughaphotographicmethodcanbeusedinstead. Photographicmethodsofevaluatingfragmentationarecurrentlysuccessful (measurementsofsectionthroughthemuckpile)butstilltherelationbetweenthe distributionmeasuredbyphotographicorimageanalysisandtheactualparticlesize distribution (measured sieving) has to be found. In general, full-scale experimentation is expensive and time consuming, and only a limited number of parameters can be varied.Modelsfromconcrete,rockorphotoelasticmaterialssuchasplexiglasshavebeen used by many workers to study rock fragmentation by explosives or fracturing and crack propagation problems (Fourney et al., 1983; Bjarnholt and Skalare, 1983).However, scale models must make the following assumptions: (a)crackinginphotoelasticmaterialsusedasmodelsissimilartocrackinginrock (Harries and Hengst, 1977);(b) the effect of discontinuities on the fragmentation process in model blast is similar to that in full scale blasts; and (c)theactualstructureoftherock,asdeterminedbytheexistingdiscontinuities, cannot be simulated in model scale blast.Many industrial explosives will not detonate reliably in small diameters because the critical diameter depends on the type of explosive. Each explosive has its own diameter-velocitycurve.Iftheboreholediameterislessthanthecriticaldiameter,thedetonation processwillnotsupportitselfandwillbeextinguished.AsaresultPETNbased 33explosiveshavetobeused.Thisappliesparticularlytotheexperimentationand evaluationofaluminizedexplosiveswherethealuminumrequiresafinitetimetoreact (Porter, 1974).Numericalmodelingdoesnothavethedisadvantagesoftheabovetwomethods. Finiteelementcodesweredevelopedthatmodelboththeshockandstresswave propagationsthroughtherockandthenucleationandgrowthofcracksintheaffected rock mass (McHugh, 1983; Margolin and Adams, 1983). While still a long way from use inroutineblastdesign,theseapproacheshelpdirectexperimentalworkinacost- effective way, and greatly improve our understanding of fundamentals mechanisms. Anexampleofthemoreempiricalmodelswhichcanbeusedwasgivenby Cunningham(1983).HismodelincorporatesKuznetsovswork(1973)onrelating explosive energy, hole size and rock characteristics to mean fragment size, and the Rosin-Rammlercurvesforassessingfragmentsizedistribution.Thisapproachisused extensively by AECI, the major South-African industrial group, for designing blast and, providingthechoseofvaluesfortherockiscorrect,givesafairlygoodmatchtodata obtained in actual tests.HarriesandHengst(1977)constructedadigitalsimulationmodeltostudyrock fragmentationduetoblasting.Thismodelwasthebasicforfurthermodelsthatcanbe usedinroutineblastingworksuchastheSABREXprogram(ScientificApproachto BlastingRockbyExplosives),andLowndsFRAGmodel(1983).Inthesemodels variousassumptionsweremadeforthepropagationofcracksandthesewere programmed into a simulation model of the blasting area. 34BLASPAhasbeenusedbyFavreau(1983)andothersformodelingblastingfor manyyears.Recently,Favreau(1993)hasdescribedsomeoftheaspectsoftheswell moduleusedinthemodelandtheresultsobtained.Thismodelcanbeonlyappliedto description of particle motion during a blast.The spherical element computer program DMC_Blast, developed by Preece in 1989, hasbeenmodifiedafewtimes.Anewversionofthatprogram(Preeceetal.,1997) performs coupled gas flow and rock motion simulations in a bench blasting environment. Severaldifferentequationsofstateareincludedformodelingthebehaviorofthe explosive.TheequationofstateforexplosivegasestraditionallyusedbytheBritishcompany ImperialChemicalIndustries,alsoknownasICI,allowsmodelingofmanydifferent explosives.Theprogrammuckpilecontoursareingoodagreementwiththoseobserved in the field (Preece et al., 1993). 2.5.1 Kuz-Ram model An empirical equation of a relationship between the mean fragment size and applied blastenergyperunitvolumeofrock(powderfactor)hasbeendevelopedbyKuznetsov (1973)asafunctionofrocktype.Hereportedthatinitialstudieshadbeendonewith models of different materials and the results were later applied to open pit mines and an atomicblast.Adegreeofscatterbetweenfragmentationmeasurementsandprediction was shown, and was to be expected, considering the nature of mining and the variability 35ofrock.Themodelpredictsfragmentationfromblastingintermsofmasspercentage passing through versus fragment size. His equation is given below Xm= A 8 . 00||.|

\|QVQ 1/6 (2.5.1.1) where: Xm- mean fragment size, cm; A - the rock factor, 7- for medium hard rocks, 10- for hard highly fissured rocks, 13- for hard, weakly fissured rocks; V0 - the rock volume (cubic meters) broken per blasthole = Burden x Spacingx Bench Height; Q - the mass of TNT containing the energy equivalent of the explosive chargein each blasthole, kg. TherelativeweightstrengthofTNTcomparedtoANFO(ANFO=100)is115. Henceequation(2.5.1.1)baseduponANFOinsteadofTNTcanbewrittenas (Cunningham, 1987):Xm = A 8 . 00||.|

\|eQVQe 1/6 30 / 19115||.|

\|anfoS(2.5.1.2) where: Qe - the mass of explosive being used, kg; S anfo- the relative weight strength of the explosive to ANFO (ANFO =100) 36Since

K QVe10= (2.5.1.3) where K - the powder factor (specific charge), kg/m3

Equation (2.5.1.2) can be rewritten as Xm = A (K) 0.8 Qe 1/6 30 / 19115||.|

\|anfoS(2.5.1.4) Equation(2.5.1.4)cannowbeusedtocalculatethemeanfragmentation(Xm)fora given powder factor. Solving equation (2.5.1.4) for K:K = 25 . 130 / 196 / 1115

||.|

\|anfoemSQXA(2.5.1.5) Onecancalculatethepowderfactorrequiredtoyieldthedesiredmean fragmentation. Cunningham (1983) indicated that in his experience the lower limit for A even in very weak rock types was A = 4 and the upper limit was A = 12.In an attempt to better quantify the selection of rock factor A, the Blastability Index initially proposed by Lilly (1986) has been adapted for Kuznetsovs model (Cunningham, 1987). Cunningham stated that the evaluation of rock factors for blasting should at least takeintoaccountthedensity,mechanicalstrength,elasticpropertiesandstructure.The equation is given below: 37 A = 0.06 (RMD + JF + RDI + HF)(2.5.1.6) where:RMD: rock mass description - powdery/ friable10 - vertically jointedJF- massive 50JF: vertical joint factor JF = JPS + JPA(2.5.1.7) JPS: vertical joint plane spacing - 0.1 m10 - 0.1 m to MS20-MS to DP50MS: oversize, mDP: drilling pattern size, m JPA: joint plane angle- dip out of face20- strike perpendicular to face30- dip into face40 RDI: rock density influence, tons/m3

