Improved blasting results with precise initiation...

Report 2013:3 ISSN 1653-5006

Swedish Blasting Research CentreLuleå tekniska universitet, SE-971 87 Luleå

Luleå University of TechnologySE-971 87 Luleå www.ltu.se

Improved blasting results with preciseinitiation – Numerical simulation ofsublevel caving blasting

Changping Yi

Universitetstryckeriet, L

uleå

Report 2013:3 ISSN 1653-5006

Improved blasting results with precise initiation – Numerical simulation of sublevel caving blasting

Changping Yi

i

Summary

A series of numerical simulations of rock blasting using LS-DYNA software have

been conducted to investigate the effect of short delay time on the fragmentation in

underground mines. The purpose was to test the hypothesis proposed by Rossmanith

that stress wave interaction could result in finer fragmentation by controlling the

initiation times. The blasted rock was simulated with RHT material model. After the

calculation, the elements with damage level above 0.6 were removed to simulate the

fracture of the rock.

The size of model and the borehole pattern were based on the blasting design of the

LKAB Malmberget mine. Several simulations were run to investigate the effects of

initiation time, primer position and boundary conditions. The results are presented as

accumulated area plots where the level of fragmentation can be observed at certain

positions in the model.

The results show that the fragmentation for simultaneous initiation is coarser

compared to initiation with delay times in SLC blasting. It is difficult to identify any

effect of stress wave interaction from the damage distribution in the blasted block

because the borehole pattern is in a fan shape. Thus, the distance between two

adjacent boreholes is not constant and the boreholes are of various lengths. The

numerical modeling results showed that the fragmentation for the case of 2 ms delay

time is finer than that of simultaneous initiation and the 1 ms delay time case. The

comparison among the cases with different primer positions shows that if the top of

the block was set as free face, the bottom primer cases yielded the finer fragmentation

than the top primers cases and the middle primer cases; if the top of the block was set

as non-reflecting boundary, the top primer cases yielded the finest fragmentation. The

effect of overlying waste rock above the block cannot be neglected in simulations.

The real boundary conditions of the top of the block and the effect of primer position

need to be studied further. Some recommendations are proposed for the future

research about SLC blasting.

iii

Contents 1 Introduction ...................................................................................................... 1

1.1 Background ...................................................................................................... 1

1.2 Objective and Scope of Work .......................................................................... 3

2 Methodology .................................................................................................... 4

3 Simulation of SLC blasting — results and discussion ..................................... 6

3.1 Description of the model .................................................................................. 6

3.2 Material modeling and constitutive parameters ............................................... 7

3.3 Simulation results for different delay times ..................................................... 8

3.3.1 Results of simultaneous initiation ...................................................... 9

3.3.2 Results of 1 ms delay time case ....................................................... 11

3.3.3 Results of 2 ms delay time case ....................................................... 12

3.3.4 Discussions of the effect of delay times .......................................... 13

3.4 Simulation results for different primer positions ........................................... 15

3.5 Simulation results for different boundary conditions .................................... 21

4 Conclusions .................................................................................................... 25

5 Recommendations .......................................................................................... 26

References .................................................................................................................... 28

Appendix A: Swebrec function parameters from curve fitting for the delay cases. .... 31

Appendix B: Swebrec function parameters from curve fitting for different primer position cases. .............................................................................................................. 31

Appendix C: Swebrec function parameters from curve fitting for non-reflecting boundary conditions cases. .......................................................................................... 32

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List of figures

Fig.2.1. Blast effect evaluation procedure......................................................................5

Fig.3.1. Geometry of the SLC model.............................................................................6

Fig.3.2 The borehole pattern......................................................................7

Fig.3.3. Initiation sequence............................................................................................9

Fig.3.4. The evaluated block and Cut I cross-section.....................................................9

Fig.3.5. Overall damage distribution for simultaneous initiation…...............................9

Fig.3.6. Overall crack pattern for simultaneous initiation .............................................9

Fig.3.7. Accumulated area plot for simultaneous initiation case….………………....10

Fig.3.8. Overall damage distribution for 1ms delay time case.....................................11

Fig.3.9. Overall crack pattern for 1ms delay time case................................................11

Fig.3.10. Accumulated area plot for 1 ms delay time case ..........................................11

Fig.3.11. Overall damage distribution for 2ms delay time case...................................12

Fig.3.12. Overall crack pattern for 2ms delay time case..............................................12

Fig.3.13. Accumulated area plot for 2 ms delay time case …......................................12

Fig.3.14. The remaining volume VS. Delay times.......................................................13

Fig.3.15. The remaining area VS. Delay times............................................................13

Fig.3.16. Fragmentation of Cut I section for different delay times .............................14

Fig.3.17. Accumulated area plot for different delay times...........................................14

Fig.3.18. The position of the primer.............................................................................15

Fig.3.19. Overall crack pattern for the case of 1 ms delay and top primer position…16

Fig.3.20. Overall crack pattern for the case of 1 ms delay and bottom primer position………………………….................................................................16

Fig.3.21. Overall crack pattern for the case of 2 ms delay and top primer position…16

Fig.3.22. Overall crack pattern for the case of 2 ms delay and bottom primer position.........................................................................................................16

Fig.3.23. Fragmentation of Cut I section for different delay times and primer positions…………………………………………………………………....17

