Improved blasting results with precise initiation...

Report 2013:2 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 of small-scale tests and full-scale bench blasting

Changping Yi

Universitetstryckeriet, L

uleå

Report 2013:2 ISSN 1653-5006

Improved blasting results with precise initiation – Numerical simulation of small-scale tests and full-scale bench blasting

Changping Yi

i

Summary

A series of numerical simulations of rock blasting has been conducted using the LS-DYNA software in order to test the hypothesis proposed by Rossmanith, stating that interaction of stress waves could result in finer fragmentation by controlling the initiation times. The rock material was simulated with the RHT material model. After the calculation, the elements with damage level above 0.6 were removed to simulate complete fracturing of the rock.

Firstly, a series of numerical simulations were conducted to model the small-scale tests performed by Johnasson et al. (2013). This work also involved simulating initial damage to the rock through previous blasting, and analyzing the resulting effects. The effect of different delay times showed that through a properly chosen delay time, improved fragmentation could be inferred. Moreover, the initial damage (from the previous row) clearly affected the fragmentation; however, the results indicated that longer delay times (in which the stress wave would have passed the boreholes) also resulted in improved fragmentation, implying that stress wave superposition may not be the primary factor governing the fragmentation.

Secondly, full-scale tests conducted at the Aitik open pit mine were modeled. The simulation results indicated that the case of no interacting stress waves (6 ms delay) gavefiner fragmentation at most of the interpretation section cuts compared to the cases of interacting stress waves (0, 1 and 3 ms delay times).

Both the simulation results of small scale tests and full scale tests indicate that the stress wave interaction effect due to delayed initiation can result in finer fragmentation compared to simultanious initiation. However, the results also indicate that relatively long delay times, leading to no stress wave superposition, induce even finer fragmentation compared to the use of very short delay times.

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Contents

1 Introduction ............................................................................................................. 1

1.1 Background ...................................................................................................... 1 1.2 Objective and Scope of Work .......................................................................... 2

2 Methodology ............................................................................................................ 3

3 Selection of simulation method .............................................................................. 6

3.1 Comparison of simulation methods ................................................................. 6 3.2 Influence of ALE Domain ............................................................................. 10

4 Simulation of small-scale tests.............................................................................. 12

4.1 Description of small-scale tests ..................................................................... 12 4.2 Material modeling and constitutive parameters ............................................. 12 4.3 Simulation results for row #1 shots ............................................................... 13

4.3.1 Evaluation of remaining area for row#1 shots ................................. 15 4.3.2 Evaluation of remaining volume for row#1 shots ........................... 17 4.3.3 Analysis of fragment area for row#1 shots ...................................... 18

4.4 Simulation results for row #2 shots ............................................................... 20 4.4.1 Evaluation of remaining area for row#2 shots ................................. 21 4.4.2 Evaluation of remaining volume for row#2 shots ........................... 21 4.4.3 Analysis of fragment area for row#2 shots ...................................... 22

4.5 Discussion and comparison with laboratory tests .......................................... 23 5 Simulation of full-scale tests ................................................................................. 25

5.1 Model set-up .................................................................................................. 25 5.2 Results………………………………………………………………………26

5.2.1 Evaluation method ........................................................................... 26 5.2.2 Overall damage and crack pattern for each case .............................. 26

5.3 Discussion ...................................................................................................... 32 6 Discussion and conclusions ................................................................................... 36

6.1 Discussion ...................................................................................................... 36 6.2 Conclusions .................................................................................................... 37

7 Recommendations ................................................................................................. 38

References ................................................................................................................... 39

Appendix A: Section cuts of full-scale test simulation ............................................ 42

Appendix B: Fitting parameters of full-scale test simulation with the extended Swebrec function ........................................................................................................ 48

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List of figures

Fig.2.1. Methodology used for numerical modeling of small- and full- scale blasting

tests...................................................................................................................3

Fig.2.2. Blasting effect evaluation procedure................................................................5

Fig.3.1. Geometry of the model.....................................................................................7

Fig.3.2. Model comparison between two methods........................................................8

Fig.3.3. Damage distribution for two modeling methods..............................................8

Fig.3.4. The position of selected nodes for the evaluation of two modeling

methods……………………………………………………………………....9

Fig.3.5. Calcualted acceleration in the y-direction vs. time for the two methods…….9

Fig.3.6. Different ALE domains..................................................................................10

Fig.3.7. The position of selected point for the evaluation of different ALE domain...10

Fig.3.8. Calculated acceleration in the y-direction vs. time for two cases of overlap.11

Fig.4.1. Left: Front of set-up for free face shots. Right: Set-up from the back ..........12