RDI = 25 RD 50(2.5.1.8) HF: hardness factor Y: Youngs modulus, GPa If Y < 50GPa, HF = Y/3 38If Y > 50GPa, HF = UCG/5UCG: uniaxial compressive strength, MPa Then the Rosin-Rammler formula is used to predict the fragment size distribution. It hasbeengenerallyrecognizedasgivingareasonabledescriptionoffragmentationin blasted rock. This equationis:

nxxmc e R||.|

\|= (2.5.1.9) where:Rm - the proportion of material retained on the screen;X - the screen size, cm; Xc - the characteristic size (scale factor), cm; n - the index of uniformity, a blasting parameter. The characteristic size (Xc) is that through which 63.9 % of the particles pass. If the characteristicsize(Xc)andtheindexofuniformity(n)areknownthenatypical fragmentation curve can be plotted.Equation(2.5.1.9)canberearrangedtoyieldthefollowingexpressionforthe characteristic size nmcRXX1ln= (2.5.1.10)Since the Kuznetsov formula gives the screen size Xm for which 50% of the material would pass, substituting these values: 39X = Xm R = 0.5 into equation(2.5.1.10) one finds that

nmcXX693 . 0= (2.5.1.11) AusefulindirectcheckontheindexofuniformityhasbeendonebyCunningham (1983). He based his prediction of fragmentation on the Kuznetsov equation and used the relationshipbetweenfragmentationanddrillingpatterntocalculatethisblasting parameter of the Rosin-Rammler formula. The blasting parameters, n, is estimated by: |.|

\||.|

\| ||||.|

\| +|.|

\| =HLBWBSDBn 12114 2 . 25 . 0(2.5.1.12) where: B -burden, m;S -spacing, m; D - borehole diameter, mm; W - standard deviation of drilling accuracy, m; L - total charge length, m; H - bench height, m..Theinterrelationshipbetweenthevariablesinablastandtheresultsofblasting establishedinthisworkareingoodagreementwithexperiments.(Cunningham,1983, 1987). 402.5.2 Hole-by-hole analysis method In bench blasting, the actual drilled pattern is not the exact designed pattern because thedrillingcancausesomeunexpectedfragmentsizes.Thegoalofthehole-by-hole method is to be able to predict the fragment size distribution and effect of faulty drilling when the exact drilling pattern is known. Each borehole is assigned a volume, that it has tofracturefortheactualdrillpatternused.Thefragmentationdistributionofeach blastholeiscalculatedandtheyaresummeduptogivethetotalfragmentsize distribution. This method is used to consider the effect of drilling pattern. Some rules of dividing the volume for each hole have been suggested by Hjelmberg (1983).Hebelievedthatthoserulescouldimprovetheprediction.Thetrianglewas chosen90degreesforsimplicity.However,therealangleofbreakageinthetriangle depends on the distance to the nearest free face and on the distance to the nearest holes, that detonate simultaneously (Bhandari, 1975b).Theliteraturereviewshowedthattheeffectofvariationsindrillingandignition patternscanbeaddedtothepresentformulas.Withtheideaoffindingthevolumeof eachhole,thisvolumeisusedintheKuz-Rammodeltopredictthefragmentsize distribution of each hole. Summing up the total fragment size distribution would take care of the influence of drilling and ignition patterns.

41 Chapter 3 Development of the Proposed Model FRAGM Optimumblastfragmentationisfundamentaltoallphasesofthesurfacemining operation.Changesintheblastdesignmayaffecttheefficiencyandtheproductivityof downstreamprocessessuchasloading,hauling,crushingandmilling,resultingincost savings or losses. The basic steps of blasting engineering are design, implementation and observation of the blast results. From the literature review it was found out that previous researchershavecalculatedthefragmentationandthesizedistributionbyconsidering rock properties, explosive properties, and the influence of actual drilling pattern. Theinfluenceoftrueburdenisveryimportantinrockfragmentation.Thetrue burden is one of the most important parameters for the execution of an efficient blasting. Measuringthetrueburdenhas,untilrecently,beenadifficultandalmostanimpossible operation. One way of doing this was to use a long stick and string hanging over the face ofabenchtoestablishpreciselythelocationofrockfaceinrelationtothefrontlineof blastholes.Thisway,evenaqualifiedsurveyor,usingstandardsurveyingequipment would find it difficult to obtain an accurate profile of the rock face. Asaresultmanyresearchersassumedthattherockvolumeinthefirstrowof blastholes could be calculated by multiplying the burden, spacing and height of a bench, andconsequentlyirregularitiesofabenchfacewerenottakenintoaccount(Fig.3.1). However, in the real life this procedure could produce a good agreement with the results of a blast if all holes in the first row were drilled at an angle equal to the bench face angle (Fig. 3.2). It simply means that the burden will be the same at different parts of a bench such as the toe and the crest. 42

Figure 3.1Diagram of a blasting pattern and the geometry of charged blastholes. 43

Figure 3.2Typical representation of the drillhole inclination versus the bench face anglepresented by Olofsson (1990). 44Generallymanyminingoperatorsprefertouseverticalblastholesintheirsurface mines as inclined drilling has many disadvantages, and some of them are listed below: 1)increased deviation when drilling long blastholes;2)difficulty in positioning of the drills in collaring operations;3)increased drilling length;4)necessity of close supervision which creates work lapses;5)lower drill feed, which means that in hard rock the penetration rate is limited in direct proportion to the angle of inclination of the mast;6)more wear on the beads, drill steel and stabilizers;7)less productivity with rope shovels due to the lower height of the muckpile; 8)poorerflushingofdrillcuttingsduetothefrictionforces,requiringanincreasein airflow;9)problemsin charging an explosive, especially in blasthole with water. As one can see from Figure 3.3 and Figure 3.4, the burden varies and commonly has the larger value in the bottom part of a bench. Due to the nonuniform burden, the actual powderfactor,ingeneral,issmallerthantheonecomputedbytheestimatingtherock volume assuming a vertical bench face.Betterpredictionofrockfragmentationcanbeachievedbyahole-by-holeanalysis for the first line of blastholes. The critical parts in the hole-by-hole analysis are: 1) how toestimatetherockvolumeinthefirstrowofblastholes;and2)howtodividethe volume for each hole. 45 Figure 3.3 Variation of burden in case of vertical hole on an inclined face by Bhandari (1997). 46