Fig.3.24. Accumulated area plot of Cut I section for different primer positions and delay times....................................................................................................18

Fig.3.25. The cross-section of Cut II..........................................................................18

Fig.3.26. Fragmentation of Cut II section for different primer positions and delay times……………………………………………………………………….19

Fig.3.27. Accumulated area plot of Cut II section for four cases.................................20

vi

Fig.3.28. Bridge elements (left) and handling method of bridge elements (right)…...21

Fig.3.29. Fragmentation of Cut I section with non-reflecting boundary conditions....22

Fig.3.30. Accumulated area plot of Cut I section with non-reflecting boundary........ 22

Fig.3.31. Fragmentation of Cut II section with non-reflecting boundary conditions...23

Fig.3.32. Accumulated area plot of Cut II section with non-reflecting boundary........23

vii

List of tables

Table 3.1 Material type, material property input data and EOS input data..................8

1

Improved blasting effect with precise initiation Swebrec Report 2013:3

1 Introduction

1.1 Background The first stage of the comminution process in metalliferous mining is the breakage and fragmentation of the orebody rock mass, generally by drilling and blasting techniques. This is the activity that may have the most leverage in the efficiency of a mining operation, as the output from a blast impacts on every downstream operation (Grant et al., 1995). In the case of underground operations, controlling both fragmentation and the degree of blast induced damage are important aspects of the mine design process. Poor drilling and blasting practices are typified by excessive over-break, dilution, oversize fragmentation, restricted access, increased local reinforcement requirements and increased mining cycle times and costs. Hence, it can have a negative effect on the efficiency of mining activities as a whole (Singh, 1993 Brown et al., 1994). An improved fragmentation can result in reduced costs for both blasting and transportation of the blasted rock, improved environmental aspects, and reductions in energy consumption during crushing and grinding of the blasted rock, as well as improved metal recovery. Within the underground mining cycle, the influence of drilling and blasting can also be significant in key aspects of material flow, handling and processing (Klein et al., 2003). For example, the impact of fragmentation on flow dynamics is considered critical in sublevel caving (SLC) operations. The effect of blasting in underground mines depends on several factors (Brunton, 2009, 2010; Rustan, 2013) and initiation delay time between blast holes is one of them.

No clear guidelines are outlined in the literature concerning appropriate initiation timing for SLC blast rings. Initiation timing can be divided into inter-hole and inter-ring delays (for multiple ring blasting). The inter-hole and inter-ring initiation times have been reported to have an impact on explosive performance, blasted material fragmentation, swell and compaction of the compressible cave material.

Rustan (1983; 2013) investigated the impact of inter-hole initiation timing on blasted material fragmentation for a 1:75 scaled SLC blast ring. The small scale SLC ring geometry consisted of 12 vertical blast holes in a ‘fan’ drill pattern, with detonating cord used as the explosive. The short delays were generated by a modular pulse generator, with delay times varying from 0 ms to 250 ms for the experiments. The results indicated that the finest fragmentation was achieved for a delay time of 0.1 ms.

Volchenko (1977) also conducted a series of small scale experiments to investigate the influence of short delay blasting on fragmentation and swell of the blasted material and compaction of the compressible material. Three rows of holes with the same spacing, burden, and powder factor were fired in each experiment into a compressible material consisting of crushed concrete with particle sizes ranging between 1 mm and 25 mm. The study investigated six initiation schemes, consisting of row by row, opposite-diagonal, wave-1, wave-2, wedge shaped and trapezoidal.

2


Unfortunately, no details of the actual initiation timing are provided by Volchenko (1977). The results indicated that the finest fragmentation P50 and percentage of oversize (> 40 mm) was achieved for the wave-2 initiation scheme, while the greatest swell and compaction of the compressible material was achieved for the row by row initiation scheme.

Quinteiro et al. (2001) reported full scale trials at the LKAB SLC operation investigating the impact of inter-hole delays on ore dilution. The experiments were conducted on 10-hole rings and involved firing the center four holes on a short delay and, after a delay of between 100 ms and 1000 ms, blasting the other holes in the ring with a delay of 50 ms between the holes. A significant reduction in dilution was observed for a delay of 300 ms between the inner and outer holes of the blast ring.

Although initiation timing has been demonstrated in the literature to have an impact upon blasted and flow material characteristics, the mechanisms for this are not clearly understood. Limited data indicates that initiation timing is related to improvements in blasted and flow material characteristics through the creation of additional swell of the blasted material (Brunton, 2009). For multiple rings blasting, initiation timing would be crucial for the creation of a void volume behind each blasted ring, while for single ring blasting additional void volume may be created due to the compaction of the caved material from the center holes.

With the application of electronic detonators and with short delay times, the hypothesis of achieving improved fragmentation through stress wave superposition has been proposed by Rossmanith (2002, 2004). In these papers, a model was proposed to describe the stress wave superposition between adjacent boreholes with Lagrange diagrams, which reveals how a positive effect of shock wave interaction of the negative tail of wave could be achieved with the assumption of an infinitely long charge length.

Vanbrabant and Espinosa (2006) chose the delay times to match an overlap of the negative tail of the particle velocity and conducted a series of field tests. They claimed that the average fragmentation improved by nearly 50%. Chiappetta (2010) also claims that short delays, such as 2 ms, between the holes improve the blast results. On the other hand, Blair (2009) stated that the delay accuracy and timing were typically not the major variables that governed blast vibration and fragmentation. Ouchterlony et al. (2010) have reported on some unexpected results in full scale experiments. It was found that the fragmentation was coarser when electronic detonators were used compared with pyrotechnics, when time intervals were 10 ms and 5 ms between the holes in a row.