Fig.4.2. Geometry of the complete model...................................................................15

Fig.4.3. The position of X1-sections in block 1..........................................................15

Fig.4.4. Overall crack pattern for the 28 μs delay case...............................................15

Fig.4.5. Fragment area pattern at the cross-section.....................................................16

Fig.4.6. The remaining area of X1-sections for the different delay times (DT) …….16

Fig.4.7. The remaining volume of block 1 as a function of delay time.......................17

Fig.4.8. Four evaluated segments................................................................................18

Fig.4.9. The remaining volume of each segment for different delay times (DT)........18

Fig.4.10. The typical fitting curves with Swebrec function(X11 section) ..................19

Fig.4.11. The position of X2-sections in block 2.........................................................20

Fig.4.12. The damage distribution before and after row #2 shot for the 28 μs delay

case..............................................................................................................20

Fig.4.13. The remaining area of X2-section for different delay times (DT) ...............21

Fig.4.14. The remaining volume of block 2 as a function of delay time.....................21

Fig.4.15. The typical fitting curves with Swebrec function (X24 section) .................22

Fig.4.16. X50 versus delay time and row (laboratory test results after Johansson,

2013)…………………………….………………………………………...23

Fig.4.17. X50 versus delay time and row (modeling results) .......................................24

Fig.5.1. The size of problem geometry.........................................................................25

Fig.5.2. Boundary conditions.......................................................................................26

Fig.5.3. Vertical cuts used in the results presentation..................................................26

Fig.5.4. Overall damage distribution and crack pattern for 0 ms delay time case.......27

Fig.5.5. Accumulated area plot for 0ms delay time.....................................................28


Fig.5.7. Accumulated area plot for 1 ms delay time....................................................29


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Fig.5.9. Accumulated area plot for 3 ms delay time....................................................31

Fig.5.10. Overall damage distribution and crack pattern for 6ms delay time case......31

Fig.5.11. Accumulated area plot for 6 ms delay time..................................................32

Fig.5.12. Accumulated area plot for cut x11................................................................32





Fig.5.17.Accumulated area plot for cut x32................................................................35

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List of tables

Table 4.1. Material type, material property input data and EOS input data................14

Table 4.2. Swebrec function parameters from curve fitting (row#1 shots) .................19

Table 4.3. Swebrec function parameters from curve fitting (row#2 shots) .................22

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Improved blasting results with precise initiation Swebrec Report 2013:2

1 Introduction

1.1 Background Blasting technology is widely employed in mining in order to fragment the rock into smaller pieces to facilitate subsequent handling (mucking, haulage, crushing, etc.). The optimum delay time to improve fragmentation has been studied by e.g. Tatsuya et al. (2000), Aldas et al. (2001), Shi & Chen (2011) and Petropoulos et al. (2013a), but different conclusions were obtained. 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 and 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 the shock wave interaction 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 claimed that the very short delays between holes, such as 2 ms, helps to 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 some unexpected results in full-scale experiments. It was found that the fragmentation, with 5 ms and 10 ms of inter-hole delay times, was coarser when electronic detonators were used compared with pyrotechnic caps.

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 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 very short delays. The results showed that fragments 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 are used, fragmentation becomes 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

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Improved blasting results with precise initiation Swebrec Report 2013:2

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 suggests that factors other than overlapping negative tails of waves govern the fragmentation.

Johansson and Ouchterlony (2013) have investigated the influence of delay time on the fragmentation with a series of small-scale tests. Their results showed no distinct differences in fragmentation when there was shockwave interactions compared to no shockwave interaction. Nevertheless, these tests provide an opportunity for validation of numerical simulation of blasting, in this case using the approach of Schill (2012).

1.2 Objective and scope of work

To further study the influence of delay time on blasting effect and fragmentation, a series of numerical simulations of the previously performed small-scale tests (Johansson & Ouchterlony, 2013) were conducted. Also, a four-hole model was constructed to model the full-scale tests conducted at the Aitik mine during the year 2012 (Petropoulos et al., 2013b). 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 method used to model the fragmentation with different delay times is presented in Chapter 2 together with the study scheme. In Chapter 3, the choice of simulation method was investigated. The results of simulation of small-scale tests are presented in Chapter 4 and the results of the full-scale test simuation are presented in Chapter 5. Finally, conclusions are given in Chapter 6 and recommendations in Chapter 7.