Figure 3.4Parts of a bench presented by Hustrulid and Kuchta (1998). 47Toaccuratelyestimatetherockvolumeforthefirstrowofblastholes,theface profilemustbeknownasrealisticallyaspossible.Onewayofdoingthisisbyusinga laserprofiler,whichcanreceiveabeamreflecteddirectlyofftherock(asopposedto usingspeciallydesignedreflectors).Itisevenpossibletolocatethecollarsoftheholes already drilled or to be drilled. Where the blast holes have been already drilled, the true profile for each hole could be obtained. This method produces a better quantitative profile ofthebenchfaceandleadingtothepossibilityofmakingabetterpredictionofrock fragmentation. This method is described in details in Appendix B of this thesis.Thesecondcriticalpartwiththehole-by-holeanalysisisdividingthevolumefor eachhole.Theassigned90degreesangleofbreakageisinadequateandmostoftentoo small for each borehole in the first line in bench blasting. The angle of breakage depends ontherockproperties,burden,spacingandthequantitiesofexplosivechargesapplied (Bhandari, 1975a, 1975b, 1996, 1997). However, calculating the angle of breakage alone is not sufficient to find the bench volume broken by each borehole in the first line. Joints and discontinuities have a tendency to influence the angle of breakage. In this situation,thepredictedangleofbreakagecanbedifferentfromtheactualone.Insome cases,ifthereareanumberofbadlyweatheredjointsinthebench,theactualangleof breakage is determined by the angle between the sets of joint faces. Inordertofindthebenchvolumebrokenbyeachholeonthefirstrow,itis proposedtodividethebenchintodifferentareasofbreakageaccordingtothedifferent mechanisms of rock breakage for each borehole (Fig.3.5). This way, two different areas foreachboreholecouldbeidentifiedandshowninFigure3.5.Theyarethemain breakage area and the secondary breakage area. 48Plan view Case 1: Unbroken rock between two boreholes Case 2: Completely broken rock between two boreholes Figure 3.5Two areas of breakage. 49The main breakage area is due to the reflected stress waves at the free face and the discontinuities,andalsoduetotheredistributionofthepressurethatenlargefractures when the burden is uncoupling from the main rock mass. Rock is weaker in tension than in compression. Hence, when the reflected shock waves pass through the rock, they cause tensile failure around the discontinuities in the rock. Most of the rock breakage occurs in tension.Therefore,thetensilestrengthoftherockisakeyfactorindeterminingthe resistanceofrock.WorseyandRustan(1987)pointedoutthatthecompressivestrength ofrockhasnomajoreffectontheblastingperformanceandthatthetensilestrength, estimated by the Brazilian test, is related to the blasting performance.The detonation wave is a strong shock wave deriving the energy from the chemical reactionoftheexplosivecomposition.Thesewavescausecrushingandcompressionof therockdependingontheexplosionpressureandthestrengthandstiffnessoftherock. Thestresswavesactproportionaltothepressuregeneratedbytheexplosive.Whenthe stress waves hit the discontinuity face or the free face, the stress waves get reflected and becometensile.Thebreakageoccurswhenthestressexceedsthetensilestrengthofthe rock.Ifthemagnitudeofthestresswaveissmall,thereflectedtensilestresswillnot cause any breakage, and the stress will travel as a seismic wave. The main breakage area isdefinedbetweentheblastholesinthistensilebreakingarea.Thentherockstarts uncoupling from the rock mass and is pushed forward by the borehole gas pressure.Thestresswavebehaviorexplainedabovecanbeestimatedbytheempirical equation (A.9) developed by Adushkin (1987) and described in details in Appendix A of thisthesis.Thisequationmaybeusedforcalculatingthelocationofbreakingpoints 50associatedwiththeaboveexplainedprocessofrockfragmentation.Connectingthe breaking points to the borehole will give the angle of the main breakage area.Thebreakageofrockinthesecondarybreakageareaisprimarilyduetothe reflection of stress waves at the discontinuities in the main breakage area. Also due to the intersectionofthestresswavesgeneratedbydifferentboreholes,acompressivestress waveisconvertedtoatensilestresswave.Thenumbersoffracturesinthesecondary breakage area may be the same as they are in the main breakage area. However, the rate ofloadreleaseinthisareaislowerthaninthemainbreakagearea.Asaresult,the fragment size in this area is commonly larger than in the main breakage area. From Figure 3.6 one can see that there are three cases of the main breakage area in relation to the burden and the amount of explosives used: 1) the borehole is too far away from the bench face; 2) the borehole is too close to the bench face; and 3) correct burden and powder factor.If the borehole is too far away from the bench face, the powder factor is too low to completelybreaktherockbetweenthebenchfaceandtheborehole.Thedetonationof the explosive charge will only create a crater around the borehole. When the shock wave hitsthebenchface,itistooweaktocauseanytensionfailureatthebenchface,and, therefore, leaves the bench unbroken. Consequently, the gas pressure will only be able to push the rock upward instead of forward until the borehole pressure is released.If the borehole is too close to the face, the angle of breakage is very large. Since the burden is very small, the borehole pressure can be very easily released and, hence, does not have enough time to enlarge the tension cracks initiated by the shockwaves. A lot of 51Plan view Case 1: Borehole too far away from the bench face Case 2: Borehole too close to the bench face Case 3: Correct burden and powder factor Figure 3.6Three cases in main breakage area. 52explosiveenergymaybewastedinthrowingasmallquantityofrock,andflyrock problem can occur in such situations.If the burden and powder factors are chosen properly, the burden allows much better utilization of stress waves and gas energy, resulting in better fragmentation. In a typical benchblasting,therearetensofholesdetonatedsimultaneously.Inmostcases,an overlap between two adjoining main breakage areas is expected. In such cases, dividing the overlapped area by two and adding it to the remaining main breakage areas seems a reasonable approach. 3.1 Overall breakage The purpose of defining the main breakage area and the secondary breakage area for thefirstrowofboreholesistocalculatetheseareasforeachholeinthefirstrowina quantitativeway.First,themainbreakagepointscanbefoundbyusingequation(A.9). Then,connectingthebreakingpointsoneachsidewiththeboreholelocationgivesthe triangle of the main breakage area. By repeating the same procedure, the main breakage areacanbefoundforeachboreholeinthefirstline.Theseareasshouldbedifferentin different areas of the bench such as the toe and the crest. After the main breakage areas arefoundforallholesinthefirstrow,theaveragefragmentsizecanbecalculatedfor every hole in the first row by using the Kuznetsov equation (2.5.1.2). By summing up the average size for each hole in the first row, the average fragment size and size distribution canbecalculatedforthefirstlineofblastholes.Furthercalculationsoftheblastedrock fragmentationaredoneusingtheKuz-Rammethod,describedinSection2.5.1.The 53example of step by step calculations of the fragment size distribution for a given blast is presented in details in Appendix A of this thesis.Givenbelowisasummaryandthesequenceofstepsfollowedintheproposed FRAGM model to determine the size distribution for a given blast using the bench profile data to estimate the volume of rock to be blasted:1)using the bench profile data to estimate the volume of rock to be blasted; 2)usingstatisticaltoolstheaveragecrestburdenforagivensetofthebench profiles data is determined; 3)theresultsofthestep1andstep2,provideinformationtoestimatetheaverage bench face profile for a given blast; 4)dividetheblastedvolumeintodifferentboundaryareascorrespondingtoeach row of boreholes. The boundary of these areas will be the face of a bench and the axisoftheboreholerows.Forthefirst rowofblastholes,theboundariesofthis areas will be the face of the bench and the axis of the first row of boreholes. For the remaining row of blastholes, the boundaries are between the axis for a given row of blastholes and its previous row; 5)use the blastability index method, initially proposed by Lilly (1986), to calculate rock factor A by using empirical equation (2.5.1.6); 6)calculatetheangleofbreakagebasedontherockproperties,explosive properties, explosive charge and drilling pattern for each hole in the first row. In somecases,ifthereareanumberofbadlyweatheredjointsinthebench,the actualangleofbreakageisdeterminedbytheanglebetweenthesetsofjoint faces.Insuchcasesthepredictedangleofbreakagecanbedifferentfromthe 54actual one and, hence, the geologic structure must be considered before designing ablastandusingtheresultsofobservationforthefragmentationprediction calculations; 7)dividetheblastedvolumeforeachholeinthefirstrowbytheboundary conditions. Calculate those areas (the main and secondary breakage areas); 8)predictthemeanfragmentsizeforeachholeinthefirstrowbyusingequation (2.5.1.2); 9)predicttheaveragefragmentsizeandsizedistributionforthefirstrowof blastholes by using the method described in Section 2.5.1; 10) calculate the average fragment and size distribution for a given blast by using the method described in Section 2.5.1. 55Chapter 4Description of the Rock Fragmentation Prediction Engineering Model FRAGM Properblastingdesignsrequirecarefulconsiderationofmanyvariables.To determinetheeffectofsimpledesignchanges,iterativecalculationsarerequired.To reducethetimeincalculation,anengineeringmodelFRAGM,whichisbasedonthe methodologyandalgorithmproposedinthethirdchapter,isusedtopredictthesize distributionforagivenblast.Thetimerequiredforcalculationsreducesfromseveral hourstoseveralminutesandreliablepredictioncanbeobtained.Withthecapabilityof modern computer to perform tremendous amount of computations in a short period of the time,FRAGMcancalculatetheblastingperformanceinanefficientmanner,which allowsthemineengineertoestimatetheblastingeffectandoptimizeblastinground design. Someofthesevariablesarecontrollable,suchastheexplosivepropertiesandthe drilling pattern. The rock properties and bench geometry are uncontrollable factors for a givenblast.Otheruncontrollableparametersarejoints,fractures,tensilestrength,rock density, P-wave velocity and the true burden. The main task for mine engineer is to find the optimal values of controllable factors to obtain the best fragmentation.The basic steps involved in choosing proper blast parameters that ensure desired rock fragmentationinFRAGMmodelaredepictedinFigure4.1.Thoughsomedegreeof flexibilityispossiblewithregardtohavingasuitablebenchprofilethatprovides optimum fragmentation, often stability consideration limit this possibility. Similarly, once a curtain kind of drilling equipment is chosen, the hole diameter also becomes fixed. 56

