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

A new principal formula for the determination of explosive strength in combination with the rock mass strength P.A. Rustan CENTEK, Luleå, Sweden

ABSTRACT: The goal has been to develop a simple international acceptable technical formula that can be standardized by explosive manufacturers and consumers and to be used for the determination of explosive strength regarding its fragmentation capability. A literature review showed that the first well accepted technical formula used to determine the strength of an explosive was developed by the Swede Ulf Langefors in the 1940’s and that this formula could be regarded as a paradigm shift at the time when it was developed. The formula includes two explosive properties; heat of explosion and the gas volume produced per kg of explosive. The formula was mainly developed for dynamite explosives. The formula can, however, not be used for ANFO and emulsion explosives. Therefore, in this paper it is proposed a new formula for international standardization including, besides the two mentioned parameters, also the detonation velocity, density of explosive, density of rock and P-wave velocity in rock. Also rock structure, confinement and initiation pattern and delay times affect the fragmentation considerably. Consumers of explosives and manufacturers will benefit from this kind of development. An analysis of the variation range of the individual parameters in the new developed formula is shown in the paper. For the validation of the developed formula the SHB-method (SHB = single hole blasting method) is recommended to be used, because laboratory—or half scale fragmentation test cannot give the full answer of explosive strength. 1

2

INTRODUCTION

In the 1940’s Langefors developed an empirical formula for the determination of explosive “weight strength” based on the energy (heat of explosion) developed upon detonation of the explosive and the gas volume produced measured at standard temperature and pressure (STP). The formula will be shown further on in the paper. In the Swedish Technical Journal submitted by Dyno Nobel “Sprängnytt April 2006” in which Granlund (2006) showed by an example from the Boliden Aitik mine, comparing a slurry explosive Reolit with an emulsion explosive Titan. Inspite Titan has a lower weight strength and about 50% lower heat of explosion but about 50% higher gas volume per kg of explosive the same drilling and blasting plan could be used. The amount of explosive could also be reduced because Titan had a lower density. Granlund also stated that laboratory tests are not enough to determine the strength of an explosive. This paper will explain why this is not possible and suggest more parameters that have to be introduced for the calculation of explosive strength to make a better estimation of its real strength regarding the fragmentation ability when blasting in rock types with different acoustic impedances.

2.1

LITERATURE STUDY Langefors weight strength formula

The old formula for the determination of the strength of nitroglycerin explosives was given the name “weight strength formula” and the symbol “s” was used. The formula was derived by Ulf Langefors in the 1940’s, however, the result was never published by Langefors, but the formula was later on published by Persson et al. (1994). The formula reads as follows: s=

5 Qe 1 Ve + 6 Qref 6 Vref

(1)

where s is the relative weight strength of the explosive in comparison with a reference explosive, at that time often LFB dynamite was used in Sweden. Qe is heat of explosion for the explosive in MJ/kg, Qref is the heat of explosion for the reference explosive. Ve is the produced gas volume at STP (standard temperature and pressure) in m3/kg for the explosive and Vref is the produced gas volume at STP for the reference explosive. Very interesting would be to know how the weighting factors 5/6 and 1/6 were derived. The heat of explosion was

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given much more weight than the gas volume. May be that a change of the weighting factors could improve the accuracy of the formula. My intuitive guess, after Granlund has given the examples with Reolit and Titan in Aitik, is that that the weighting factors should be changed to 1/2 for each. For the calculation of the strength of explosives this empirical formula was of large importance when it was developed. Several researchers, inclusive Granlund, have verified that this formula can not be used for slurry, ANFO and emulsion explosives because the fragmentation capacity for these explosives is much higher than what can be calculated by the weight strength formula. The energy of the explosive delivered into the rock mass is also affected by other parameters like blasthole diameter, confinement of the blasthole, water content in surrounding rock mass, density of explosive after packing into the blasthole etc. Blasthole diameters in the 1940’s in Sweden were normally less than 52 mm compared with today’s international blasthole diameters up to 500 mm. Granlund is discussing in his paper three interesting parameters; heat of explosion, gas volume and detonation velocity. 2.2