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Improved blasting results with precise initiation Swebrec Report 2013: 2

2 Methodology To model the small-scale and full-scale tests, the overall study scheme according to Fig.2.1 was followed.

Fig.2.1 Methodology used for numerical modeling of small- and full- scale blasting

tests

Several numerical methods in LS-DYNA can be employed to model blasting. The conducted small-scale tests comprise a decoupling charge structure with both ends of each blasthole being open. The explosive detonation products first expand into the air gap between the charge and blast hole and then interact with the concrete structure. A part of the products will expand into the air outside the block. According to the charge structure in the small-scale tests, the most suitable method was selected by comparing different methods.

After the determination of modeling method, the simulations of the small-scale tests

were conducted. A model including two rows with five φ10mm blastholes in each row was created. In the laboratory tests, eight delay time schemes were designed and tested. The nominal delay times were 0 μs, 28 μs, 37 μs, 46 μs, 56 μs, 73 μs, 86 μs, and 146 μs respectively. In the small-scale tests, the two rows of blast holes were blasted one at a time, and the resulting fragmented material removed in between. Thus, row#1 shots were modeled with LS-DYNA code and the results were evaluated firstly. To test the initial damage influence on the fragmentation, row #2 shot was modeled with LS-DYNA code with the initial damage caused by row #1 shot. After the calculation for row #1 shot, the stress and damage results of model at the last state were written in an output file. This file was then rewritten back into the model and only the damage values were kept as the initial condition for row #2 shot simulation. For the simulation of the full-scale tests, the exact same approach as Schill (2012) was used.

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A continuum simulation approach was used for the full-scale tests. 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 fragments determined. This fragment identification procedure is not easily done in 3D, but in 2D it is fairly straightforward and a routine was implemented in LS-PREPOST (which is the pre- and post- processor for LS-DYNA). Then by measuring the fragments in a number of vertical and horizontal cuts through the model it was possible to evaluate the fragment area (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, 2005) was employed to fit the fragment areas distribution. Using this method it is possible to study the accumulated area for different fragment areas and compare the fragmentation between different cross-sections and simulations. 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 due to the limited level of discretization, it is not possible to determine fragments less than the element size.

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. 2.2.

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Fig.2.2 Blasting effect evaluation procedure

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3 Selection of simulation method

3.1 Comparison of simulation methods As mentioned earlier, several methods in LS-DYNA can be employed to model blasting. There are two general methods to model the blasting in rock mass. A brief description of both methods is presented as follows.

Method 1: Lagrangian approach

In this method, all elements in the model are Lagrangian. There are two ways to model blasting. One is the sharing nodes method, in which the explosive and the blasted objects have common nodes at the interface. The other approach is the contact method, in which there are no common nodes at the interface between the explosive and the blasted objects. The interaction between the explosive and the blasted objects is calculated by the defining contact. In LS-DYNA, several contact types, such as surface-to-surface contact, sliding-only contact and eroding surface-to-surface contact, can be used to model blasting.

Method 2: Eulerian/ALE approach

In this method, the materials flow (or advect) through the Eulerian/ALE mesh, which is either fixed in space (Eulerian) or moving according to some user-issued directives (ALE. This method is much better suited to modeling of fluid or fluid-like behavior compared to a Lagrangian approach. Usually, the explosive is disintegrated with the ALE mesh and the blasted objects are disintegrated with Lagrangian meshes. Actually, Eulerian is a special case of ALE wherein the prescribed reference mesh velocity is zero. In LS-DYNA, Lagrangian and ALE solutions can be combined in the same model and the fluid structure interaction handled by a coupling algorithm. There are two approaches for coupling ALE and Lagrangian elements when this method is used (Do and Day, 2005). One way is to couple Lagrangian parts to ALE parts with the command of *Constrained_Lagrange_in_solid. In this way, ALE part and Lagrangian part have no merged nodes. Both parts overlap in the space, and their interaction is connected with the command of *Constrained_Lagrange_in_solid. This methody is popularly used to model the Fluid-Structure-Interaction (FSI) problems. As an alternative to the coupling, one can, in some cases, share nodes at the interface between a Lagrangian part and an ALE part. In this way, the shared nodes will move as Lagrangian nodes.

The Lagrangian approach is direct and efficient. But in modeling fluid or fluid-like behavior, the Lagrangian approach, wherein the deformation of the finite element mesh exactly follows the deformation of the material, is often not suitable owing to the very large deformation of the material. Mesh distortion can become severe, leading to a progressively smaller explicit time step and eventual numerical

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instability. The ALE approach with the command of *Constrained_Lagrange_in_solid is good for modeling large deformation problems. Furthermore, the ALE part and Lagrangian part have no common nodes and overlap in space, which is convenient to generate the model and mesh. But ALE approach needs more computation time and memory as compared to Lagrangian owing to the additional advection, interface reconstruction and coupling computations.