Figure 4.1Procedures of blast round design and evaluation of blasting performance. Profiling Bench Face Bench Shape Survey Rock Volume Estimation Borehole Size and Type Selection Explosive Selection Drilling Pattern Blasting Performance Prediction By Using FRAGM Improved Drilling Pattern Design, Charge Design, orExplosive Selection NOAccept Blast RoundDesignYES Satisfied ? 57Hence,thealternativeliesinvaryingtheexplosivetypeordrillingpatterntogetthe desiredrockfragmentation.TheFRAGMmodelprovidesaneasyandreliablewayto examinetheeffectofchangingtheblastparametersonrockfragmentationwithout resolving to expensive and time consuming field trials. Also, it helps the blast designer to examine the degree of fragmentation obtained in a blast on a routine basis. This chapter is a general description of the input and output data ofFRAGM. 4.1 Bench and borehole information To determine the rock fragmentation, the input data of FRAGM consists of bench and borehole information. The bench information contains the bench face profile data and the location of the boreholes. An X-Y-Z relative coordinate system is utilized to reference thebench(Fig.4.2).Theleftuppercorneris(0,0,0)andXvaluesincreasefromleftto right.Yvaluesincreasetowardthebenchface.Zvaluesincreasedownwords.The boreholeinformationcontainsloadingdensity,powderfactor,diameteroftheborehole, diameterofthechargecolumn,lengthofthepowdercolumn,lengthoftheborehole, stemminglength,andX-Ycoordinatesofeachhole.FRAGMusesthesegroupsof information to determine the actual burden, spacing, angle of breakage, and rock volume being broken in a given blast. 4.1.1 BurdenBurdenisthenearestdistancefromablastholetoafreefaceorbetweenrowsof blastholes.Experienceandempiricalequationsobtainedfromfieldtestscanleadtoan appropriate distance for burden. 58

