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Flyrock A Basis for Determining Personnel Clearance Distance And Quantifying Risk of Damage to Equipment Flyrock can be defined as uncontrolled rock projection during blasting, and implies two important issues – uncontrolled movement and unplanned projection of rock fragments, and the potential for damage or injury. When trying to establish safe clearance distances for personnel and equipment, the definition begs the questions of “What is the normal range of rock movement?”, and “What procedure can be followed to provide a reasonable and consistent estimate of flyrock range?”. It is clear that under normal blasting conditions, there will be rock movement associated with blasting, since it is the specific objective of blasting to both reduce the rock material to manageable size as well as to introduce looseness to the pile of broken rock by displacing the broken fragments. In some operations, the focus is to apply as much energy as possible to achieve extremes of breakage and muckpile looseness. In particular, these operations must be expected to have a greater potential to produce large rock movements, including some degree of uncontrolled movement (flyrock). Normal Rock Displacement In order to estimate normal rock projection distances, it is necessary to first recognise the different sources of flyrock and to account for the different mechanisms of generation. The two sources of flyrock are (a) the free face of the bench, and (b) the drilling surface or individual hole collars. Flyrock emanating from the free face will tend to be concentrated in a zone in front of the blast, with little or no material projected to the side or behind the blast. The distance of projection is controlled by the burden dimension (as a ratio of the blasthole diameter) and the explosive strength. Flyrock emanating from the hole collars has an equal probability of being projected in any direction, with the distance of projection controlled by the depth of burial of the charge (ratio of stem length to blasthole diameter) and the explosive strength. The different zones of flyrock influence are illustrated in Figure 1, where it must be noted that the relative projection distances of material from the free face and the hole collars will depend upon: 1. the presence of a free face; 2. the free face burden dimension and its variability along the length of the hole (or for different front row holes); 3. the stemming length and its variability in individual holes.



Free face projection zone



Free face projection zone



Free face Blasthole



Free face Blasthole



Hole collar projection zone



Free Face Dominant



Hole collar projection zone



Hole Collars Dominant



Figure 1. Flyrock zones around a single blasthole.



All of the authoritative studies on flyrock identify the blasthole collar region as the source of flyrock with the greatest range. Roth (1981) Flyrock Model One estimate of the maximum range of rock displacement from normal blasting comes from the work of Roth1 who applied the Gurney equation used for estimation of military projectile range. 2 2    0.44 VOD   5  d h  L = 0.1  − 200    7.42 × 10     1880    Bmin   



(1)



where L is the projection distance (metres), VOD is the velocity of detonation of the explosive (m/s), dh is the blasthole diameter (metres), and Bmin is the minimum burden (metres). The equation was intended for estimation of projectile range from the free face, but by replacing the minimum burden term, Bmin, with the minimum stemming, Stmin, the equation is also used to estimate the range of material produced around hole collars. Roth’s equation to estimate rock displacement included, as would intuitively be expected, the ratio of the burden (stem height) to hole diameter, as well as a term relating to the borehole pressure (i.e. VOD2). Clearly, as explosive energy increases, or as the burden (stem height) dimension decreases relative to the hole diameter, the expected flyrock projection distance increases. The relationship is illustrated in Figure 2 for typical explosive charges used in Chile. Importantly, the potential for large projection distances increases with: 1. increasing explosive energy (powder factor, explosive density, explosive VOD); 2. decreasing burden/diameter ratio; 3. increasing blasthole diameter; 4. rock hardness (hard brittle rock produces greater burden velocity and greater projection distance). Figure 3 shows how increasing blasthole diameter affects the potential flyrock projection distance. Where blasting is confined by previously blasted material, displacements will obviously be less, and will likely occur predominantly in the vertical direction and appear as vertical swell after the blast. Blasting into previously blasted material, i.e. in the absence of a “free face”, is an obvious and very effective way to eliminate flyrock from bench faces, providing the depth of broken rock is the same as the bench height, and provides an effective buffer for the entire bench height. However, there is no similar way to control or eliminate rock projections from the zone around the blasthole collars, and the authoritative studies on flyrock agree that the blasthole collar is the usual source of dangerous flyrock. Since it is unusual to have a production row burden less than 7 metres with a 270 mm (10⅝ inch) blasthole, or 8 metres for a 350 mm (13¾ inch) blasthole, 200 metres seems to be a reasonable practical maximum projection distance from Figure 3. This distance is likely to be appropriate for equipment clearance, and to avoid rock projected in front of a blast which is fired with a free face with a minimum burden of 7 or 8 metres on each front row hole. The equation proposed by Roth appears to have some limitations. When burdens are small, projection distances become extreme (e.g. in excess of 12 km for 1 m burden and 13¾ inch blast hole diameter). This is a serious limitation, since the specific objective of a flyrock model is to provide estimates of projection distances under various “worst case” conditions such as