In modeling blasting in rock mass, the materials around the explosive are at very high pressure, temperature, and/or strain rate. Under these conditions even structural materials (metal, concrete, soil, etc.) may behave in a fluid-like manner. Thus, such cases may be more suitably modeled with ALE elements. For the small scale tests, both ends of each blasthole are open and there is air in the gap between the explosive and the wall of blasthole, which is a problem of FSI. Therefore, the ALE approach is suited to model this kind of problem.

As mentioned earlier, there are two ways to model blasting with ALE technique. To select the most suitable of these, a three-hole model was built to compare the two methods, see Fig.3.1. The difference between two methods is shown in Fig.3.2. As seen in Fig.3.2 (a), there are no merged nodes between the ALE and the Lagrangian parts. LS-DYNA calculates the interactions between ALE and Lagrangian parts via the command of *Constrained_lagrange_in_solid. As seen in Fig.3.2 (b), The ALE and Lagrangian parts have the merged nodes and their interactions are conducted via the merged nodes.

Fig.3.1 Geometry of the model

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(a)*Constrained_lagrange_in_solid (b) Sharing common nodes

Fig.3.2 Model comparison of two methods: a) *Constrained_lagrange_in_solid and b) Sharing common nodes

A case with a delay time of 73 μs for inter-hole delay was modeled with two methods and the termination time was set as 500 μs. The results in terms of damage are shown in Fig.3.3.The red means full damage.

(a) Constrained_lagrange_in_solid (b) Sharing nodes Fig.3.3 Damage distribution for two modeling methods

When the method of sharing nodes was employed, the simulation terminated due to element distortion around the blast holes at 136 μs. But the calculation reached the defined termination time if the approach of using the command of *Constrained_Lagrange_in_solid was employed.

The y-direction accelerations of the same point during the first 136 μs (see Fig.3.4) with two methods are shown in Fig.3.5.

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(a) Constrained_lagrange_in_solid (b) Sharing common nodes

Fig.3.4 The position of selected nodes for the evaluation of two modeling methods

(a) Constrained_lagrange_in_solid

(b) Sharing nodes

Fig.3.5 Calcualted acceleration in the y-direction vs. time for the two methods studied: a) *Constrained_lagrange_in_solid, and b) Sharing nodes.

Both curves have the similar peak value and similar wave shape initially, see Fig.3.5.But the modeling stopped early with the method of sharing common nodes because of the severe deformation of elements, i.e. the modeling cannot reach the defined time. This approach is thus not suitable to model multi-hole delay initiations. Therefore the method of using the command of *Constrained_Lagrange_in_solid was employed in the continued work.

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3.2 Influence of ALE Domain An overlap between ALE part and Lagrangian part is necessary in order to use the command of *Constrained_Lagrange_in_solid. The influence of overlap domain is studied as follows. Two cases were simulated with radiuses of 10 r0 and 3 r0 of the blasthole, see Fig.3.6. A case with a delay time of 46 μs for inter-hole delay was modeled with two ALE domains.

(a) R=10r0

(b) R=3r0 Fig.3.6 Different ALE domains

R is the radius of ALE domain and r0 is the radius of blast hole. Similarly, the y-direction accelerations of same point (see Fig.3.7) during the first 200 μs with two radius ALE domain are shown in Fig.3.8.

(a) R=10r0 (b) R=3r0

Fig.3.7 The position of selected points for the evaluation of different ALE domains

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(a) R=10r0

(b)R=3r0

Fig.3.8 Calculated acceleration in the y-direction vs. time for two cases of overlap.

Both curves have similar peak values and wave shapes, see Fig.3.8, which indicates that taking the radius of ALE domain as three times the radius of the blasthole is sufficient.

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4 Simulation of small-scale tests

4.1 Description of small-scale tests To test the hypothesis that the short delay times can improve fragmentation, Johansson and Ouchterlony (2013) carried out a series of small-scale tests. The tests were made on magnetic mortar blocks. The blocks had a size of 660×205×300 mm

(L×W×H) with two rows with five φ10 mm blastholes in each row. The spacing and burden was 110 mm and 70 mm respectively. To minimize reflecting waves and to emulate full-scale geometry, the block was confined by a U-shaped yoke, see Fig.4.1.

Fig.4.1 Left: Front of set-up for free face shots. Right: Set-up from the back.