Plan View Figure 4.2X-Y-Z coordinates data of the bench boreholes. 59Burdenisdeterminedbythestrengthofrockinthebench,geometryofthebench and the bench face, and the specific explosive energy applied, which in turn is related to thediameterofacharge,weightstrengthandloadingdensity,andspacing-to-burden ratio.TheobservationbyPreeceetal.,(1991)usingmotionpicturephotographproved that premature gas leakage in small burden occur. Therefore, large burdens with heavier chargeisrecommendedonlyforcastingbecauseitwillreducethepossibilityof prematureleakageofgasesfromtheblastholethroughthefragmentedrockswhile providingsufficientheaveenergytothrowtheoverburdenmaterial.Thepushonthe overburdenmaterialbythegaspressureintheblastholewillbeatitsmosteffective situation.It is necessary to measure the true burden in the first row of boreholes for effective prediction of rock fragmentation. In this model, the bench face profile data are collected andstored.Thenthesurfaceareaofeachprofileiscalculatedandanalyzed.Asaresult onecanestimatetheactualvolumeinthefirstrowofholesandevaluatethepowder factor distribution. It is very important to remember that the uniformity of fragmentation is found with decreasing powder factor (Lownds, 1983). 4.1.2 Spacing Spacing is the distance between adjacent blast holes in the same row. In most cases, evidenceshowthatspacingshouldnotbegreaterthantwotimestheburdeninorderto makeacleanuniformfreefacewhetheritis forconventionalbenchblastingorcasting. Spacing smaller than the burden can be efficient in blasting of very hard rock (Shapurin and Kutuzov, 1990). 60Traditionallyburden,spacing,andbenchheightdeterminetherockvolumebroken by each blasthole. However, in a typical bench this estimation cannot be applied for the first row of blastholes unless the boreholes position are parallel to the bench face. The toe burden,thecrestburden,thespacing,andthebenchheightshouldallbeconsideredto determine the rock volume broken by each borehole in the first line of blastholes. A good and useful model must be able to consider the actual burden and spacing. Especially this is a case in the first row of blastholes. The design values of the first line of blastholes are oftenmisleading.Theonlywaytofindthose values is by examining them hole-by-hole in the actual bench. The hole-by-hole analysis method can measure the effects of burden and spacing, and determine the angle of breakage of rock broken. 4.1.3 Powder factorPowderfactorrepresentstheamountofexplosiveenergyappliedtoeachspecific volume of blasted material. It can be expressed in terms of pounds of explosive used for each cubic yard of material or in kilograms of explosive used for each cubic meter in the bench.Itistheindicatorofconsumptionofexplosiveinashot.Ingeneral,thevalue variesbetween0.9and1.5poundspercubicyard.Aheavierpowderfactornotonly provides a better fragmentation, but also provides energy for throwing, which is truly an advantage to surface coal mining operations. 4.1.4 Loading densityThe explosive density is one of the important properties that should be considered in blast design. The density of most commercial explosives ranges from 0.8 to 1.6 gram per 61cubic centimeter. ANFO and aluminized ANFO are in the low density range 0.8 to 1.15 grampercubiccentimeter.Cartridgeexplosives(slurryordynamite)areinthehigh density range 0.9 to 1.6 gram per cubic centimeter.Loading density is commonly measured by dividing the weight of explosive over the boreholevolume.Loadingdensityaffectstheexplosivequantityintheborehole, detonationvelocity,pressure,andenergy.However,anexplosivessensitivitycanbe reduced or destroyed by an excessive increase in density. If the density becomes too high,exceeding the critical density, the explosive will not detonate. This phenomenon is called. dead pressed.Theloadingdensityisdeterminedbytheloadingequipmentandtheskillsofthe loaders.Sincethesefactorsarefixed,theloadingdensityinthesamebenchshouldnot differ significally from borehole to borehole. 4.1.5 Diameter of blastholesBlastholesaredrilledinthebenchtocontainachargecolumnaswellasthe stemmingmaterial.Whenablastholeiscoupled with the charge column, the effect of a shotisenhanced.Thisisadesirablesituation.Therefore,thelargerthediameterofa blasthole,themoreexplosivecanbeloadedintotheboreholeperlineardistance.The practicalrangeofdiameterisbetween7and14inches.Forcastingdesign,alarge diameter is preferred because a higher powder factor is required. However, the diameter of drillholes is not the only contributor to a high powder factor. Loading density, burden, and spacing may also change the powder factor. 62Theblastdesignerhastorememberthateachexplosivehasitsowndiameter-velocitycurve.Iftheboreholediameteris lessthanthecriticaldiameter,thedetonation processwillnotpropagate.Theeffectofboreholediameterondetonationpropertiesis significant.Mostblastdesignersareawareofthisandavoidusingsmallborehole diameters. The practical range of borehole diameter in surface mining practices is from 5 to 14 inches, which produces a detonation velocity from 4000 to 5000 meters per second forANFO.Thedifferenceofdetonationvelocityandpressurewithinthisrangeisnot significant. 4.1.6 StemmingStemmingdistancereferstothetopoftheblastholenormallyfilledwithinert material to confine the explosive gases. In order for a high explosive charge to function properly and release the maximum energy, the charge must be confined in the borehole. Adequateconfinementisalsonecessarytocontrolairblastandflyrock.Inmostcases,a stemming distance of 0.7 times the burden is adequate to keep the material from ejecting prematurely from the hole. It must be remembered that stemming distance is proportional totheburden.Thereforechargediameter,specificgravityofexplosives,andspecific gravityofrockareallneededtodeterminetheburden,andstemmingdistanceisalsoa functionofthesevariables.Ifdrillingcuttingsareusedasastemmingmaterialthe stemmingdistanceequalsto0.7timestheburdenmaynotbeadequatetokeepthe stemming from blowing out (Konya and Walter, 1985). On the other hand, doubling and tripling the stemming distance may not ensure the holestofunctionproperly.Ifthestemmingdistancesareexcessive,poortopbreakage 63willresultandtheamountofbackbreakwillincrease(KonyaandWalter,1985).The common material used for stemming is drill cuttings, since they are conveniently located at the collar of the blasthole. However, very fine cuttings commonly called drilling dust make a poor stemming material. In case such as this, it is common to bring crushed stone tothejobsitetouseasastemmingmaterial.Ifdrillingdustwereusedinsteadof crushedstoneordrillingchips,itmaybenecessarytoincreasethestemmingdepthto equaltheburdendistance.Drillingdustmakesapoorstemmingmaterialsinceitwill notlockintotheboreholewallsandiseasilyejected.Itwasalsopointedoutthatthe optimumsizeofstemmingmaterialwouldbematerialthathasanaveragediameterof approximately 0.05 times the diameter of the blasthole and the material must be angular to function properly (Konya and Walter,1985). 4.1.7 SubdrillingSubdrillingisthedepththatblastholeswillbedrilledbelowtheproposedgradeto ensure that breakage will occur to the grade line. Blastholes normally do not break to full depth. Most surface mines are using subdrilling. The subdrilling will lead to a result of a flatbottominanexcavation.Ifdrillingisdoneslightlydeeperthanrequiredandsome holes are too deep at the time of loading, the blaster can always place drill cuttings in the bottom of those holes to bring them up to the desired height. The blaster, however, does not have the ability at the time of loading to remove excessive cuttings or materials that has fallen down into the hole. 644.2 Explosive typesTherearebasicallyfourdifferenttypesofcommercialexplosives,i.e.emulsion, Heavy ANFO, ANFO, and ALANFO (Table 4.1). Each explosive has its own detonation velocity,pressure,strengthandenergy.Thesepropertiesvarywithboreholediameter, temperature,loadingdensity,andweatherconditions.Theidealdetonationvelocity varies from 3,750 to 6,000 meters per second, and the detonation pressure from 0.055 to 0.13 Mega bars, for different types of explosives. Comparingthedifferenttypesofexplosivesinfieldconditionsandselectingthe right type of explosive suitable for the specific field conditions are the major tasks of the mineengineersandblasters.FRAGMcanbeusedtopredicttheperformanceof different explosives that can be very helpful in the changing surface mine environments. 4.3 Rock strengthRockstrengthisanimportantfactorinblastingperformance.Rockhasthree differenttypesofthestrength:compressive,tensile,andshearstrength.Rockismuch weakerintensionthanincompression.Whentheshockwavespassthroughrock,they causetensilefailurearoundthediscontinuitiesintherock.Mostoftherockbreakages occurintension.Thetensilestrengthofrockisthekeyfactortodeterminerock resistance to blasting.Compressionfailureonlyoccursaroundtheborehole.WorseyandRustan(1987) stated that the compressive strength of rock has no major effect on blasting performance insurfaceminingoperations.TheyalsopointedoutthattheBraziliantensilestrengthis related to blasting performance. 65 Table 4.1 Explosive strength based on composition Explosive name Water % AN % CN % FO % Al % AN(pp) % Density g/cc Strength Emulsion 15.00 69.509.006.50 0.00 0.001.2078-91 Emulsion 15.00 79.500.005.50 0.00 0.001.2080-94 Emulsion 14.75 75.500.005.25 5.00 0.001.2097-109 Emulsion 13.50 71.500.005.0010.00 0.001.20 112-126 Heavy ANFO 9.00 38.000.006.000.0047.001.3089-108 Heavy ANFO 9.00 38.000.006.000.0047.001.1088-100 Heavy ANFO 9.00 25.50 12.507.000.0046.001.3088-103 Heavy ANFO 9.00 25.50 12.507.000.0046.001.1087-96 Heavy ANFO 12.00 33.00 0.008.000.0047.001.3082-98 Heavy ANFO 12.00 33.00 0.008.000.0047.001.1079-91 ANFO 0.00 94.00 0.006.000.000.000.80100 ANFO 0.00 97.00 0.003.000.000.000.8068-77 ANFO 0.00 92.00 0.008.000.000.000.8092-96 ANFO 0.00 94.00 0.006.000.000.000.90 100-105 ALANFO 0.00 90.00 0.005.005.000.000.90 110-120 ALANFO 0.00 86.00 0.004.0010.000.000.90 118-132 66 Table 4.2 Rock properties published by Mohanty (1987) Rock type Granite Quartz-diorite Griesen Limestone Density (g/cc) 2.58 2.81 2.84 2.78 Longitudinal Wave (m/sec) 5,110 5,000 5,570 5,100 Shear Wave (m/sec) 3,020 3,240 3,610 3,230 Poissons Ratio 0.23 0.14 0.14 0.17 Youngs Modulus (GPa) 58.0 45.2 84.2 67.5 Compressive Strength (MPa) 125 180 215 198 Brazilian Tensile Strength (MPa) 8 15 16 11 Dynamic Tensile Strength(MPa)