Empirical formulas for calculation of fragmentation

Traversing a large number of literature references and formulas used for fragmentation calculations I found the following parameters being used in these formulas with the most common mentioned first. − Specific charge q (powder factor) (kg/m3 or kg/t). − Weight of equivalent amount of TNT corresponding to the amount of explosive being used in the blasthole, e.g. Kuz-Ram formula (Cunningham 1983). − Weight strength is mainly used in Langefors equation for determination of burden and spacing. Later on SveDeFo developed a formula for calculation of fragmentation where weight strength was included. It was an expansion of the Langefors formula for calculation of burden. − Heat of explosion Q, e.g. Bergman (1974). − Detonation velocity of the explosive, e.g. Bergman (1974). − P-wave velocity in the rock mass, e.g. Bergman (1974) and Rustan & Vutukury (1983). Many more references to P-wave velocity are given in Rustan (1998), under the entry “acoustic impedance”. − Decoupling ratio, e.g. Bergman (1974). The most common used parameter is the specific charge, defined as the mass of explosive per cubic meter of rock or ton of rock. The use of different

strengths of explosives is normally not included at all in the calculations. We are therefore normally working on a very rough level in the calculation of fragmentation. The conclusion is that the weight strength has not been used on an international level for calculation of fragmentation. It is only the detonation velocity that we can find being used in a fragmentation formula developed from half scale fragmentation tests in different rock types by Bergman et al. (1974). Important parameters lacking, not mentioned in the Granlund’s paper, are the density of the explosive ρe, the density of the rock mass ρr and the sound wave velocity in the rock mass cp. These parameters are needed to calculate the energy transformation from explosive to the rock mass according to the acoustic impedance ratio ZR of two adjacent contacting materials. For the contact acoustic impedance of rock and explosive one obtains; ZR =

ρecd ρrcP

(2)

where ZR is the acoustic impedance ratio (dimensionless), ρe is the density of the explosive in kg/m3, cd is the detonation velocity of the explosive in (m/s), ρr is the density of the rock mass in kg/m3, and finally cP is the longitudinal wave velocity in the rock mass in (m/s). ZR should be equal to 1 for maximum energy transfer from the explosive to the rock mass according to classical wave transmission theory. Atchison & Pugliese (1964) at USBM (United States Bureau of Mines) have shown that the theory is applicable also for energy transmission from the reacted explosive to the surrounding rock mass. Some smaller deviation from this rule was later on shown by Leinz & Thum (1970). This will be shown further on in this paper. From this we can learn that to quantify explosive strength regarding fragmentation, it is needed at least four explosive properties (heat of explosion, gas volume per kg, density of explosive and detonation velocity) and two rock mass properties (rock density and P-wave velocity in the rock mass). 2.3

Heat of explosion in the “Langefors weight strength formula”

The heat of explosion used in the Langefors formula (Equation 1) must be followed by information on how fast the energy is released, because if the energy is released extremely slow no fragmentation will occur at all. An important parameter lacking in the old Langefors formula (Equation 1) is therefore energy released per time unit or indi-

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rectly detonation velocity. The detonation velocity (m/s) is a unit for energy release per time because 1 m of explosive detonated corresponds to a defined quantity of explosive but because the detonation velocity depends on the blasthole diameter it is not easy to calculate the explosive strength if the diameter of the blasthole is not known. Also the confinement of the blasthole, the water content in the rock mass will affect the detonation velocity. From full-scale field studies we know that the detonation velocity normally varies from one blasthole to another in spite that the blastholes are located in the same surrounding environment. The conclusion from this is that the detonation velocity is of outmost importance for the strength of an explosive and can therefore not be neglected in an explosive strength formula. An important task for the explosive manufacturers has been, since 1950’s, to be able to calculate the detonation velocity unconfined and confined (metal tubes) at different blasthole diameters with the help of computer codes. Let us now look on how the detonation velocity influences the detonation- and borehole pressure because this determines the dynamic and quasistatic pressure on the rock mass and thereby the fragmentation degree. 2.4

Detonation pressure

According to Atchison & Pugliese (1964), at USBM, the detonation pressure is the most important factor for the calculation of the maximum amplitude of the vibrations in the vicinity of the explosive in the surrounding rock mass. This zone is also called the shock zone. The amplitude of the ground vibrations at larger distances from the blasthole are mainly determined by the total amount of charge in the blasthole. When several holes are used with delays between the blastholes, that hole that have the largest amount of explosive will determine the maximum amplitude of the ground vibrations. The detonation pressure pd (MPa) is the pressure that acts in the reaction zone of the explosive and this zone is called the Chapman-Jouget plane. The detonation pressure in this zone can approximately be determined by the following formula, pd ≈

1 ρecd210 −6 2

(3)

where ρe is the density of the explosive in kg/m3 and cd is the detonation velocity of the explosive in m/s. The knowledge of the explosive density and detonation velocity is therefore necessary in a strength formula for explosives. Both these parameters are

lacking in the Langefors weight strength formula (Equation 1). If an explosive is packed to a too high density or is initiated wrongly the explosive can be dead pressed (too high density is achieved) and detonation will not occur or the energy for initiation is not enough. It is therefore the environmental conditions in the field that determines how much of the energy content of the explosive can be used for fragmentation. 2.5