(Johansson and Ouchterlony, 2013)

The explosive source was decoupling PETN-cord with the strength of 20 g/m, giving a specific charge (q) of 2.6 kg/m3. The coupling ratio was 2.4 based on an explosive density of 1400 kg/m3. The delay times were achieved by using different PETN-cord lengths to adjust the delay times between the blastholes. Above each blasthole, a 59 mm high cylindrical initiation mounting block of plastic was positioned; thus both ends of each blasthole can be treated as open. After the blasting, the fragments were sieved and the fragment size distribution was taken as the evaluation indicator.

The model set-up made it possible to shoot two rows per mortar block. The initiation sequence of row #1 was from left to right. After row #1 shot of one mortar block, row #2 was initiated with the same delay time as row #1 shot but with opposite initiation sequence to row #1 shot. Eight delay time schemes were designed and tested. The nominal delay times of inter hole delay were 0 μs, 28 μs, 37 μs, 46 μs, 56 μs, 73 μs, 86 μs, and 146 μs respectively.

4.2 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).

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1 2

1 2

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

− − = − + − +

(4.1)

where p is the pressure, A, B, R1, R2 and w are constants; V and E are the specific volume and the internal energy respectively. The parameter values of PETN used in simulation are from the material library of Autodyn (Ansys/Autodyn, 2007).

The air was modeled with the null material model combined with the linear-polynomial equation of state.

2 3 20 1 2 3 4 5 6 0ipvP C C C C C C C eμ μ μ μ μ = + + + + + + (4.2)

Perfect gas can be modeled by letting 0 1 2 3 6 0C C C C C= = = = = and 4 5 1C C γ= = − .

eipv0 is internal energy/reference volume0

-1ρμρ

= with 0

ρρ

the ratio of current

density to initial density. γ is the ratio of specific heats. The parameter values of air

are from Do et al. (Do and Day, 2005).

The concrete was modelled 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 & Riedel, 2011). The parameter values of concrete used in simulations are from Johansson (Johansson, 2008) and Borrvall (Borrvall & Riedel, 2011).

The yoke was modeled as a rigid body because it was much stiffer than the concrete. All the used parameters for each material model are given in Table 4.1.

4.3 Simulation results for row #1 shots The complete calculation model is shown in Fig.4.2. There are over 7 million elements and the resolution (minimum element size) is 2 mm. To study the influence of row #1 shots on the row #2 shots, the block was divided into three parts with the same material parameters. The initiation sequence of row #1 was from left to right.

Here, the red part is defined as block 1, the blue part (the middle one) is defined as block 2 and the green part is defined as block 3, respectively.

To evaluate the fragmentation of each case, four cross-sections were evaluated, see Fig.4.3. A consistent naming convention was used in which e.g. X12 in Fig.4.3 means the second cross-section with its x-normal direction in block 1 (the rest may be deduced by analogy). Each X1-section is located at the exact center between the two adjacent blastholes. Then the remaining area of each cross section was calculated and compared where elements with damage levels above 0.6 were blanked out. The damage levels were evaluated at 1000 μs for all simulations and then the fragment

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size distribution of each cross section was calculated and compared. An example of the overall crack pattern for the 28 μs delay case is shown in Fig.4.4.

Table 4.1 Material type, material property input data and EOS input data

Mater-ials

Parameters of different materials(unit:g,cm,μs)

Concre-te

*MAT_RHT

RO SHEAR ONEMPA EPSF B0 B1 T1

2.511 8.98E-2 1.e-5 2. 1.22 1.22 3.527e-1

A N FC FS* FT* Q0 B T2

1.6 0.61 50.7e-5 0.18 0.08 0.6805 0.0105 0.0

E0C E0T EC ET BETAC BETAT PTF

3.e-11 3.e-12 3.e22 3.e22 0.032 0.036 0.001

GC* GT* XI D1 D2 EPM AF NF

0.53 0.7 0.5 0.04 1. 0.01 1.6 0.61

GAMMA A1 A2 A3 PEL PCO NP ALPHA0

0. 3.527e-1 3.958e-1 9.04e-2 0.233e-3 6.e-2 3.0 1.1884

Explos-ive

*MAT_HIGH_EXPLOSIVE_BURN

RO D PCJ

1.4 0.736 0.20

*EOS_ JWL

A B R1 R2 OMEG E0 V0

6.253 2.3290E-2 5.25 1.60 0.280 8.56E-2 1.00

Air

*MAT_NULL

RO PC MU

1.29E-3 0 0

*EOS_LINEAR_POLYNOMIAL

C0-C3 C4 C5 C6 E0 V0

0.0 0.4 0.4 0.0 2.5E-6 1.0

Rigid *MAT_RIGID

RO E PR

4.5e2 21 0.3

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Fig.4.2 Geometry of the complete model

Fig.4.3 The position of X1-sections in block 1

Fig.4.4. Overall crack pattern for the 28 μs delay case

4.3.1 Evaluation of remaining area for row#1 shots The fragment area patterns at the X12 and X14 cross-sections for the 28 μs delay case are shown in Fig.4.5. The remaining areas of the X1-sections for different delay times are shown in Fig.4.6.