32 56 67 51 67 Table 4.3 Rock properties presented by Cook (1976) RockType Marble Limestone Granite Sandstone Shale Density (g/cc) 2.70-2.902.30-2.502.60-2.702.10-2.60 2.70 Longitudinal Wave (km/s) 5.3-6.42.9-5.0 5.63.05------ Poissons Ratio------- 0.24-0.320.20-0.30 ------ 0.26 Youngs Modulus (GPa) 20-100 10-70 50-90 5-4570-100 Compressive Strength (MPa) 60-250 30-250 150-29030-24070-230 Brazilian Tensile Strength (MPa) 2-6 3-8 79------

RockType Greenstone Basalt Taconite Quartzite Density (g/cc) 3.02 3.00 3.23-3.442.17 Longitudinal Wave (km/s) 5.26.6 5.1-5.95.0 Poissons Ratio0.150.33 0.26-0.24 0.28-0.15 Youngs Modulus (GPa) 80 8591-10269 Compressive Strength (MPa) 300 80-360 330-340380 Brazilian Tensile Strength (MPa) ------ 1520-30 18 68 FRAGM uses the Brazilian tensile strength value to predict the blasting performance. The rock property information is usually obtained by laboratory testing. Mohanty (1987) presented the rock properties for four types of rock as shown in Table 4.2. Cook (1976) also presented the rock properties for nine types of rock as listed in Table 4.3. 4.4 Delay timeTheavailabilityofshort-delayinitiatingmakesitpossibletocreatedesiredfiring intervalsamongcharges.Theruleofthumbfordelayofinitiationbetweenrowsis generally one to two milliseconds for every foot of burden in conventional blasting. In case of casting design, the tendency is to increase the delay to provide appropriate room for the subsequent rows of overburden material to move. Delay of five or even ten millisecondsforeachfootofburdenwasreported(Favreau,1983).Providingadequate forwardreliefbetweenrowsofblastholesisveryimportantforcasting.Theprolonged delaybetweenrowsofblastholeswasalsoidentifiedasonefactorthatactuallyreduces ground vibrations in surface mining operations.A delay of initiation between holes in the same row can be arranged by using short-delay initiating devices. However, in bench blasting simultaneous initiation of all holes in arowcanhaveanenhancedeffect.Topreserveheaveenergyofashot,thisisalsoa sound approach. In casting design, the delay of initiation along holes in a row should be maintainedataminimumoratzero.Thestudiesontheeffectofdelaytimeon fragmentationhavebeenconductedbyKonyaandWalter(1985).Intheirexperiments, the best delay time was 2 milliseconds per foot of spacing. They stated that the effect of delaytimeonfragmentationwouldnotdiffersignificallyinthenormalrangeofdelay 69timeinblastingpractice.FRAGMandthepreviousfragmentationmodelsdonot consider the effect of delay time. 4.5. Geological conditionsThe geological conditions of a blasted bench is the most important and complicated factortobeexaminedwhenasurfacemineisbeingplannedandatthebeginningof designingablastround.Thestrengthofrockinthebench,existenceofweakand fractured layers, and dip and strike of the bench are to be considered.An open pit should be developed to accommodate the needs of blasting and material handlingamongconsiderations.Thedistributionofhaulageandaccessroadsisone concerns of mine planning.At the same time, the requirements of successful blasting are subject to the geological conditions of the bench and those requirements must be strictly observed.Inordertoachievethedesiredfragmentation,thestrengthofrocks,the direction of strike and dip, and the location and direction of fractured zones or soft layers such as clay are important factors to be evaluated. Soft strata, such as mud layers, cause more problems than other geological features. They allow an almost instant release of the explosion gas pressure, due to their low shear strength among the layers. The fragments in the mud strata can be thrown a significant distance and cause poor fragmentation. Thejointdirectionandorientationeffectblastingperformance.Theresearchwork byAsh(1973)showedthatabetterfragmentationoccurswhendrillholesareoriented alongthelinesperpendiculartothemostprominentjointfaceoftherockmass.Large fragments result from those lines of drillholes parallel to that joint face. Local geological conditions are often very difficult to assess. The effect of geological conditions vary from 70boreholetoborehole.Duetothecomplexconditionsofgeologicalstructureinmining practice,itisverydifficulttopredicttheprecisegeologicaleffectonblasting performance.Theuseofempiricalformulastopredictgeologiceffectwouldcertainly causesomeerrors,butitmightbesthandlesomegeneralblastingeffectsdueto geologicalstructure.Inthismodelequations2.5.1.7,2.5.1.8,2.5.1.9areusedtopredict the effect of the geological structures on blasting performance. 4.6. Output data description Theaveragefragmentsizeandsizedistributionpredictedforagivenblastare computedbyfollowingthealgorithmintheChapter3.Thebrokenareasforeach blasthole in the first row can be found on the computer screen. These areas are the major concerns for blast designers. For an irregular bench, the broken areas for each blasthole in thefirstrowaredifferent.Therefore,theaveragefragmentsizeforeachblastholeis different. Sometimes, the difference might be very significant for a poor designed drill bench.Themaintaskofblastdesignersistokeepthisdifferencesmallandkeepthe averagefragmentsizeclosetothedesignedvalue.Theaveragefragmentsizeisan importantfactorinsubsequentoperations.Ifthereareoversizedfragmentsthatrequire secondaryblasting,thetimeandmoneywastedinthisoperationcanbeverycostly. FRAGM can be used to predict these areas. The ones with large areas are most likely to produceoversizedfragments.Increasingthepowderfactorintheseblastholeareas,or drillinganewboreholeintotheseareasmightassistincorrectingtheseproblems.The averagefragmentsizeandsizedistributionarepresentedinanExceltabularform.The size distribution curve can be plotted on the computer screen for a given blast. 71Chapter 5Verification of the Proposed Engineering Model 5.1. Introduction Therehasbeenconsiderableresearchconductedinrockfragmentationprediction. However,notallthepublisheddatacanbeusedtoverifytheproposeddevelopment. Mostofthepublisheddatadoesnothaveenoughinputinformationaboutbenchface angle,rockproperties,explosivestypes,and,inthesamecases,drillingpattern.Of course,themissinginputdatacanbesubstitutedbyusingaveragevalues.Butsuch substitutions will cause some prediction errors. Also, there are no published literature that have the complete information including: 1) angle ofbench face; 2) angle of breakage; and 3) size distribution.As a result, new field data have been used to verify the proposed development. The effect of varying blast designs was analyzed with respect to the predicted and actual size distributionsinalimestonesurfacemine.Imageanalysismethodhasbeenusedto determinetheactualsizedistributionbyusingthedigitalcameraandimageprocessing programSplitDesktop.TheSplitDesktopistheresultofovernineyearsof researchanddevelopmentattheUniversityofArizonaandtheJuliusKruttschnitt Mineral Research Center of Brisbane, Queensland, Australia (Higgins et al., 1999). Visualobservationsofmuckpilesimmediatelyfollowingtheblastingarewidely used by mine operators to arrive at an approximation. These observations are qualitative. In conjunction with the subsequent experience in loading and crushing, they may form an important factor in the operators decision in the design ofblasting practice. However, for normaleverydaypurposesimageanalysismethodhasthefollowingadvantagesover 72otherformsofvisualevaluationmethodssuchassievingandbouldercounting:1)itis simple to use; 2) it gives a good approximation of the size distribution for a given blast; 3) measurements in the field are quick and less intrusive in the production process; 4) the imagesobtainedformagoodrecordoftheblast;and5)thecostofequipmentis affordable. 