Borehole pressure

The borehole pressure pb (MPa) is about 4 times smaller than the detonation pressure and is calculated according to a similar formula as detonation pressure. 1 pb ≈ ρecd210 −6 8

(4)

where ρe is the explosive density in kg/m3 and cd is the detonation velocity of the explosive in m/s. The borehole pressure is defined as the pressure in the blasthole at maximum expansion of the diameter of the blasthole. In Equations 3 and 4 it is possible to rewrite them to the product of acoustic impedance of the explosive (ρe⋅cd) multiplied by the detonation velocity of the explosive cd. Therefore the explosive density and detonation velocity is of large importance for the blasting result and fragmentation and therefore both these parameters must be included in a weight strength formula. The borehole pressure increases from zero up to maximum pressure and thereafter the pressure decays and is believed to be useful for fragmentation until the blast gases have expanded about 10–20 times. After that it is believed that the influence from blast gases on fragmentation is negligible. This is also mentioned in the paper by Granlund and has also been noticed by other researchers. If the surface under the pressure versus time curve is calculated, the maximum useful energy for fragmentation can be calculated. The borehole pressure versus time is also dependent on the properties of the surrounding rock mass. It would be very interesting if borehole pressure and its change with time could be measured in the field to a low cost. However, cheap measurement devices do not exist on the market today. If we know the pressure-time curve for a specific blasthole, we would also know the influence of the explosive on the rock mass or we could also say that we have a fingerprint on how the explosive acts on the rock mass. The shape of such a pressure-time curve is dependent on blasthole diameter, stemming material and length, joint

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frequency in the rock mass, burden, the crushing ability of the rock in the vicinity of the blasthole. Therefore the conclusion is that measurements have to be undertaken for the actual used blasthole diameter, burden and stemming that is used in the fragmentation process. Based on this knowledge the single hole blasting in full scale was developed and tested in a limestone quarry on Gotland, Sweden in 1986 (Rustan & Nie 1987). Explosives can therefore first be classified after being tested in single hole blasts in full scale at that blasthole diameter and burden that actually is going to be used in the field. 2.6

Gas volume in Langefors weight strength (Equation 1)

The gas volume produced by the explosive must be very interesting as a strength parameter because the larger the gas volume produced, the larger is the pressure that will act on the blasthole wall and the larger the fragmentation effect will be on the surrounding rock mass. The gas volume produced is normally calculated theoretically at standard pressure and temperature and this volume is different from the actual produced volume in the blasthole at higher temperature and pressure. The gas volume produced by an explosive in full scale can therefore not be determined by a small scale lab tests. It is important for the blast gases how fast they are developed and how long the gas pressure will stand in the blasthole. If the blast gases are produced very slowly the gases would leak out through joints into the atmosphere and less pressure will be left for fragmentation. The real produced gas volume could be determined a little more accurate in a pond tests, under water, because here the actual diameter of the explosive can be used. The volume of the produced gas under water can here be determined. The volume of the gas bubble produced in the pond test can be measured and the volume is representative of the volume of blast gas produced. The confinement of the explosive detonated under water is, however, different to that in rock blasting and therefore these results are not fully representative for blasting in rock. If the strength of Dynamex A and an ANFO— explosive are compared we will find that the strength is about the same in spite the heat of explosion is 32% larger for Dynamex A. The gas volume produced at STP is 49% larger for ANFO compared to Dynamex A according to Brännfors (1973), see Table 1. The only explanation why ANFO is so strong is that the gas volume is 49% higher than for Dymamex A. Therefore heat of explosion and gas volume are both important properties

regarding explosive strength. According to my opinion Langefors weighting factor for heat of explosion seams to be too large and should be reduced to 2/3 for heat of explosion and 1/3 for gas volume. Granlund (2006) makes a parallel comparison between two explosives used in the Boliden Aitik mine 20 years ago, Reolit, an aluminized water gel explosive made sensitive by trotyl, and the emulsion explosive used today Titan. If the traditional calculations are done according to Langefors formula for weight strength the following values are reached, see Table 2. The blasthole diameter, used at that time, was 250 mm and the blast plan was 7.5 m burden and 9.5 m spacing. If the bulk strength of Reolit A6 is set to 1.00 the calculated strength of Titan would only be 0.89. If the explosives were going to be used in the same blast plan this would not be possible. More holes would be needed if Titan was going to be used and the cost for drilling and blasting would increase. Field tests showed however that Titan could be used in the ordinary blast plan, and also, due to different explosive densities lower specific charge was achieved with Titan. The specific charge for Titan was only 86% of Reolit A6 slurry. The conclusion is that Langefors weight strength formula (Equation 1) is not applicable for explosives developed after the formula was developed. Besides heat of explosion and gas volume in the Langefors formula, also detonation velocity

Table 1. Comparison of properties between Dynamex A and ANFO (Brännfors 1973). Explosive

Heat of explosion (kJ/kg)

Gas volume at STP (l/kg)

Dynamex A ANFO

5125 3895

655 975

STP = standard temperature and pressure.