1



Roth, J., 1981. A model for the determination of flyrock range as a function of shot conditions United States Department of the Interior, Contract No. JO387242, OFR 77-81.



reduced burden. Furthermore, the equation provides no indication about the size of fragments which achieve the estimated projection distances.



Normal Front Row Displacement 300



Normal Projection Distance (m)



Blendex 950 250



200



ANFO



150



100



50% ANFO/Air



50



0 4



5



6



7



8



9



10



11



12



Front Row Burde n (m)



Figure 2. Normal rock projection in front of a free face (270 mm dia), using the equation of Roth (1981).



Normal Front Row Displacement



Normal Projection Distance (m)



300



Bx 950 (270 mm)



Bx 950 (350 mm)



250



200



ANFO (270 mm)



ANFO (350 mm)



150



100



50



0 4



6



8



10



12



14



16



Front Row Burde n (m)



Figure 3. Normal rock projection as a function of diameter and explosive strength using equation of Roth (1981).



Lundborg (1975) Flyrock v Powder Factor Model Lundborg2 presented the relationship between maximum projection distance and powder factor, as illustrated in Figure 4, based on work conducted by Ladegaard-Pedersen and Persson. This graph shows that flyrock projection distance depends on both blasthole diameter and powder factor, and shows that projection distances increase linearly once powder factor exceeds



2



Lundborg, N, 1975. Keeping the Lid on Flyrock in Open-pit Blasting, Engineering and Mining Journal, May, 1975.



approximately 50 g/t. Below this powder factor, confinement is too great to produce significant projection of material. Max. Projection Distance v Powder Factor 1000



Max. Projection Distance (m)



900



13.750 in



10.625 in



800 700 600 500 400 300 200 100 0 0



50



100



150



200



250



300



350



400



Powder Factor (g/t)



Figure 4. Maximum projection distance as a function of powder factor (after Lundborg, 1977).



The equation to predict flyrock range from powder factor as presented by Lundborg is:



Lmax = 0



for PF < 40 g/t



Lmax = 0.358 PF − 24 Dh



for PF > 40 g/t



where PF is the powder factor (g/t), Lmax is the



maximum flyrock projection distance (metres), and Dh is the blasthole diameter. The research conducted to derive the powder-factor v flyrock graph (Figure 4) considered single blastholes drilled in granite boulders. The relationship seems difficult to apply to normal multi-hole, multi-row bench blasting operations, since in those cases average powder factor is not an adequate description of the state of confinement or burial of individual explosive charges. A high powder factor could be achieved, in a multi-row blast, while still having good control over front row burden and stemming. Similarly, a poorly confined charge in a multi-row blast with a low average powder factor may still represent a major risk as regards flyrock potential. A better model will permit evaluation of how maximum projection range varies as specific changes are made to limit flyrock projection distance, such as increased stemming and increased front row burden. Lundborg (1974) Flyrock Model Another estimate of flyrock projection distance from free face blasting comes from Lundborg3. Lundborg’s model to estimate maximum flyrock range has a sound theoretical basis and takes into account both the initial velocity of projection of the rock fragments, and air resistance, and is able to estimate both the range of flyrock, and the size of particle able to achieve various ranges of projection. The model appears to provide a much more realistic estimate of maximum throw distance, as well as having the advantage of estimating the size of particles likely to be projected various distances, and the ability to allow for variable explosive density and the effect of air deck charges. Lundborg’s model to estimate the initial particle velocity, using theoretical analysis and experimental observations, is presented as:



3



Lundborg, N., 1974. The Hazard of flyrock in rock blasting, Swedish Detonic Research Foundation, Sweden.



d  2600   where V0 is the initial velocity (m/s) of a particle of size xf (metres), dh is V0 = 10 h  x f  ρr  the blasthole diameter (inches), and ρr is the rock density (kg/m3). The equation as presented was stated by Lundborg to represent the case for projection of fragments from crater blasts, in which approximately spherical charges were located in shallow blastholes in either solid boulders of granite, or in the ground. This type of charge is known to produce high velocity rock fragments, and probably represents the “worst case” for flyrock generation, likely to occur when charges are inadequately confined either by inadequate stemming, or inadequate burden. Flyrock generation from cratering is illustrated in Figure 5 below. The ability of the explosive to eject the conical plug of rock material around the hole collar depends on the depth of burial of the charge, the dimensions of the charge, the energy of the charge, and the strength and fracture properties of the rock. As the charge is buried deeper, the momentum imparted to the wedge decreases, and the velocity of movement of the fragments also decreases. Ejected wedge (flyrock)



Depth of burial Explosive Figure 5. Source of collar flyrock in rock blasting.



This equation presented by Lundborg predicts the initial velocity as a function of hole diameter and particle size, and is normalised for particles of density 2.6 g/cc. The constant changes according to rock type, with the displayed value (10) representing the case for hard and brittle rock such as granite, commonly found in Sweden where the original experimental work was conducted. For a particular blasthole diameter and rock density, the product of velocity and particle size is constant, according to the equation proposed above by Lundborg based on the impulse density of spherical and cylindrical charges and momentum imparted to loose rock fragments surrounding the charge. Although Lundborg did not present the equations for calculating flyrock projection distance as a function of particle size, it is clear from analysis of his results that his model included the effects of air resistance, since smaller particles displayed a much shorter range than larger particles. Flyrock projection equations were presented by Chernigovskii4, showing that, for a given initial particle velocity, the maximum projection distance can be calculated using the equations below.



z=



z



1 ln (1 + bd v0t ) bd



y



2t b g



1 e d +1 y = ln t b g bd 2e d



1.3 bd = xf ρ



θ



Particle trajectory



L( t ) = z cos θ 4



A.A. Chernigovskii, 1985. Application of directional blasting in mining and civil engineering.



where L(t) is the horizontal displacement at some instant in time, t (sec), after propulsion of the particle, z is the distance (metres) measured along the initial line of projection of the particle at an angle θ to the horizontal, y is the vertical displacement (metres) from the original line of projection (i.e. below the inclined z axis), xf is the size of the rock fragment (sieve size, measured in metres), g is the acceleration due to gravity (9.81 m/s2), and ρ is the rock density (kg/m3). The equation accounts for air resistance as a function of particle size, and allows calculation of the particle trajectory over its full flight path, including final elevations either above or below the initial elevation. To find the maximum projection distance, the above equations must be solved for: 1.



time of flight to a specified final elevation for each particle size and each angle of projection;



2.



initial angle of projection to maximise the horizontal displacement for each particle size.