5.2 Image analysis technique and sampling Theuseofimageanalysistechniquesforfragmentationanalysisrequirescareful considerationofthethreestagesintheprocess:sampling,imageacquisitionandimage analysis itself.Sampling concerns the taking of images that represent the blasted material beinganalyzed.Imageacquisitionconcernstakingofimageswhichareofsufficient qualityfortheintendedanalysisprocess.Imageanalysisreferstothemeasurementof sizedistributionoffragmentsidentifiedintheimage.Firsttheimageiscapturedbythe analysis computer and stored as an array of picture points (pixels) of varying brightness. Then image processing may be used to modify it to enable the computer to identify each individualfragment.Theresultsarethenconvertedfromatwo-dimensionaltoathree- dimensional parameter by empirical or stereological techniques.Consideringtheanalysisprocessasawhole,someerrorswillbeintroducedbythe use of two- dimensional images to represent three- dimensional blasted material, but the magnitudeofitcanbeminimizedifeachofthethreestagesiscontrolled.Thethree parametersaffectingthesamplingerrorsaretype,scaleandthenumberofimages.The typeofimagesreferstothelocationandstateofthematerialbeingsampledandisthe 73most important factor in capturing a representative image. Operational constraints dictate what methods can be used. In surface mining operations, photographs can be taken on the muckpilesurface(NieandRustan,1987),atthefaceorofmaterialintherackofhaul trucks ( Maerz et al., 1986; McDermott et al., 1989 ). The specific blasting conditions can dictatewhichoftheseisthemostrepresentative.Considerationshouldalsobegivento thefactthatrandomorsystematicsamplingisarequirementinordertominimizebias (Gy, 1979).Atanygivenscale,imageanalysiscanmeasurefragmentswithinasizerange determinedbytheminimumresolvablesizeandthemaximumvisiblesize.Thesize range is dependent on the image analysis technique. The minimum sizes are comparable but for a large fragments the surface texture may cause automatic methods to detect false edgestoproduceagroupofsmallfragments.Thisoftentermeddisintegrationandits occurrence depends primarily on rock texture and lighting conditions (McDermott et al., 1989). A trade-off has to be found between taking close-up images in which fines can be resolvedandthesamplingerrorintroducedbyanalyzingareducedareaofblasted material. It should also be kept in mind that to achieve an adequate sample size requires the analysis of an increased number of images thus increasing the processing time.Obviously, the greater the number of images, the nearer the result will be to the truth. ThisconceptwaswellpresentedbyNieandRustan(1987).Empiricalestimateshave been made in the past of the minimum sample size necessary to be analyzed in order to achieveagivenaccuracy.However,considerationofsamplingtheoryforparticulate materialsshowsthatthemaximumexpectedfragmentsizedeterminestheproportionof thematerialrequiringtobeanalyzedforagivenaccuracy(Gy,1979).Thesmaller 74fragmentssizefractionsrequirelessmaterialtobesampledforgoodaccuracy.Most published works in image analysis give good accuracy in the small to medium fragment size fractions, even so it is recommended that sample sizes are maximized. 5.3. Constraints Methodsoffragmentationanalysisofferquantitativemeasurementofblast performance and thus opens the door to effective optimization of the blasting process. In surface mining operations, blast optimization is of concern, but regular quality control of the full size distribution of the product is of prime importance.Thealternativestoimageanalysisforfragmentationmeasurementareeither subjectiveortimeconsuming.Blastperformanceiscommonlymeasuredbyvisual estimation after blasting and during loading, which can be subjective. For product quality control,samplingandscreeningeverydayisusuallycarriedoutwhichcannotprovide rapid feedback and can introduce significant sampling errors.Oftenthelargestconstraintinasurfaceminingoperationisthetakingof photographswithoutdisturbingproductionactivities.Thisusuallyleadstophotographic samplingschemesthatislessthanideal.Blastedmaterialcanbesampledeitherbefore digging (the muckpile surface), during digging (at the face), or while in haul trucks. The firsttwomethodscanleadtoerrorsduetosubjectivejudgementofthematerialtobe photographed,sincemorematerialcanbeseenthancanbesampled.Theuseofhaul truck sampling is advantageous as the camera location can be fixed in a position and can beautomated,althoughtheeffectofmaterialsortingduringloadingneedstobetaking 75intoaccount.Anothermajorconstraintistheenvironmentalconditionsaffectingthe quality of images. These conditions, such as poor lighting, shadows and dust, are difficult to control in surface mines and may cause poor quality images. 5.4 Verification of rock blasting engineering model in the field In this section, the field verification ofFRAGMmodelisdescribed.Thefielddata was obtained at a limestone surface mine in West Virginia, U. S. A. Comparison between predictedandactualrockfragmentationwasmadeforfivedifferentblastsfroma geologicallysimilarareaofthequarry.Asalltheinputinformationrequiredforthe model could not be obtained in the field, some of them, such as the explosive properties, were taken from the literature and the other, such as the rock factor A, was obtained from back calculations of fragmented data for the first blast. Once this parameter was adjusted forthefirstblast,thesamevalueswereusedinthepredictioncalculationsoffragment size distribution for the remaining four blasts. a.Case 1: ThefullsizefieldtestwasperformedataminesiteoflimestonequarryinWest Virginia, U. S. A. The following technical data were obtained. The compressive strength of the blasted rock mass had a mean value of 12,100 psi. The density was 2.68 g/cc. The benchheightrangedfrom54.54ftto56.70ft.Boreholediameterwas6.25inches. Columns were filled with a Heavy ANFO type of explosives. The designed burden value was 16 ft. However, the bench profiles data were collected for each hole for the first row of boreholes to find out the exact values of burden. The crest burden varied from 14.81 ft 76to 18.35 ft with a calculated mean value of 16.01 ft. The fragmentation was measured by photographic(imageanalysis)method.TheSplit-Desktopsoftwarewasusedforthe calculation of actual size distribution. A detailed description of this softwares application is shown in the Appendix C of this thesis. Figure 5.1.1The quarry highwall before actual shot (blast # 1). Themissinginputinformationistensilestrengthofrockmass,explosivestrength, energy, detonation velocity, Youngs modulus, and rock factor. The rock factor value had been taken as 6.67, which is reflective of the geological conditions existing at the quarry site.Thepicturesofthequarryhighwallbeforeactualshot(Fig.5.1.1)andmuckpile (Fig.5.1.2) are presented below. The input data are predicted with the average values and adjusted for the borehole size influence. 77 Figure 5.1.2Muckpile immediately after the shot (blast # 1) The following input data were used: Detonation velocity = 4,350 m/sec,Explosive strength = 96,Explosive energy = 3.9 MJ/ m3,Youngs modulus = 8.0 * 106 psi, Rock factor = 6.67,Crest burden = 16.01 ft,Toe burden = 28.59 ft, 78Bench height = 55.79 ft, Stemming = 8 ft,Number of rows = 3,Number of holes in row = 13,Loading density = 1,300 kg/ m3,Powder factor = 1.1 lb/yd3,Rock density = 2.68 g/cc.