Table 2. Comparison of the strength of Reolit A6, trotyl slurry, used in the Boliden open pit Aitik mine 20 years ago with the Titan emulsion explosive used today (Granlund 2006).

Explosive Reolit A6 slurry Titan emulsion

158

Heat of explosion (MJ/kg)

Gas volume at STP (l/kg)

Density (kg/m3)

4.52

638

1450

3.20

908

1250

and explosive density must be included. There are therefore four explosive parameters we must include in the new proposed formula. There is however no simple interrelation between these four parameters. If that would be the case, it would be possible to exclude some parameters. General we could, however, say that an increase of any of this parameters will increase the weight strength but there are upper limits as shown earlier for the density (dead pressing of explosive).

4. Throw. Maximum throw and the movement of the gravity point for the round and how this depends on the burden. 5. Composition of blast gases and its dependency on blasthole diameter, stemming, water content in the rock mass and confinement etc. 6. Backbreak and its dependency on burden. 7. Angle of breakage and its dependency on burden. 8. Breakage at the bottom of the bench and its dependency on burden. 9. Critical burden.

2.7

For a certain blast, it is important to determine which of the parameters are the most important. A property of an explosive good for some result parameter could be bad for other result parameters. To believe that small scale tests could give us the full answer are in many cases not possible and the earlier mentioned single hole blasting method in lab scale, SHB-LS, was therefore used to compare with the results from single hole blasting in full scale SHB-FS (Rustan & Vutukuri 1983, Rustan & Nie 1987). The latter method is described more in detail in the following. Many result parameters were found similar in model and full scale.

Conclusion

The relation between heat of explosion, gas volume, detonation velocity and explosive density and the blast result in the form of fragmentation has to be examined in different rock types with different acoustic impedances. Single hole blasting in full scale (SHB-FS) is recommended for that purpose, see section 3.2 in this paper. A final weight strength formula must therefore include all the four mentioned parameters.

3

THE BASIC MECHANISM OF ROCK BLASTING

At rock blasting we have three important parts regarding the ability to fragment rock. 1. The properties of the explosive and how these properties influence the detonation pressure. This determines the amplitude of the shock wave in the crushing zone close to the explosive and the borehole pressure that determines the fragmentation process and throw of the detached material. 2. The effectiveness of the energy transformation from the explosive to the rock mass is important for ground vibrations and fragmentation. 3. The rock mass reaction on the shock wave in the near field zone and the outgoing pressure wave in the surrounding rock massive. 3.1

Definition of the result parameters of interest in rock blasting

According to my opinion it is not possible to classify explosives after a simple numerical scale. One reason is that there are several different result parameters when blasting in rock. Here some are mentioned: 1. Fragmentation and its dependency on burden. 2. Ground vibrations and its dependency on burden. 3. Air pressure waves and its dependency on burden.

3.2

Single hole blasting in full scale, SHB-FS

In full scale blasting tests with multiple blastholes is complicated because many parameters can be varied like burden, spacing, delay times etc and this will affect the fragmentation. It is therefore necessary to have a simple standardized test method and therefore single hole blasting with only a variation of burden was selected as the test method. Normally the tests should be made in a vertical bench face and blasted to a smooth surface. These kinds of tests were first performed at the Storugns limestone quarry in 1986 on Gotland. The quarry belonged to Nordkalk AB. The earlier mentioned result parameters 1 to 9, but not blast gas volume, were measured at blasting with ANFO-explosive in 95 mm diameter holes. The result was very useful for understanding the working ability of an explosive in rock and to explain for the blaster in the field the blasting process and how it is affected by the size of the burden. The idea was that the explosive manufacturers in collaboration with the customers should test the explosives with this method and use it as a routine test method. The logical consequences of such a change in test method implies that personal working in the lab should go out in the field and do more tests there instead of working in the lab. This would have vitalized the whole civil explosive manufacturing industry.