The above equations have been solved using Newton’s Method to determine both the time of flight and the angle of projection which maximise the horizontal displacement, for each particle size. The angle of projection to achieve maximum displacement is always less than 45 degrees, due to the influence of air resistance, and generally varies between 10 and almost 45 degrees. The above equations reproduce the curves presented by Lundborg (although the value of the velocity coefficient was found to be 10.92 rather than 10), and are therefore assumed to be the ones used in his studies. From these curves, Lundborg’s equation to predict maximum throw 2/3 as a function of hole diameter is readily obtained: Lmax = 260 (Dh ) where Dh is the hole diameter in inches. For the case of “normal” bench blasting operations, Lundborg states that the ejected fragments display exactly the same behaviour as the particles ejected in crater tests, but with lower velocities, and he further states that projection distances are typically around one sixth of those observed from crater tests. To simulate this behaviour, the constant in Lundborg’s velocity equation was reduced from 10.92 to 0.659, which decreases the maximum range to approximately 1/6 of that which occurs in crater blasting, as per Lundborg’s observations and comments. The maximum throw equation for bench blasting therefore becomes: Lmax = 40 (Dh )2 / 3 where Dh is the hole diameter in inches. According to the above modelling using Lundborg’s and Chernigovskii’s equations, the maximum projection distances from 270 mm and 350 mm blastholes in “normal” bench blasting are in the range of 200 to 250 metres. These values are in reasonable agreement with the estimations made by Roth (1981). Lundborg’s analysis also reveals that the size of the rock which can be projected this distance is approximately 0.1 metres (i.e. diameter of equivalent sphere), corresponding to a weight of approximately 1.2 kg. His model also allows estimation of the maximum range for any size of particle (for example, a particle of size 1 metre can be projected only 10 metres), as illustrated in Figure 4 below. Using Lundborg’s crater results as “worst case” conditions, maximum projection distances from 270 mm and 350 mm blastholes increase to the range 1200 to 1500 metres, and the size of rock that can be projected this distance increases to around 0.5 metres, corresponding to a weight of approximately 150 kg. Under “normal” bench blasting conditions, the maximum projection distance is reduced to approximately 200 metres, and the size of fragment which will travel this distance is approximately 0.1 metres, or 1.2 kg.



Max. Horiz. Range (m)



10000



1000



Crater Blasting



Bench Blasting 100



10 1 mm



10 mm



100 mm



1000 mm



10000 mm



Particle Size (mm)



Figure 6. Flyrock projection curves for crater and bench blasting (after Lundborg).



Scaled Depth of Burial Lundborg was not explicit about the experimental conditions which produced the maximum flyrock projections which he presented, other than to describe the tests as “crater blasting”. However, he did suggest that when the stemming length for bench blasting was equal to approximately 40 times the hole diameter, flyrock was effectively eliminated, and when it was around 20 to 30 times the hole diameter, flyrock was “controlled”. These observations are also consistent with observations and normal practices in Chilean copper mines using large blasthole diameters. An assumption is therefore made as regards the depth of burial of the charges used in his experiments, and a linear relationship is assumed between the Scaled Depth of Burial and the Velocity Coefficient, Kv, in Lundborg’s velocity equation: V0 = K v



dh xf



 2600    .  ρr 



100 -3.3164



Velocity Coefficient, Kv



y = 41.927x 2



R =1 10



1



0.1 1



10 Sca le d De pth of Buria l (ft/lb^1/3)



Figure 7. Assumed correlation between fragment velocity coefficient and Scaled Depth of Burial (US units).



It is important to note that Lundborg’s equations do not account directly for explosive strength or explosive density, and indicate that flyrock distance is dependent only on hole diameter and particle size. Lundborg was not specific about the explosives used in his experiments. Intuitively however, one must anticipate that the projection distance of flyrock will depend on explosive strength, if other conditions such as depth of burial are kept constant. By relating the velocity coefficient, Kv, to a Scaled Depth of Burial, which is dependent on explosive density, Lundborg’s equations become sensitive to explosive strength. Since Lundborg’s tests



were conducted in hard rock (e.g. granite), the estimated projection distances are likely to represent maximum, or conservative, values. Weaker and softer rock material will not be projected as far as hard and brittle material. The cratering effect of buried charges, and the velocity of particles ejected, depend on their depth of burial, the diameter of the hole in which the charge is buried, and the weight and strength of charge. In normal bench blasting, in which a long column of explosive is buried, only a part of the explosive near the top of the column contributes to cratering. Hence, a 10 metre charge and a 20 metre charge located in vertical holes of the same diameter will produce the same cratering effect if the top of each charge is located at the same depth below the surface. The Scaled Depth of Burial considers a maximum of 10 times the hole diameter as contributing to cratering, and therefore contributing to flyrock projection. Chiappetta5 presented the following diagram illustrating the effect of varying Scaled Depth of Burial on flyrock.



Figure 8. Scaled depth of burial (SD) and flyrock generation according to Chiappetta (1983). Note that Scaled Depth of Burial (SD) utilises US units in this diagram.