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X12-section X14-section

Fig.4.5 Fragment area pattern at the cross- section

20

30

40

50

60

70

80

90

X11 X12 X13 X14

Rem

ain

ing

Are

a [c

m2]

The number of X1-sections

DT0

DT28

DT37

DT46

DT56

DT73

DT86

DT146

Fig.4.6 The remaining area of X1-sections for the different delay times (DT).

DT0 means that the inter-hole delay time is 0 μs in Fig.4.6, and the rest may be deduced by analogy. The figure indicates that the remaining areas at the X11 section show a decreasing tendency with the increase of delay time except for the 46 μs and 146 μs delay case. The figure shows that the remaining area is slightly larger for the 46 μs delay case than for the 37 μs delay case. The figure also shows that the remaining area is greater for the 146 μs delay case than for the 86 μs delay case at the X11 section.

The remaining areas at the X12 section show similar tendencies apart from the 146 μs delay case. The remaining area at the X12 section is greater for the 146 μs delay case than for 56 μs, 73 μs and 86 μs delay cases, see Fig.4.6.

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For the X13 section, the remaining area decreases with increasing delay time while the delay time is less than 37 μs. When the delay time is longer than 37 μs, the change of remaining area is more complex. The 46 μs, 56 μs and 146 μs delay cases have approximately same remaining area and the remaining area is smallest for the 73 μs delay case, see Fig. 4.6.

For the X14 section, the 86 μs delay case results in the smallest remaining area compared to the other cases. Simultaneous initiation yields the largest remaining area at each cross section compared to the initiations with longer delay time, see Fig.4.6.

In general, the remaining area at the same cross-section decreases with increasing delay time except for the 146 μs delay case. For all delay cases, the X11 section always has the largest remaining area and the X14 section always has the smallest remaining area. The remaining area at X12 section is greater than that at X13 section for some cases but it is the opposite for other cases.

4.3.2 Evaluation of remaining volume for row#1 shots The overall remaining volume of block 1 vs. delay times is shown in Fig.4.7. It indicates that the 86 μs delay case has the lowest remaining volume, which implies that most elements for the 86 μs delay case were damaged above the 60%-level compared to other cases.

3000

3500

4000

4500

5000

5500

0 30 60 90 120 150

Rem

aini

ng v

olum

e/cm

3

Delay time/μs Fig.4.7 The remaining volume of block 1 as a function of delay time

To evaluate the influence of the stress wave superposition on fragmentation, the remaining volumes of four segments in Fig.4.8 were compared. The results are shown in Fig.4.9. The figure shows tendencies similar to Fig.4.6 except for the 146 μs delay case. The figure indicates that the remaining volumes of the S13 segment is not smallest where stress waves interaction could be expected for short delay times. The 146 μs delay case resulted in the lowest remaining volume at the S11, S12 and S13 segments. The cases of 73 μs, 86μs and146 μs delay times had approximately equal remaining volumes at the S14 segment.

18


Fig.4.8 Four evaluated segments

300

400

500

600

700

800

900

S11 S12 S13 S14

Rem

aini

ng v

olum

e/cm

3

The number of segment

DT0

DT28

DT37

DT46

DT56

DT73

DT86

DT146

Fig.4.9 The remaining volume of each segment for different delay times (DT).

4.3.3 Analysis of fragment area for row#1 shots 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 (2005), was confirmed to be effective to describe the fragment size distribution (Ouchterlony, 2009; Sanchidrian et al., 2012). The Swebrec function includes the basic Swebrec function and the extended Swebrec function. They have three parameters and five parameters, respectively. The basic Swebrec function was employed to fit the fragment area distribution of the numerical results of small-scale tests.The basic Swebrec function reads, with P(x) being the fraction passing a sieve of size x:

}{ max max 50( ) 1/ 1 [ln( / ) / ln( / )] bP x x x x x= + (4.3)

The fitting parameters are the size values 50x and maxx plus the undulation exponent b.

In this study, some areas were defined to resemble the sieve mesh sizes. The function was then employed to fit the fragment area distribution of each cross-section. The typical fitting curve is shown in Fig.4.10. The fitting parameters for each cross-section are listed in Table 4.2. The minimal value of the coefficient of determination r2 is 0.955, which indicates that the fit is good.