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Known single hole blasting tests in full scale were so far undertaken by Nitro Nobel in Sweden, by Mohanty in Canada and by Bilgin et al. (1993) in Turkey. The start to use SHB-FS test could be regarded as a paradigm shift in the history of development of explosives, because this test method would be the only possible way to classify explosives in its used blasthole diameter, confinement, saturation of rock mass and geometry used at blasting. The cost for testing of explosives would increase but in the long run the method would give the best answers to what we are seeking for. The explosive manufacturers should therefore, in collaboration with blasting research institutes, take part in SHB-FS tests. The explosive data gained in testing of explosive properties in the lab can only be used for a rough relative indication of the strength of explosives and cannot be used in sail against customers regarding the result parameters 1 to 9. 3.3

Single hole blasting test in lab, SHB-LS

At Luleå University of technology single hole blasting tests were undertaken already in 1983 in diamond cut blocks with the size 100 × 300 × 300 mm (Rustan & Vutukuri 1983). The blastholes were drilled perpendicular to the blocks (blasthole length 100 mm) so the geometry was more like slab blasting than bench blasting where we have a confined bottom. Detonating cord was used as an explosive and the burden was varied up to and over the critical burden. Tests were originally made in six different rock and rock like materials and the result from blasting in Storugns limestone was very similar to that later on found in SHB-FS tests in Storugns limestone quarry on Gotland in Sweden. The following parameters of the blocks were determined: compressive strength, tensile strength, fracture toughness, shear strength, P-wave velocity, Young’s modulus and Poisson’s ratio. The tested materials were four Swedish rock types Kallax gabbro, Öjeby granite, Storugns limestone, Henry quartzite and two artificial materials Siporex (a light concrete similar in structure to a volcanic tuff) and magnetite concrete. The fragmentation was best be correlated to the acoustic impedance of the rock mass where the acoustic impedance is the product of sound velocity (Pwave velocity) in the rock mass cp (m/s) multiplied by the rock density ρr (kg/m3). The sound velocity in a specific material can be determined by the following derived formula, cp =

⎤ E⎡ 1− υ ⎢ ρr ⎣ (1 + υ )(1 − 2υ ) ⎥⎦

(5)

where E is the Young’s modulus of the rock in (Pa) and υ is Poisson’s ratio dimensionless, and ρr is the density of the rock mass in kg/m3. Therefore all the three parameters given in Equation 5 are important parameters at rock blasting. The P-wave velocity cp is roughly a measure of the strength of the rock mass, because the velocity is affected not only by the intact rock properties but also the joint frequency and their conditions in the rock mass. The fact that the density of rock is important in rock blasting is very natural because it is needed more energy to move something with high density than a lower density. At rock blasting in Swedish bed rock, the rock density is normally not varying much and therefore mainly the variation in P-wave velocity is determining the blastability of the rock. It is relative simple to determine the sound velocity in the field. Rock with joints has a lower P-wave velocity than a rock mass with few joints. The model tests have also given a base data to develop unique empirical formulas, e.g. of how the critical burden Be (mm) depends on the acoustic impedance of the rock I (kg/m2s) and how the tangent of the angle of the size distribution curve n for the rock material in a double logarithmic sieve analysis diagram (Accumulated material passing versus square mesh size) depends on the rock mass acoustic impedance I (kg/m2s) etc. Bc ≈ 68.5 − 1.69 ⋅10 −6 I n = 0.54e33 ⋅ 10 k50 =

−9

I

−3

5.18 ⋅10 ⋅ I q 2,14

(6) (7)

0.588

θ = 131 + 6.98 ⋅ 10 −3 c p + (0.580 − 3 ⋅ 10 −4 ⋅ c p )B

(8) (9)

Bc is the critical burden in (mm) and I is the acoustic impedance in (kg/m2s), n is the fragmentation gradient (dimensionless), k50 is the mean fragment size in (mm), θ is the angle of breakage in degrees, cp is the P-wave velocity in (m/s) and B is the burden in (mm). The importance of the acoustic impedance ratio explosive/rock has also been shown in model tests by Leinz & Thum (1970), see Figure 1. As explosive, a mixture of PETN and wax was used in the lab tests. The properties of the rock material were varied according to Figure 1, from a low strength rock like “marl” to a high strength rock like “basalt”. A small deviation from the acoustic impedance theory could here be observed because the energy transfer increased even if the impedance ratio explosive/rock is less than 1, see left diagram in Figure 1.

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Rock types tested: 1) Basalt, 2) Limestone, 3 Greywacke, 4) Granite 1, 5) Granite 2, 6) Sandstone, 7) Tuff and 8) Marl.

Figure 1. Left diagram: The amount of energy in % (range 20–70%) transferred from the explosive to rock versus the acoustic impedance ratio for explosive/rock (range 0–6). Right diagram: The amount of energy in % (range 20–70%) transferred from the explosive to rock versus the dynamic E-modulus (range 0–1200 × 103 kp/cm2). The two diagrams are based on cylindrical test samples and with a linear charge placed in the centre of the cylinder (Leinz & Thum 1970).