It has therefore been assumed that Lundborg’s tests which produced the maximum flyrock range corresponded to a Scaled Depth of Burial of 1.5 (US units) in Chiappetta’s tests (0.6 in metric units). This depth of burial is known to produce extreme flyrock. The Scaled Depth of Burial, SDB, can be calculated using the following equation (metric units):



SDB =



St + 0.0005 m Dh 0.007323 3 mDh3 ρe



where St is the length of stemming (metres), Dh is the blasthole



diameter (mm), ρe is the explosive density, and m is defined as below. If charge length < 10 * Hole dia, m = Charge length / hole dia 5



Chiappetta, R., Bauer, A., Dailey, P. and Burchell, S., 1983. The Use of High-Speed Motion Picture Photography in Blast Evaluation and Design, Proceedings of the Ninth Annual Conference on Explosives and Blasting Technique. Dallas, TX. International Society of Explosives Engineers, pp 258-309.



If dia > 4”, m = 10 If dia < 4”, m = 8 For large diameter blastholes and normal charges of length greater than 10 times the hole diameter, the Scaled Depth of Burial is therefore equal to the stemming length plus 5 times the diameter of the hole (the charge contributing to the cratering effect is considered to be only 10 times the hole diameter). Similarly, a Scaled Depth of Burial of 6 (Figure 4) has been assumed to represent the point at which flyrock is effectively eliminated, and a Scaled Depth of Burial of 3.5 (Figure 4) has been assumed to correspond to what Lundborg referred to as “normal bench blasting”. Using these assumptions, blasting with a stemming length corresponding to a Scaled Depth of Burial of 1.5 (e.g. 1.8 metres for 10⅝” diameter hole and 1.0 g/cc explosive density) will produce Lundborg’s worst case “crater blasting” flyrock projection. Blasting with a stemming length corresponding to a Scaled Depth of Burial of 3.5 (e.g. 6.1 metres for 10⅝” diameter hole and 1.0 g/cc explosive density) will produce Lundborg’s “normal bench blasting” flyrock projections. Blasting with a stemming length corresponding to a Scaled Depth of Burial of 6 (e.g. 11.5 metres for 10⅝” diameter hole and 1.0 g/cc explosive density) will effectively produce zero flyrock. This model of Lundborg’s seems best suited to the task of understanding flyrock, controlling it, and attempting to quantify the Risk of Flyrock, which is important when considering safety of both personnel and mining equipment. Personnel Clearance Distance Lundborg states that people must never be exposed to flyrock. National laws in Chile relating to workplace safety also require that workers never be exposed to flyrock. This requires that the probability of flyrock be zero for personnel located outside the Personnel Clearance Distance for all blasts. The clearance distance for personnel is quite easily determined from the equations of Lundborg and Chernigovskii. This distance should not be less than the calculated maximum projection range. Further, it would be prudent to add a safety factor to the calculated distance. For the purposes of calculating safety of personnel, any rock projected beyond the Personnel Clearance Radius must be considered capable of causing injury or death, irrespective of the direction in which it travels from the blasthole. The probability of projection beyond the Personnel Clearance Radius then becomes equal to the probability that the Scaled Depth of Burial is less than some critical depth. If the process of charging and stemming blastholes is considered stochastic, and that the stemming length can be accurately described by a Normal Distribution, then the probability that a hole with a nominal stemming length of Ln will have a stemming length shorter than some critical length Lc, can be calculated from the mean and standard deviation of the stemming lengths. In Excel, this is calculated using the formula NORMDIST(Lc,Ln,σ,TRUE), where σ is the standard deviation of the actual stemming lengths, in metres. For example, if a design specifies a stemming length of 7 metres (i.e. average stemming length = 7 metres), and the standard deviation of the actual stemming lengths is 1 metre, the probability that a hole will have a stemming length shorter than 4 metres is obtained in Excel from the formula NORMDIST(4,7,1,TRUE) = 0.135%. If the blast contains 100 blastholes, the probability that at least one hole in the pattern has a stemming length shorter than 4 metres is 1-(1-0.00135)100 = 12.6%, i.e. on 12% of occasions when blasting with 100 holes, flyrock will be projected beyond the clearance zone. Clearly, this level of risk is too high for personnel, and the calculation procedure highlights that if a continuous distribution function is used to describe the variability in stemming length, the probability of flyrock extending beyond the clearance zone will become unacceptably high once the total number of blastholes being fired is taken into consideration.