Mardones et al. (2009) have investigated potential gains in fines generation by introducing short delays (e.g. 2 ms to 10 ms) between the holes in a row in field experiments. The results showed that there was little gain with the use of inter-hole delays of 2 ms. He stated that although fragmentation may be improved, it is

3


important to note that “high intensity” blasting with the use of short inter-hole delays may be counter-productive if the risk of rock mass damage is increased and loading productivity is influenced by the lack of muckpile looseness.

Katsabanis et al. (2006) shot a series of small scale blocks of granodiorite with short delays. The results showed that fragment size decreases with delay time from a maximum size, during simultaneous initiation of all charges, to an approximately constant size, for delays up to 1 ms. When larger delays were used, fragmentation became coarser.

Schill (2012) studied the influence of delay times on the blasting effect in a two-hole model with the LS-DYNA (Hallquist, 2007) computer code and the RHT (Riedel et al., 1999) material model and concluded that there was an effect of interacting stress waves. However this effect was local around the interaction plane, implying that precise ignition will not generate a dramatic increase in fragmentation contrary to what was proposed by Rossmanith (2002). The results of Schill (2012) also indicated that longer delay times (in which the stress wave would have passed the neighboring boreholes) also resulted in improved fragmentation, which implies that other factors than tensile wave overlapping govern the fragmentation.

1.2 Objective and Scope of Work

To study the influence of delay time on blasting effect and fragmentation in underground mines, a series of numerical simulations of SLC blasting were conducted. These simulations were carried out using the same methodology as Schill (2012), i.e., applying the LS-DYNA computer code (Hallquist, 2007) and the RHT material model (Riedel et al., 1999).

The methodology used to model the fragmentation with different delay times is presented in Chapter 2. The results of simulating SLC blasting and discussion are presented in Chapter 3 and conclusions are presented in Chapter 4. Finally, some recommendations are given in Chapter 5.

4


2 Methodology To model the SLC blasting, the blasting design of the LKAB Malmberget mine was taken as a reference. A continuum simulation approach was used. Hence, it was not possible to explicitly model the crack formation and propagation in the model. Therefore, an alternative approach was used in which the level of damage in an element is considered. First, a threshold value was set to correspond to a fully crushed rock fragment. In this study, a damage level of 60% was taken to indicate complete crushing. Next, an algorithm was developed, in which fragments delineated by cracks (=fully crushed elements) were identified, and the area of each such fragment determined. This fragment identification procedure is not easily done in 3D, but in 2D it is fairly straight-forward and a routine was implemented in LS-PREPOST (which is the pre- and post-processor for LS-DYNA). Then it was possible to evaluate the fragment area by measuring the fragments in a number of vertical and horizontal cuts through the model (Schill, 2012).

After the fragment area was calculated, some area sizes resembling the sieve mesh sizes were defined to obtain intervals for different fragment areas. Then the Swebrec function (Ouchterlony, 2009) was employed to fit the fragment area distribution. By using this method, it is possible to study the accumulated area for different fragment areas. The accumulated area plot should resemble the mass passing plot (“sieve curves”), which is commonly used in fragmentation analysis. The drawback of the method is that it is mesh size dependent and it is not possible to determine fragments less than the element size due to the limited level of discretization.

To evaluate the blasting effect, the “remaining area” and “remaining volume” were first studied. The “remaining area” is defined as the residual area of the cross section selected to be evaluated after the elements with a damage level above 60% have been blanked out. The “remaining volume” is defined as the residual volume of block after the elements with a damage level above 60% have been blanked out. “Remaining area” and “remaining volume” can reflect the damage extent in the cross-section and the overall extent of damage in the block, respectively. The fragment area distribution was then analyzed for each case. The evaluation procedure is shown in Fig. 2.1.

5


Blank out elements with damage level above 0.6 in the last simulation plot state.

Transfer the remaining elements back to the initial position in order to cancel out any particle movement.

Evaluate remaining volume.

Do vertical section cut of the model.

Output the section cut as a shell mesh.

Run the fragment identification and area calculation routine.

Fit the fragment area distribution with the Swebrec

function.

Evaluate remaining area.

Fig.2.1 Blasting effect evaluation procedure.

6


3 Simulation of SLC blasting — results and discussion

3.1 Description of the model As mentioned earlier, the blasting design of the LKAB Malmberget mine is taken as a reference for numerical simulation. The LKAB Malmberget mine is a large scale underground iron mine that produces approximately 15 million tonnes of crude ore annually. Currently, all mining is done using sublevel caving. The sublevel heights vary between 25 and 30 m (in different portions of the mine) and the blast holes are 115 mm in diameter. The production drifts are 5.5 m high and 7 m wide. The geometry of SLC model is shown in Fig.3.1 and the borehole patterns of the model and the Malmberget mine are shown in Fig.3.2. There are about 23 million elements in the model. Both sides and the back and the bottom of the model, are defined as no-reflecting boundaries in the simulation. The top of the block and the front of the block are simulated as free faces.