4

IMPORTANT PARAMETERS FOR EXPLOSIVE STRENGTH

In the following the parameters important for the explosive strength regarding its fragmentation ability in rock will be analysed. The weathering of the rock type and joint conditions is very important for the real outcome of fragmentation in the field. We might introduce a new term for the combined effect of explosive strength and rock strength, and to distinguish it from weight strength, I suggest it is called the effective weight strength of the explosive. The parameters needed in such formula are analysed regarding its possible variation as follows. 4.1

Analysis of explosives parameter variation

1. Velocity of detonation may vary from about 1000 to 8000 m/s—a variation of 800% (Wetterholm 1959). 2. Gas volume, may vary from about 420 to 975 l/kg a variation of 232%. 3. Heat of explosion, or energy, may vary from about 2650 to 5125 kJ/kg a variation of 193%. 4. Density of explosive may vary from about 900–1500 kg/m3 a variation of 167%. There is a tendency that when the heat of explosion decreases for an explosive, the gas volume will increase. If there is a good correlation between these two parameters it should be possible to

eliminate one of the parameters. When studying 12 different explosives given by Persson et al. (1994, table 4.12) and a variation of the relative heat of explosion ratio from 0.8 to 1.35 or 169% and a variation of gas volume ratio was found from 0.7 to 1.05 or 150% the correlation between the two parameters was not enough for an elimination of one of the parameters. Normally there is also a tendency that a higher explosive density is associated with a higher heat of explosion or influence of rock mass measured as a strain energy factor see Persson et al. (1994, table 4.11). A correlation was found, based on 21 values, but the scatter was too large to eliminate one of the two parameters. Another hypothesis was that the detonation velocity can be correlated with heat of explosion. By using the 21 explosives data given by Persson et al. (1994, table 4.14) we can conclude that this is not possible because of too large scatter. A good relation was however found between heat of explosion and the density of explosive for 13 explosives according to Persson et al. (1994, table 4.14) and if this is valid for most used explosives it would be possible to eliminate one of the six parameters in Equation 10. 4.2

Rock parameter variation

1. Low acoustic impedance range is defined from 0 to 5 × 106 kg/m2s. The lowest value found

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so far is 1.12 × 106 kg/m2s and this value was measured in light weight concrete which in its structure is like a soft volcanic lava. Most rock types in Sweden will be in the medium acoustic range or 10 × 106 kg/m2s to 15 × 106 kg/m2s and this makes a variation of 50%. The highest value found so far is 21.6 × 106 kg/m2s for Divrigi hematite in Turkey. This makes a total variation range of 1929% (Rustan 1998). 2. Rock mass density in situ could vary from 800 to 4900 kg/m3 or 613%. 3. P-wave velocity (sound wave velocity) could vary in rock from 1000 to 5000 m/s, a variation of 500%.

For comparison of the fragmentation effect of different explosives, a common used water resistant explosive must be used as a reference explosive and I would therefore suggest ANFO as a reference explosive. It can be found all over the world, but it has to be charged carefully into watertight plastic sleeve to avoid damage of the explosive by water. A test procedure for single hole blasting is suggested in Appendix.

With these enormous variations in parameter values it is fully clear that a weight strength definition of explosive strength by Langefors is not enough to make a prognosis of fragmentation. It must be combined with the rock properties given above. I would therefore suggest the following principal formula for calculation of the resulting effect of explosive in the rock mass. Let us call this the effective weight strength. The following principal formula is suggested seff.

The derivation of computer codes for calculation of explosive strength is based on chemical and physical laws. Normally the models are, however, not tested if they are correct for a large number of explosives and rock masses and in a large amount of different blasthole diameters. The codes are normally used to calculate the detonation velocity and how it varies with the blasthole diameter and different confinement for a certain explosive. The work with computer codes is, according to my opinion, lacking a clear research strategy. For example the blasting process needs to be described by different sub models and each sub model has to be tested according its accuracy. First after this have been done, the sub models can be combined to model the the explosive action. In the formulas used today, the rock mass is regarded as a compressible media but close to the blasthole wall it is a plastic crushing zone of the rock. This zone will act as a damping zone on the shock waves and this has to be modelled if the final result should be correct. Such work is now performed by ITASCA (Ouchterlony 2006). At the Fragblast 8 Symposium in Santiago, Chile, the last news regarding the development of computer codes for explosive calculations “Vixen Detonation Code” was presented. The code was developed by Dyno Nobel in cooperation with African Explosive Limited (Cunningham et al. 2006). The model is calculating the detonation velocity and its dependency of blasthole diameter and confinement and the borehole pressure variation with time and these parameters are used to calculate fragmentation of the rock mass by a PFC3D material model of the rock mass (a three dimensional particle flow model of the rock mass). Cunningham is of the opinion that the code can characterize a large group of explosives and that it is today a powerful and practical working tool. Numerical modelling will be the future but for the sake of understanding rock blasting in a pedagogic way we must include the relevant parameters as shown in Equation 10.