Thecomparisonsbetweenthefielddataandthepredicteddatabythenewmodel FRAGM and the traditional Kuz-Ram model are listed in Table 5.1.From the comparison (Fig.5.1.3), the prediction of FRAGM is in good agreement withthefieldobservations.ItcanbeconcludedthattheapplicationofFRAGMto case 1 was successful. 79 Table 5.1Predicted and actual size distribution for the blast # 1 Screen Size, cm Kuz-Ram Method, % FRAGM, % Field data, % 588.6890.3492.34 1072.9376.5778.57 1557.3862.5264.52 2043.6249.5952.59 2532.2338.3940.39 3023.2329.1131.11 3516.3721.6524.98 4011.3115.8420.65 457.6711.4014.32 505.118.0910.54 553.355.668.07 602.163.915.78 651.372.664.07 700.861.802.75 750.531.201.48 950.070.210.34 1000.040.130.06 1200.000.020.00 1240.000.010.00 1300.000.010.00 1400.000.000.00

80

Figure 5.1.3Cumulative Size Distribution Blast # 1. Cumulative Size Distribution01020304050607080901000 25 50 75 100Screen size, cmPercentage of the material retained on the screenKuz-Ram, %FRAGM, %Field data, % 81b.Case 2: ThefullsizefieldtestwasperformedataminesiteoflimestonequarryinWest Virginia, U. S. A. The following technical data were obtained. The compressive strength of the blasted rock mass had a mean value of 12,100 psi. The density was 2.68 g/cc. The benchheightrangedfrom33.18ftto42.68ft.Boreholediameterwas5.0inches. Columns were filled with a Heavy ANFO type of explosives. The designed burden value was 12 ft. However, the bench profiles data were collected for each hole for the first row of boreholes to find out the exact values of burden. The crest burden varied from 12.03 ft to 13.08 ft with a calculated mean value of 12.55 ft. The fragmentation was measured by photographic(imageanalysis)method.TheSplit-Desktopsoftwarewasusedforthe calculationofactualsizedistribution.Theimagesofthequarryhighwallbeforeactual shot (Fig. 5.2.1) and muckpile (Fig. 5.2.2) are presented below. Themissinginputinformationistensilestrengthofrockmass,explosivestrength, energy, detonation velocity, Youngs modulus, and rock factor. The rock factor value had been taken as 6.67, which is reflective of the geological conditions existing at the quarry site.Theinputdataarepredictedwiththeaveragevaluesandadjustedfortheborehole size influence. 82 Figure 5.2.1The quarry highwall before actual shot (blast # 2) 83 Figure 5.2.2Muckpile a few days after the shot (blast # 2) 84 The following input data were used: Detonation velocity = 4,350 m/sec,Explosive strength = 96,Explosive energy = 3.9 MJ/ m3,Youngs modulus = 8.0 * 106 psi, Rock factor = 6.67