Fig.3.1 Geometry of the SLC model

7


(a) (b) Fig.3.2 The borehole pattern; (a) The borehole pattern in the model; (b) The borehole pattern of the Malmberget mine.

The explosive used in the LKAB Malmberget mine is emulsion. The primers are placed at the middle of the blast holes and the distance between the primers and the collar of the drift is 15 m.

3.2 Material modeling and constitutive parameters The explosive was modeled with an explosive material model in LS-DYNA and with the Jones-Wilkins-Lee (JWL) equation of state (Lee et al., 1968) as Eq. (3.1).

1 2

1 2

1 1R V R Vw w wEp A e B eRV R V V

− − = − + − +

(3.1)

where p is the pressure; A, B, R1, R2 and w are constants and V and E are the specific volume and the internal energy respectively.

The rock was modeled with the RHT material model in LS-DYNA, which is an advanced plasticity model for brittle materials such as concrete and rock. It was proposed by Riedel, Hiermaier and Thoma (Riedel et al., 1999) for dynamic loading of concrete and implemented in LS-DYNA code in 2011 (Borrvall and Riedil., 2011). The used values for the modeling of the rock and the explosive are shown in Table 3.1. The rock material used is Westerly granite (Schill, 2012) and the parameter values of explosive are decided by cylinder expansion tests (Hansson, 2009).

8


Table 3.1 Material type, material property input data and EOS input data.

Materials

Parameters of different materials (unit: kg, m, s)

Rock

MAT_RHT

RO SHEAR ONEMPA EPSF B0 B1 T1

2627 1.86E+10 1.0E+6 2. 1.22 1.22 4.0E+10

A N FC FS* FT* Q0 B T2

2.62 0.80 200.0E+6 0.18 0.05 0.5674 0.0105 0.0

E0C E0T EC ET BETAC BETAT PTF

3.0E+8 3.0E+9 3. E+22 3.0E+22 0.032 0.036 0.001

GC* GT* XI D1 D2 EPM AF NF

1.0 0.7 0.5 0.04 1. 0.01 0.873 0.559

GAMMA A1 A2 A3 PEL PCO NP ALPHA0

0. 4.0E+10 0 0 1.33E+8 6.0E+9 3.0 1.00

Explosive

MAT_HIGH_EXPLOSIVE_BURN

RO D PCJ

1180.0 5122.0 9.531E+9

EOS_ JWL

A B R1 R2 OMEG E0 V0

2.762E+11 8.436E+9 5.215 2.112 0.501 3.868E+9 1.00

3.3 Simulation results for different delay times

The initiation sequence in simulations is shown in Fig.3.3. The sequence numbers in Fig.3.3 mean the initiation sequence. The stars in Fig.3.3 mean the location of primers. They are at 15 m distance from the collar of drift. Three cases with delay times of 0 ms, 1 ms and 2 ms were modeled. The purpose of the simulations with delayed initiation times was to study the effect of the shock waves and their reflections. The simulation of simultaneous initiation was taken as a reference to evaluate the results of the delayed initiation times. The simulation time was 20 ms for the cases with simultaneous initiation and 1 ms delay time. The case with 2 ms delay time had a simulation time of 25 ms. In order to evaluate the blast effect in each case, one block and one cross-section of this block were selected for evaluation, see Fig.3.4. The cross-section, named Cut I, is at 1.5 m distance from the free face. According to the evaluation process in Section 2, after the calculation, the elements with damage levels above 0.6 were blanked out and the remaining volume of the selected block and the remaining area of the cross-section were calculated.

9


Fig.3.3 Initiation sequence Fig.3.4 The evaluated block and Cut I cross-section

3.3.1 Results of simultaneous initiation The damage distribution and overall cracks at 20 ms for the simultaneous initiation case are shown in Fig.3.5 and Fig.3.6, respectively. The red color in Fig.3.5 represents fully damaged rock.

(a) Front view (b) Back view (a) Front view (b) Back view

Fig.3.5 Overall damage distribution Fig.3.6 Overall crack pattern for for simultaneous initiation. simultaneous initiation.

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Looking at the crack pattern in front view it is clear that simultaneous initiation induces fine fragmentation at the part below the initiation point and near the top of block. The fragmentation at the middle of the block is coarse, see Fig.3.6. It is difficult to identify any stress wave interaction effect from the damage distribution in the blasted block because the borehole pattern is in a fan shape, the distance between two adjacent boreholes is not constant, and the lengths of the boreholes are different.

The fragment size distribution is usually used to evaluate the blasting effect. The data from the sieving is usually fitted with a smooth curve. The Swebrec function proposed by Ouchterlony (2009) was found to be effective to describe the fragment size distribution. There are two Swebrec functions proposed by Ouchterlony (2005). One is the basic Swebrec function (including three parameters) and the other is the extended Swebrec function (including five parameters). Practical applications indicate that the extended Swebrec function can fit the effect of both fine and coarse fragment (Ouchterlony, 2009; Ouchterlony et al., 2013.). The function reads, with P(x) being the fraction passing a sieve of size x:

}{ max max 50 max max 50( ) 1 / 1 [ln( / ) / ln( / )] (1 )[( / 1) / ( / 1)]b cP x a x x x x a x x x x= + + − − − (3.2)

The fitting parameters are the size values and the undulation exponents a, b and c. In this study, some areas were defined to resemble the sieve mesh sizes. The extended Swebrec function was then employed to fit the fragment area distribution of selected cross-sections.