seff =

QαVg β ρeγ cdλ

ρrε cϕp

(10)

Where Q is explosive heat in (MJ/kg), Vg is the gas volume produced (m3/kg) at STP, ρe is the density of the explosive in (kg/m3), cd is the detonation velocity of the explosive in (m/s), ρr is the density of the rock mass in (kg/m3), and finally cP is the longitudinal wave velocity in the rock mass in (m/s). The exponents must be determined from field tests by multiple regression analysis. The effective weight strength is the combined effect of explosive and rock properties under the high stress interaction by blasting. The numerical value should e.g. be used in formulas for the calculation of mean fragment size k50 and the fragmentation gradient n (the slope of the fragmentation curve in a double logarithmic sieve analysis diagram (amount of material passing versus the square mesh size of the sieve). Totally there are therefore needed 6 parameters to describe the effective weight strength in rock fragmentation, instead of the two parameters defined by Langefors given in Equation 1, namely heat of explosion and gas volume. Rock blasting is not a precise science because in the field, it is difficult to make tests where the parameters are kept constant. The most difficult parameter to control is the detonation velocity, and especially when water sensitive explosives are used.

5

162

THE USE OF COMPUTER CODES TO DETERMINE EXPLOSIVE STRENGTH

6

CONCLUSIONS

− It is not possible to classify the strength of an explosive in lab- or half scale because the strength is dependent of many other factors at the use of the explosive like blasthole diameter, confinement of blasthole, packing degree of explosive, density of rock, P-wave velocity of rock and water content in the rock mass. − It is also not possible to rank explosives after some scale regarding the explosive influence in rock because there are so many different result parameters at blasting that might be of interest. You have to know what result parameter is the most important. − A new principal formula has been suggested in the paper for the calculation of the effective weight strength which here is defined as the combined effect of explosive and rock mass strength. The formula needs 6 parameters and to the already suggested and used parameters by Langefors explosion heat and gas volume the following four parameters has to be added; detonation velocity, explosive density, rock density and P-wave velocity. It would be fine if the detonation velocity and its dependency of the blasthole diameter could be included in the formula. − There is a relation between heat of explosion and explosive density and it might be perhaps possible in the future to eliminate one of these two parameters. − P-wave velocity can be calculated if Young’s modulus Poisson’s ratio and the rock density are known. − Resources should be focused on finding accurate and simple methods to measure borehole pressure during long time in full scale. The knowledge gained by measurement of borehole pressure should be used to develop more accurate models to calculate borehole pressure and its dependency on time. − More SHB-FS (single hole blasting tests in full scale) must be done under controlled conditions and with those hole diameters which are interesting in full scale blasts. These tests have to be undertaken with different explosives and extreme variations of heat of explosion and explosive gas volume, detonation velocity, explosive density, rock density, and P-wave velocity in different rock types and with extreme variation of rock acoustic impedance. Thereby a data bank is achieved over different explosives and its influence on surrounding rock mass. The result from these test blasts can later on be used for development of a new effective weight strength formula and more precise computer codes.

− The new effective weight strength formula will be a powerful and pedagogic tool to teach students which are the most important parameters for calculating the effective weight strength in full scale blasting.