19


0,1

1

0,01 0,1 1 10 100

Acc

umul

ated

are

a [-

]

Rock fragment area [cm2]

DT0 Numerical result

DT0 Fitting curve

Fig.4.10 The typical fitting curves with Swebrec function (X11 section)

Simultaneous initiation induced the largest average fragment area at all four cross-sections; see Table 4.2, which means that the fragmentation is coarser for simultaneous initiation than for delayed initiation. Table 4.2 also shows a general tendency that the average fragment area decreases with the increase of delay time at each cross-section except for the 146 μs delay case. The 73 μs and 86 μs delay cases generally results in finer fragmentation at each cross-section than the other cases.

Table 4.2 also indicates that the fragmentation of the X11 cross-section is not always coarser than that of other cross-sections, which implies the stress wave superposition does not improve the fragmentation of these cross-sections.

Table 4.2 Swebrec function parameters from curve fitting (row#1 shots)

Delay [μs]

X11 X12 Xmax[cm2] X50[cm2] b[-] r2[-] Xmax[cm2] X50[cm2] b[-] r2[-]

0 55.07 1.72 3.25 0.999 27.42 2.44 2.32 0.992 28 47.04 0.76 3.06 0.999 21.11 0.71 2.70 0.998 37 36.65 0.37 3.94 0.991 72.07 0.36 3.50 0.982 46 28.03 0.44 3.03 0.992 57.19 0.34 3.74 0.982 56 16.85 0.31 2.56 0.985 20.74 0.16 3.03 0.981 73

23.76 0.19 3.17 0.985 14.87 0.14 3.11 0.97

1 86 26.08 0.19 3.30 0.985 47.27 0.13 3.81 0.971

146 4.56 0.23 1.27 0.959 29.49 0.18 2.97 0.968 Delay [μs]


0 28.11 1.87 2.67 0.997 31.69 1.75 2.93 0.992 28 51.67 1.24 2.26 0.982 11.00 1.02 1.92 0.992 37 23.83 0.65 2.63 0.993 48.45 0.70 2.53 0.984 46 15.28 0.30 2.49 0.990 8.00 0.37 2.13 0.990 56 11.95 0.32 1.83 0.967 85.45 0.23 3.46 0.971 73 5.19 0.21 1.41 0.955 10.67 0.14 3.11 0.970 86 27.68 0.26 2.15 0.968 6.25 0.08 3.88 0.973

146 8.51 0.31 2.02 0.986 30.89 0.13 3.59 0.967

20


4.4 Simulation results for row #2 shots To test the initial damage influence on the fragmentation, row #2 shots were modeled with the initial damage caused by row #1 shot. The initiation sequence of row #2 shots was right to left, which is opposite to that of row#1 shots. The position of evaluation cross-sections in block 2 is shown in Fig.4.11.

Fig. 4.11 The position of X2 sections in block 2

As an example, the initial damage distribution and the ultimate damage distribution for the 28 μs delay case are shown in Fig.4.12. The red color in Fig4.12 means full (100%) damage.

(a) The initial damage distribution before row #2 shot

(b) The damage distribution after row #2 shot

Fig.4.12 The damage distribution before and after row #2 shot for the 28 μs delay case

21


4.4.1 Evaluation of remaining area for row#2 shots The remaining area of each section of row #2 shots is shown in Fig.4.13.

0

20

40

60

X21 X22 X23 X24

Rem

aini

ng a

rea

[cm

2 ]

The number of section

DT0

DT28

DT37

DT46

DT56

DT73

DT86

DT146

Fig.4.13 The remaining area of X2 section for different delay times (DT).

Because of the effect of initial damage and the opposite detonation sequence compared to row #1 shots, the interpretation of the remaining area at each cross-section is more complex compared to the corresponding cross-sections in row 1, see Fig.4.13. The figure indicates that when the delay time is shorter than 46 μs, the remaining area at each cross-section decreases with the increase of delay time. Fig.4.13 also shows that the 146 μs delay case has less remaining area than other two cases at X23 and X24 sections; the same is however not true at the X21 section.

4.4.2 Evaluation of remaining volume for row#2 shots The overall remaining volume of block 2 vs. delay time is shown in Fig.4.14. The figure indicates that the remaining volume decreases with the increase of delay time for the cases when the delay time is less than 73 μs. For longer delay times, the remaining is more-or-less the same for all cases. The largest and lowest remaining volumes belong to the cases with simultaneous initiation and 73 μs respectively.