The fragment area distribution of the Cut I cross-section fitted with the Swebrec function is shown in Fig.3.7. The value of the coefficient of determination, r2, is 0.991, which indicates that the fit is good. The detailed Swebrec function parameters from curve fitting are presented in Appendix A.

0,01

0,1

1

0,01 0,1 1 10 100

Acc

umul

ated

are

a [-

]

Rock fragment area [m2]

Numerical result

Fitting curve

Fig.3.7 Accumulated area plot for the simultaneous initiation case.

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3.3.2 Results of 1 ms delay time case The damage distribution and overall crack pattern at 20th ms for the 1 ms delay time case are shown in Fig.3.8 and Fig.3.9, respectively. The effect of the delay time between the boreholes becomes obvious if the damage distribution and crack pattern are compared between the simultaneous initiation case and the 1 ms delay time case. It seems that the 1 ms delay time case yields finer fragmentation than the simultaneous initiation case, see Fig.3.9.


Fig.3.8 Overall damage distribution Fig.3.9 Overall crack pattern for for the 1 ms delay time case. the 1 ms delay time case.

The fragment area distribution of Cut I fitted with the extended Swebrec function is shown in Fig.3.10. The value of the coefficient of determination, r2, is 0.995. Details of the Swebrec function parameters from curve fitting are given in Appendix A.

0,01

0,1

1

0,01 0,1 1 10 100

Acc

umul

ated

are

a [-

]


Numerical result

Fitting curve

Fig.3.10 Accumulated area plot for the 1 ms delay time case.

12


3.3.3 Results of 2 ms delay time case The damage distribution and overall crack pattern at 25 ms for the 2 ms delay time case are shown in Fig.3.11 and Fig.3.12, respectively.


Fig.3.11 Overall damage distribution Fig.3.12 Overall crack pattern for for the 2 ms delay time case. the 2 ms delay time case.

The fragment area distribution of Cut I selected cross-section fitted with Swebrec function is shown in Fig.3.13. The value of the coefficient of determination, r2, is 0.997. Details of the Swebrec function parameters from curve fitting are shown in Appendix A.

0,01

0,1

1

0,01 0,1 1 10 100

Acc

umul

ated

are

a [-

]


Numerical result

Fitting curve

Fig.3.13 Accumulated area plot for the 2 ms delay time case.

13


3.3.4 Discussions of the effect of delay times The effect of delay times on the fragmentation is obvious from the above qualitative analysis. A more quantitative comparison is provided in this section. As mentioned earlier, the remaining volume of the selected block and the remaining area of the selected cross-section can be used as indicators of fragmentations. The remaining volume of the selected block for different cases and the remaining area of the selected cross-section are shown in Fig.3.14 and Fig.3.15, respectively.

0 1 21240

1280

1320

1360

1400

1440

Rem

aini

ng v

olum

e(m

3 )

Delay time(ms) Fig.3.14 Remaining volume vs. delay times.

0 1 2

420

440

460

480

Rem

aini

ng a

rea(

m2 )

D elay tim e(m s) Fig.3.15 Remaining area vs. delay times.

An increase in delay time causes in a decrease in remaining volume, see Fig.3.14. In other words, the longer delay time results in more elements with damage level above 0.6, compared to short delay times. Increasing delay time also leads to a decrease in remaining area, see Fig.3.15.

The fragmentation of Cut I cross-section for different delay times is shown in Fig.3.16 and the effect of delay times on fragmentation is shown in the accumulated area plot, see Fig.3.17. At the Cut I section, the fragmentation of the top and the

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bottom of the block is fine. The boulders are mainly located in the middle of the cross section, see Fig.3.16.The reason is that the stress wave caused by blasting propagates upwards and downwards from the initiation point, then the reflected stress waves cause the tensile stress around the top and the bottom of the block because the top and the bottom were defined as free faces. The case showing the finest fragmentation is the case of 2 ms delay time.

(a) (b) (c)

Fig.3.16 Fragmentation of Cut I section for different delay times (a) 0 ms delay; (b) 1 ms delay; (c) 2 ms delay.

0

0,2

0,4

0,6

0,8

1

0,01 0,1 1 10 100

Acc

umul

ated

are

a [-

]

Rock fragment area[m2]

0 ms delay

1 ms delay

2 ms delay

Fig.3.17 Accumulated area plot for different delay times.

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3.4 Simulation results for different primer positions

Previous research has shown that the blast effect is influenced by the position of the primer. Generally speaking, for bench blasting, bottom priming gives the maximum use of explosive energy, increasing fragmentation and displacement of the rock with a minimum of fly rock (Jimeno et al., 1995). Some researchers stated that bottom priming also gives the maximum use of explosive energy and increasing fragmentation for SLC blasting (Xue et al., 2001; Wang, 2003). Some years ago, the primers were placed at the lowest charged position of a blast hole in the Malmberget mine. The advantages and disadvantages of lowest primer position were investigated by Zhang (2005). Nowadays, the primers are placed at the middle of the borehole, at 15 m distance from the borehole collar. The results from production show that the fragmentation is much better than before and the average ore extraction is increased by 107%, compared with that from the lowest primer position scheme in the same drifts (Zhang, 2005). In order to investigate the influence of the position of the primer on the blast effect in SLC, the cases of top primer position and bottom primer position with different delay times were studied. The geometry of the top primer position and the bottom primer position are shown in Fig.3.18. The geometry of the middle primer position is shown in Fig.3.2.