REFERENCES Atchison, T.C. & Pugliese, J.M. 1964. Comparative studies of explosives in limestone. USBM RI 6395. Bergman, O.R., Wu, F.C. & Edl, J.W. 1974. Model rock blasting measures effect of delays and hole patterns on rock fragmentation. Engineering and Mining J. 175 (June): 124–127. Bilgin, H.A., Paşamehmetoğlu, A.G., & Özkahraman, H.T. 1993. Optimum burden determination and fragmentation evaluation by full scale slab blasting. Proc. 4th Int. Symp. on Rock Fragmentation by Blasting, Vienna, 5–8 July, pp. 337–344. Brännfors, S. (ed.). 1973. Bergsprängningsteknik. Stockholm: Esselte Studium. (In Swedish). Cunningham, C.V.B. 1983. The Kuz-Ram model for prediction of fragmentation from blasting. Proc. 1st Int. Symp. on Rock Fragmentation by Blasting, Luleå, Sweden, 22–26 August, pp. 438–453. Cunningham, C.V.B., Braithwaite, M. & Parker, I. 2006. Vixen Detonation Codes: Energy input for the High Stress Blasting Model (HSBM). Proc. 8th Int. Symp. on Rock Fragmentation by Blasting, Santiago, Chile, 7–11 May. Granlund, L. 2006. Viktstyrka, Energi, Gasvolym och VOD—passé?! (Weight strength, gas volume and VOD—passé?! Sprängnytt 1, Vol. 20 April. (In Swedish). Leinz, W. & Thum, W. 1970. Ermittlung und Beurleitung der Sprengarbeit von Gestein auf der Grundlage des spezifischen Sprengenergieaufwandes. Westdeutscher Verlag, Köln und Opladen. Forschungsbericht des Landes Nordrhein-Westfahlen, Nr 2118. Ouchterlony, F. 2006. Personal communication, October 2006 and December 2008. Persson, P.A, Holmberg, R. & Lee, J. 1994. Rock Blasting and Explosives Engineering. Boca Raton, FL: CRC Press. Rustan, A. & Vutukuri, V.S. 1983. The influence from specific charge, geometric scale and physical properties of homogenous rock on fragmentation. Proc. 1st Int. Symp. on Rock Fragmentation by Blasting, Luleå, Sweden, 22–26 August, pp. 115–142. Rustan, A. & Nie, S.L. 1987. New method to test rock breaking properties of explosives in full scale. Proc. 2nd Int. Symp. on Rock Fragmentation by Blasting, Keystone, Colorado, 23–28 August, pp. 36–47. Rustan, A. (ed.). 1998. Rock Blasting Terms and Symbols. A dictionary of symbols and terminology in rock blasting and related areas like drilling, mining and rock mechanics. Rotterdam: Balkema. Wetterholm, A. 1959. Explosives, Charging, Firing. In K.H. Fraenkel (ed.), Manual on Rock Blasting. Vol. 3, Ch. 16-01: 14. Atlas Copco AB, Stockholm and Sanvikens Jernverks AB, Sandviken. Stockholm: Esselte AB.

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APPENDIX Suggested method for testing new explosives by single hole blasting in full scale (shb-fs) Goal The purpose of single hole explosive strength blasting is to find primarily the rock mass fragmentation properties and how it depends on the combination of explosive and rock properties. For the sake of comparison between different explosives and rock types it is necessary to do the test in a manner that is standardized. New explosives should at least be tested in the typical rock types where they are going to be used but testing in rock masses with a large variation of acoustic impedances is preferred because of the full understanding of how the rock mass acoustic impedance influences the fragmentation of the rock mass. The term rock mass is used here instead of rock type because the weathering of a certain rock type may change the fragmentation properties completely. Sometimes suitable rock masses for a wide acoustic impedance range may not be found in the own country and therefore international cooperation may be necessary for testing in wished rock masses. Performance 1. The actual hole diameter that is needed in the open pit or quarry should be used. The single blasthole must be vertical and if necessary sub drilling should be used and the length noted. (In some quarries sub drilling is not needed because a weakness plane may be at the bottom of the bench). The actual blasthole diameter must be measured, because nominal diameters could be changed by the wear of the bit. Total amount of explosive and primer charged must be measured and noted. 2. The blasthole must be charged by only one kind of explosive, the tested explosive, or the reference explosive (ANFO). The letter explosive has been chosen because it can be manufactured on site all around the world. A plastic sleeve (important) must be used inside the blasthole to avoid excessive explosives penetrating into surrounding caves or open cracks in the rock mass.

3. The stemming length should preferably be that one actually being used in the pit or quarry. Stemming length in different rock types may vary dependent on the strength of rock mass from 12 to 30 times the blasthole diameter (Rustan 1998). Stemming length and type of stemming should be noted and presented. Coarse material >15 mm should be used as stemming because it is more effective. The size distribution of the stemming material should be presented. 4. Initiation should be made at the bottom of the blasthole and the primer strength and weight in kg should be noted and presented in the result. The following measurements should be done: 1. Rock mass properties must be recorded according to the RMR or Q-system. This will include mapping of the rock structure on the vertical bench face and also on the top of the bench if it is cleaned before blasting. 2. Measurement of fragmentation by sieving or manual digital analysis. The boulders must be measured by hand. 3. Measurement of broken volume and angle of breakage and calculation of the real specific charge. 4. Measurement of weight of explosive used in in the bottom, column of the blasthole and the primer. The column charge must have the same explosive as the bottom charge, because only one explosive can be tested in one blast. 5. Measurement of back break, crater diameter and volume of crater at the top of the blasthole. 6. Measurement of maximum throw length and direction and the gravity point of the rock pile after blasting. 7. Measurement of ground vibrations, preferable at half the bench height, behind the blast in vertical boreholes at four different distances e.g. 5, 10, 20 and 40 m behind the blasthole. Measurements inside the rock is to prefer compared to on the top surface because of more reliable data will be gathered. 8. If possible high speed video of the blast should be made to study the throw of the rock mass.

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