An alternative method of calculation is to specify a minimum acceptable stemming length. This effectively truncates the distribution curve describing stemming length variability. If any hole is charged so that its stemming length is less than some minimum acceptable length, then action must be taken such as increasing clearance radius, removing explosive from the hole, or some other means to avoid flyrock projections. The minimum stemming length for any charge configuration is that length of stemming for which the Scaled Depth of Burial produces a projection curve (Figure 9) with a maximum projection distance equal to the clearance distance, multiplied by a safety factor, Fs > 1.2. In Figure 9, if the stemming length which produces a maximum projection distance of 300 metres is 4 metres, then the minimum stemming length should be at least 4.8 metres.



Max. Horiz. Range (m)



1000



Clearance 100 Max Flyrock



10 1 mm



10 mm



100 mm



1000 mm



10000 mm



Particle Size (mm) Figure 9. Maximum projection distance equal to clearance distance. Minimum personnel clearance should be at least 1.25 times the maximum projection distance for any hole.



If a hole has a stemming length less than the minimum length as calculated above, the clearance radius should be increased to the maximum projection distance for the particular charge configuration, multiplied by a safety factor of at least 1.25. Hence, if the smallest actual stemming length is 4 metres, and the minimum stemming length was calculated to be 4.8 metres, the above model predicts a maximum projection distance of 400 metres. The clearance distance should be increased to at least 500 metres. The Factor of Safety for the Personnel Clearance Distance should be at least 1.25, i.e. the ratio of the clearance distance to the maximum estimated projection distance (for the hole with the shortest stemming length) should be at least equal to 1.25 (Figure 10). Personnel involved in charging blastholes must be aware that the stemming length is the factor having the greatest single impact on the safety of personnel and equipment when blasting. For each type of explosive, hole diameter and rock type, there is a critical length of stemming which must be achieved in every blasthole in order that people can work in complete safety anywhere outside the clearance zone. To avoid injury and death, stemming lengths must never be allowed to be less than the critical length. Where stemming length in any hole is less than the critical length, for any reason, action must be taken to ensure that the safety of personnel is not compromised. Appropriate actions include: • increasing the clearance radius, with a minimum factor of safety of 1.25 applied to the maximum projection distance for the hole with the minimum stemming length; • removing explosive to comply with the minimum stemming length;



•



flushing the hole with water to desensitise the upper section of the charge column (when using ANFO).



Max. Horiz. Range (m)



1000



Clearance 100 Max Flyrock



10 1 mm



10 mm



100 mm



1000 mm



10000 mm



Particle Size (mm) Figure 10. Personnel clearance distance equal to at least 1.25 times the maximum estimated projection distance.



Equipment Clearance Distance When assessing reasonable clearance distances for bench blasting throughout Chile, it is assumed that equipment will not be left directly in front of a free face. It is also assumed that free face blasting will not usually be practised, and that the primary risk of flyrock is from the blasthole collars. Although both Roth and Lundborg estimate 200 to 250 metres as a reasonable clearance distance for equipment to avoid flyrock projected from the free face, under “normal” bench blasting conditions and with a blasthole diameter in the interval 10⅝” to 12¼”, it is considered prudent to consider the risks associated with a reduced stemming length, possibly caused by over-charging or bridging of the stemming column, or associated with a variable rock character from hole to hole. It is not uncommon, for example, to find a stemming column which is 1 or 2 metres shorter than the design or nominal stemming length. Variability in depth of burial and in rock properties must be expected to increase the risk of flyrock generation. The converse should also hold true, that as the degree of quality control over stemming length and stemming quality increases, the risk of flyrock should decrease. Clearly, the risk is highest when blasting in hard and blocky rock masses where short stemming columns are required in order to achieve fine fragmentation and high productivity from the shovels and other excavators. In these cases, even a high level of quality control over stemming lengths will not prevent an increased flyrock projection range relative to a softer rock with longer stemming columns. According to the models outlined above, the probability of flyrock is related directly to the probability of a short stemming column, i.e. to the probability of a low value of the Scaled Depth of Burial. The risk of flyrock therefore is related to the likely projection distance of rock fragments compared to the equipment clearance distance around blasts. If the clearance distance exceeds the maximum flyrock projection distance, there is no risk that the equipment will be damaged. If the clearance distance is less than the maximum flyrock projection distance, the risk of flyrock is related to the probability that rock fragments of appropriate size will be ejected at the appropriate angle in the appropriate direction. It is normal practice to