(a) The bottom primer position (b) The top primer position

Fig.3.18 The position of the primer

The overall crack geometry with 1 ms delay and top primer position is shown in Fig.3.19 and the overall crack geometry with 1 ms delay and the bottom primer position is shown in Fig.3.20.

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(a) Front view (b) Back view (a) Front view (b) Back view Fig.3.19 Overall crack pattern for the case Fig.3.20 Overall crack pattern for the

of 1 ms delay and top primer. case of 1 ms delay and bottom primer.

For the case of 1 ms delay and top primer position, the stress wave incited by blasting propagates downwards and reflects at the roof of the drift, which induces fine fragmentation near the drift and coarse fragmentation near the top of the block, see Fig.3.19. Contrary to this, for the case of 1 ms delay and bottom primer position, the stress wave propagates upwards and reflects at the top of the block where the top of the block is defined as a free face, which induces fine fragmentation near the top of the block and coarse fragmentation near the borehole collar, see Fig.3.20. Another reason for the coarse fragmentation near the drift for the case of 1 ms delay and bottom primer position is the absence of stemming in the uncharged segment of boreholes.

(a) Front view (b) Back view (a) Front view (b) Back view Fig.3.21 Overall crack pattern for the Fig.3.22 Overall crack pattern for the

case of 2 ms delay and top primer. case of 2 ms delay and bottom primer.

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The overall crack geometry with 2 ms delay and top primer position is shown in Fig.3.21 and the overall crack geometry with 2 ms delay and the bottom primer position is shown in Fig.3.22. A similar phenomenon was found for the 2 ms delay case with different primer positions. The fragmentation of the Cut I cross-section is shown in Fig.3.23.

(a) (b) (c)

(d) (e) (f)

Fig.3.23 Fragmentation of Cut I section for different delay times and primer positions; (a) 1 ms delay and top primer; (b) 1 ms delay and bottom primer; (c) 1 ms delay and middle primer; (d) 2 ms delay and top primer; (e) 2 ms delay and bottom primer; (f) 2 ms delay and middle primer.

It seems that the fragment area of the cases of top primer position is more uniform than that of the cases with bottom and middle primer positions, see Fig.3.23. The

18


fragment area distribution of Cut I cross-section is shown in Fig.3.24. The curves in Fig.3.24 are fitted with the extended Swebrec function. The detailed extended Swebrec function parameters from curve fitting are presented in Appendix B.

0

0,2

0,4

0,6

0,8

1

0,01 0,1 1 10 100

Acc

umul

ated

are

a[-]


1 ms delay and top primer


1 ms delay and bottom primer


1 ms delay and middle primer


Fig.3.24 Accumulated area plot of Cut I section for different primer positions and delay times.

The simulated 2 ms delay time cases always yield finer fragmentation than the 1 ms delay time. Morevoer, the bottom primer cases always yield finer fragmentation than the top primer cases and the middle primer cases, for the same delay times, see Fig.3.24. The numerical results give a contrary conclusion to practical tests (Xue et al. 2001; Wang, 2003; Zhang, 2005), which indicate that the top primer and the middle primer result in the better fragmentation than the bottom primer. To further study the effect of primer position, another cross-section, named Cut II, was selected to be evaluated, see Fig.3.24. The selected cross-section is at 0.1 m distance from the free face. The fragmentation of Cut II cross-section is shown in Fig.3.25.

Fig.3.25 The cross-section of Cut II.

19


(a) (b) (c)

(d) (e) (f) Fig.3.26 Fragmentation of Cut II section for different primer positions and delay times; (a) 1 ms delay and top primer; (b) 1 ms delay and bottom primer; (c) 1 ms delay and middle primer; (d) 2 ms delay and top primer; (e) 2 ms delay and bottom primer; (f) 2 ms delay and middle primer.

The fragment area distribution of Cut II cross-section for different primer positions and delay times is shown in Fig.3.27. The detailed extended Swebrec function parameters from curve fitting are shown in Appendix B.

20


0

0,2

0,4

0,6

0,8

1

0,01 0,1 1 10 100

Acc

umul

ated

are

a[-]








Fig.3.27 Accumulated area plot of Cut II section for different primer positions and delay times.

The bottom primer cases still yield finer fragmentation than those of the cases with top primer and middle primer at Cut II cross-section, see Fig.3.27. The case of 2 ms delay and bottom primer position gives the finest fragmentation and the most uniform fragment area compared with other cases. The fragment area of the case of 1 ms delay and top primer position is scattered, i.e., this case yields many small fragments and many boulders too.

The results from both two cross-sections indicate that the bottom primer position cases yield the better blast effect than the top primer position cases and the middle primer position cases. One of the possible reasons is that the top of the block is defined as a free face in simulation. For the bottom primer cases, the stress wave caused by blasting and the detonation shock wave propagate upwards and then the reflected tensile stress wave from the top of the block causes the fine fragmentation near the top of the block. In reality, the top of the block is overlaid by waste rock. The boundary condition at the top of the block is thus likely something between non-reflecting boundary and free face boundary conditions. Actually, the reflection coefficient of the stress wave at the top of block has been shown to have a great influence on the fragmentation (Johansson and Ouchterlony, 2011). Another possible reason is the limitation of the fragment size identification routine (Schill, 2012). One of the main issues when doing the fragment size identification is how to handle “bridge” elements, see Fig.3.28. These “bridge” elements could close the gap between two adjacent fragments and yield a fragment which is very large compared to the individual fragments. In the fragment size identification routine, if an elements has two opposing sides that are not connected to an element, this is considered to be a “bridge” element and is cancelled out, see I area in Fig.3.28. The fragment size identification routine takes the fragments near the I area as two fragments. However, if the elements connect two fragments like the elements in II area, see Fig.3.28, the

21


identification routine takes the fragments near the II area as one large fragment, which is one of possible reasons why the maximum fragment area is greater than 100 m2 sometimes. Because there is the limitation of the fragment size identification routine, one case appears the finer fragmentation than another case from the section cut fragmentation, while it appears the coarser fragmentation from the accumulated area plots. For example, the case of 1 ms delay and top primer appears the finer fragmentation than the case of 1 ms delay and bottom primer at the Cut I, see Fig.3.23. But the accumulated area plots indicate that the case of 1 ms delay and top primer yields the coarser fragmentation than the case of 1 ms delay and bottom primer, see Fig.3.24.

Fig.3.28 Bridge elements (left) and handling method of bridge elements (right)

3.5 Simulation results for different boundary conditions In this section, a different boundary condition, corresponding to the top of the block being defined as non-reflecting boundary, was analyzed. Two cases were studied: (i) delay time of 1 ms and the primers located at the top of the borehole, and (ii) delay time of 1ms and the primers located at the lowest position of explosive. The fragment area distribution of the Cut I and Cut II cross-sections were studied and compared.

The fragmentation of Cut I cross-section with different primer positions is shown in Fig.3.29. The effect of boundary conditions is shown in the accumulated area plot, see Fig.3.30. The accumulated area plots of the cases that the top of the block is free face and the delay time is 1 ms were added in Fig.3.30 to compare the influence of the boundary conditions. The label of top primer and top-free in Fig.3.30 detonates the case that the primer is placed at the top of borehole and the top of the block is treated as free face. The label of top primer and top-non in Fig.3.30 detonates the case that the primer is placed at the top of borehole and the top of the block is treated as non-reflecting boundary. The detailed Swebrec function parameters from curve fitting are shown in Appendix C.

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(a) (b) (c)

Fig.3.29 Fragmentation of Cut I section with non-reflecting boundary conditions; (a) Top primer; (b) Bottom primer; (c) Middle primer (1 ms delay time).

0

0,2

0,4

0,6

0,8

1

0,01 0,1 1 10 100

Acc

umul

ated

are

a [-

]


Top primer and Top-free

Bottom primer and Top-free

Middle primer and Top-free

Top primer and Top-non

Bottom primer and Top-non

Middle primer and Top-non

Fig.3.30 Accumulated area plot of Cut I section with non-reflecting boundary and 1 ms delay time.

At Cut I cross-section, the accumulated area plots indicate that the cases that the top of the block is treated as free face yield the finer fragmentation than the cases that the top of the block is set as non-reflecting boundary. When the top of the block is set as non-reflecting boundary, the accumulated area plots of different primer positions are very close at Cut I cross-section, especially for the weights of the fine fragments, see Fig.3.30.

The fragmentation of Cut II cross-section with different primer positions is shown in Fig.3.31. The accumulated area plots at Cut II cross-section are shown in Fig.3.32.

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The accumulated area plots of the cases that the top of the block is free face and the delay time is 1 ms at Cut II cross-section were also added in Fig.3.32 to compare the influence of the boundary conditions.

(a) (b) (c)

Fig.3.31 Fragmentation of Cut II section with non-reflecting boundary conditions; (a) Top primer; (b) Bottom primer; (c) Middle primer (1 ms delay time).

0

0,2

0,4

0,6

0,8

1

0,01 0,1 1 10 100

Acc

umul

ated

are

a[-]


Top primer and Top-free

Bottom primer and Top-free

Middle primer and Top-free

Top primer and Top-non

Bottom primer and Top-non

Middle primer and Top-non

Fig.3.32 Accumulated area plot of Cut II section with non-reflecting boundary and 1 ms delay

time.

At the Cut II cross-section, the accumulated area plots indicate that if the top of the

block is set as non-reflecting boundary, the top primer position case yields much finer

fragmentation than the bottom primer position case and the middle primer position

24


case, see Fig.3.32. The results indicate that the effect of the overlying waste rock

above the top of the block cannot be neglected in the numerical simulations.

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4 Conclusions Based on the simulations of an SLC blast design, the following conclusions can be

drawn:

1) Simultaneous initiation leads to coarser fragmentation compared to the initiation

with delay times in SLC blasting.

2) 2 ms delay time case yields finer fragmentation compared to the cases with

simultaneous initiation and 1 ms delay time. The improved fragmentation is thus

not due to the stress wave interaction effect.

3) The effect of overlying waste rock above the block cannot be neglected. Treating

the top of the block as a non-reflecting boundary is preferable to a free boundary

in the numerical simulations.

4) The primer position has a significant effect on fragmentation. If the top of the

block is treated as free face, simulation results show that the bottom primer

yields the finest fragmentation. If the top of the block is set as non-reflecting

boundary, the top primer gives the finest fragmentation.