accept some degree of risk as regards equipment damage, since the clearance distances to eliminate the risk are usually too large and the loss of productivity associated with moving large equipment is too high. The situation where the clearance distance is less than the maximum projection distance is illustrated in Figure 11 below.



Max. Horiz. Range (m)



1000



Clearance 100 Max Flyrock



10 1 mm



10 mm



100 mm



1000 mm



10000 mm



Particle Siz e (mm) Figure 11. Equipment clearance distance less than maximum flyrock projection.



The flyrock curve, specific to a particular stemming height and depth of burial, indicates that flyrock could be projected beyond the clearance radius, and equipment could be hit by fragments in the size range 50 to 300 mm (Figure 11). It is likely that fragments larger than 0.1 metres will cause damage to equipment if struck. Each particle of a size between the lower and upper intersections of the red line with the projection curve will have 2 possible trajectories, i.e. two possible angles of ejection which will permit the particle to land at a particular location. One of these trajectories will be steeper than the trajectory which produces the maximum projection range, and the other will be more shallow. However, such fragments must be projected at the correct angle of trajectory in order to exceed the clearance radius. The probability of flyrock beyond the clearance zone therefore becomes the product of (a) the probability that fragments greater than 0.1 metres will be generated in the zone around the hole collar, and (b) the probability that these fragments will be projected at an angle which will cause them to travel beyond the clearance area. It is probably prudent to assume that the probability that fragments of size 0.1 metres or greater will be projected is 100%. It is possible to take the estimates further to determine the probability that a particular piece of equipment will be hit by a particle sufficiently large to cause damage. However, to do this, an assumption must be made regarding the number of eligible fragments ejected at each blasthole. This will clearly depend on the depth of burial of the charge, and is likely to be little more than a guess. Risk of Damage to Equipment Analysis of Risk requires a definition of damage as well as a quantitative measure of how the probability of damage changes as the clearance distance changes. To evaluate the probability that a sufficiently large rock will hit and damage a piece of equipment requires assumptions to be made which are difficult to justify, and difficult to relate to different operating conditions.



An alternative method for quantitatively assessing risk, which is sensitive to the major blast design parameters, is therefore proposed. The method is sensitive to the size of rock fragment capable of causing damage, to the clearance distance, to the variability in stemming lengths, and to the type of explosive being used. The method utilises the projection curves derived from the Lundborg and Chernigovskii equations. 1000



Min size for damage, xmin A1



Max. Horiz. Range (m)



A0



Clearance distance



Dist for Pr (hit) = 100%, Dmin



100



10 1 mm



10 mm



100 mm



1000 mm



10000 mm



Particle Size (mm) Figure 12. Quantifying Risk to equipment.



The minimum size of rock fragment expected to cause damage is taken as xmin, and the maximum distance at which the probability of being hit by flyrock of any size equals 100% is taken to be Dmin (Figure 12). The area bounded by the projection curve and the Dmin line is then defined as A0. The zone bounded by the projection curve, the xmin line, and the Clearance Distance line is defined as A1 (Figure 12). The Risk of Damage can then be defined as the ratio of the areas A1 to A0. As the clearance distance decreases, the Risk approaches 100%, and when the clearance distance exceeds the maximum projection distance, the Risk is zero. As the size of particle capable of causing damage decreases (equipment sensitivity), the risk increases. Past experience can indicate what the current level of Risk of Damage is, for any current clearance distance. Changes in the level of risk due to reductions or increases in clearance distance can then be evaluated.