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5 Recommendations In the simulation of SLC blasting, the elements of explosive share the nodes with the elements of rock at the interface between the explosive and the rock. Elements with severe deformation are deleted in calculation to avoid calculation instability, which causes mass loss in simulation. The ALE algorithm with the command of constrain_lagrange_in_solid in LS-DYNA code could be a better way to model large deformations. At the same time, the potential effect of air within the uncharged segment of the borehole can be taken into account in this way. Although the computational cost in this way is high, a small size model or a model with a slightly coarser mesh is worthy to be studied in this way.

The rock material used in this report is Westerly granite (Schill, 2012). The real parameter values of studied rock will give more rational simulation results to be compared to the field test results. For RHT material model, a series of uniaxial tests and triaxial tests are needed for numerical simulation to determine the basic mechanical parameter values, the shape of the failure surface and the Load angle dependency etc. An impact test is also necessary to determine the parameter values of equation of state of rock.

According to the analysis above about the boundary conditions of the top of the block, the boundary conditions have a significant effect on blasting fragmentation. Unfortunately, the boundary conditions only can be set as free face or non-reflecting boundary in the LS-DYNA code. It is great interest to further study the effect of boundary conditions via small scale tests and filed tests.

In practical engineering, the rock to be blasted usually contains initial damage and cracks caused by the last ring blasting operation. These cracks divide the rock mass to be blasted into smaller regions where reflections etc. could occur, like joints in rock (Johansson, 2011). A larger model (more than one ring) is worth to be simulated to investigate the influence of initial cracks on the fragmentation. After the first ring blasting, the damage in remaining rock caused by the first ring blasting is taken as the precondition for the next ring blasting.

The effect of primer position on the fragmentation is obvious. Despite numerical simulation can reveal some phenomenon, there is a need to continue study via small tests and field tests. The potential benefits of the top primer are confining the detonation gas in the borehole for a longer time than the bottom primer, reducing the damage to brow and reducing the risk of misfire, etc.

Initial stress in rock mass was not taken into account in simulations in the report, which is acceptable to low initial stress area. With the increased mining depth, the in-situ stress in the rock mass is higher and higher. For the deep underground mine, the rock fragmentation is resulted from the combination action of the blast-induced dynamic stress and the initial in-situ stress. So it is interest to study the influence of

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the initial in-situ stress on the rock fragmentation. Meanwhile, the effect of the transient release of in-situ stress because of blasting operation which might induce rock destruction or even rock bursts is attracting concern recently ( Yang, et al., 2012; Tao, et al., 2012).

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Appendix A: Swebrec function parameters from curve fitting for the delay cases.

Delay

[ms]

Cut I Xmax

[m2]

X50

[m2] a[-] b[-] c[-] r2[-]

0 259.82 34.84 0.907 1.393 0.907 0.991

1 108.82 5.59 0.730 0.690 1.138 0.995

2 53.09 4.11 0.612 1.296 0.861 0.997

Appendix B: Swebrec function parameters from curve fitting for different primer position cases.

Delay

[ms]

Cut I for the top primer position cases Xmax

[m2]

X50

[m2] a[-] b[-] c[-] r2[-]

1 49.00 12.84 0.581 0.348 0.869 0.993

2 27.23 3.58 0.403 0.826 0.920 0.999

Cut I for the bottom primer position cases

1 37.70 5.79 0.551 0.564 0.918 0.997

2 20.16 2.76 0.144 1.351 0.945 0.998

Delay

[ms]

Cut II for the top primer position cases Xmax

[m2]

X50

[m2] a[-] b[-] c[-] r2[-]

1 72.13 14.45 0.768 0.365 0.801 0.993

2 59.61 12.03 0.982 1.430 1.370 0.992

Cut II for the bottom primer position cases

1 56.46 6.51 -0.17 1.044 0.726 0.996

2 19.46 4.16 0.698 0.811 1.301 0.999

Cut II for the middle primer position cases

1 175.02 5.12 0.712 0.453 1.119 0.995

2 29.91 7.14 0.602 0.815 0.936 0.997

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Appendix C: Swebrec function parameters from curve fitting for non-reflecting boundary conditions cases.

Case

Cut I Xmax

[m2]

X50

[m2] a[-] b[-] c[-] r2[-]

Top primer 165.32 45.73 0.489 0.349 0.616 0.995

Bottom primer 181.25 34.42 0.748 0.701 0.855 0.993

Middle primer 331.90 43.81 0.601 0.969 0.676 0.997

Cut II

Top primer 48.22 9.29 0.929 1.138 0.960 0.993

Bottom primer 131.32 24.79 0.247 3.131 0.581 0.992

Middle primer 262.08 31.56 0.158 1.395 0.791 0.995

Rapport 2010:3 ISSN 1653-5006

Swedish Blasting Research CentreMejerivägen 1, SE-117 43 Stockholm

Luleå University of TechnologySE-971 87 Luleå www.ltu.se

Styckefall i produktionssalvor och kvarn-genomsättning i Aitikgruvan, sammanfatt-ning av utvecklingsprojekt 2002-2009

Fragmentation in production rounds andmill throughput in the Aitik mine, a summaryof development projects 2002-2009

Finn Ouchterlony, SwebrecPeter Bergman, Boliden Mineral ABUlf Nyberg, Swebrec

Universitetstryckeriet, L

uleå

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