1500

2000

2500

3000

0 30 60 90 120 150

Rem

aini

ng v

olum

e/cm

3

Delay time/μs Fig.4.14 The remaining volume of block 2 as a function of delay time

22


4.4.3 Analysis of fragment area for row#2 shots A typical fragment area distribution fitted with Swebrec function at the X24 section is shown in Fig.4.15 after row #2 shots. The fitting parameters for each cross-section are listed in Table 4.3.

0,1

1

0,01 0,1 1 10

Acc

umul

ated

are

a [-

]

Rock fragment area [cm2]

DT28 Numerical results

DT28 Fitting curve

Fig.4.15 The typical fitting curves with Swebrec function (X24 section)

Table 4.3 shows that X50 of each cross section is small compared to that in Table 1, which implies that the fragmentation of block 2 is finer. The same conclusion was stated by Johansson and Ouchterlony (2013).

Table 4.3 Swebrec function parameters from curve fitting (row#2 shots)

Delay [μs]


0 58.78 0.195 3.66 0.980 16.40 0.411 2.11 0.984 28 14.63 0.143 2.66 0.945 102.03 0.114 4.02 0.970 37 15.46 0.056 5.39 0.979 40.00 0.122 3.04 0.971 46 47.86 0.043 5.58 0.968 8.76 0.046 3.88 0.953 56 1.11 0.044 3.34 0.959 14.91 0.035 3.41 0.920 73 30.28 0.041 4.72 0.963 10.95 0.042 5.78 0.926 86 1.91 0.043 4.35 0.979 3.12 0.031 4.14 0.966 146 2.20 0.029 4.83 0.976 1.64 0.029 5.24 0.983

Delay [μs]


0 18.68 0.215 3.02 0.988 6.19 0.399 1.48 0.948 28 11.35 0.129 2.06 0.970 4.94 0.291 1.34 0.971 37 22.54 0.051 4.72 0.940 19.83 0.059 3.78 0.944 46 61.17 0.069 5.47 0.973 23.35 0.077 3.41 0.968 56 3.61 0.042 5.43 0.961 12.49 0.043 2.97 0.901 73 2.41 0.039 5.54 0.903 21.62 0.029 5.00 0.924 86 2.00 0.036 5.47 0.864 9.23 0.046 3.02 0.976 146 33.84 0.053 4.01 0.947 1.06 0.032 5.27 0.980

23


4.5 Discussion and comparison with laboratory tests For row#1 shots, by comparing the remaining volumes, the remaining areas and the fragment area distribution of each cross-section, the results show that a short delay time can improve the blasting effect compared to simultaneous initiation. The simulation results also indicate that the cases of 73 and 86 μs delay, which are Vanbrabant’s recommendations scheme (Johansson & Ouchterlony, 2013) results in a finer fragmentation compared to the other cases. Thus, the optimal delay time may be in the interval between 73 and 86 μs for row #1 shot. However, the fragmentation of the 73 and 86 μs delay cases is only slightly finer than that of the 146 μs delay case and there is no stress wave interaction in the 146 μs delay case.

For row#2 shots, the numerical simulations results show that the fragmentation of row#2 shots is finer than that of row#1 shots. Table 4.3 indicates that the value of X50 of each cross-section with the increase of delay time is oscillatory. The reason is that which implies that the initial damage has a significant effect on the fragmentation.

To compare the modeling results and the test results, the average values of the mean fragment size of four evaluated cross-sections for row 1 and row 2 were calculated. The relation between the mean fragment size and the delay time of the test results are shown in Fig. 4.16 and the modeling results are shown in Fig.4.17.

0

20

40

60

80

0 50 100 150 200

Delay time[μs]

Mean fragment size[mm]

Row 1

Row 2

Fig.4.16 X50 versus delay time and row (laboratory test results after Johansson and Ouchterlony, 2013)

24


0

50

100

150

200

250

0 50 100 150 200

Delay time[μs]

Mean fragment size,X50[mm2]

Row 1

Row 2

Fig.4.17 X50 versus delay time and row(modeling results)

Both results show that for row 1 shots, there is a general tendency of the fragmentation to decrease with increasing delay time over the interval 0 ≤Δt≤ 146 µs. The tendency is more obvious in the modeling results. For row 2 shots, both results have the similar tendency. The laboratory test results and the modeling results show that simultaneous ignition induces the coarsest fragmentation. The results of small-scale tests indicate that the mean fragment size of row 2 shots are always less than that of the row 1 shots except for the 146 µs delay case, which implies the initial damage caused by row 1 shots has a positive effect on the fragmentation of row 2 shots.

25


5 Simulation of full-scale tests

5.1 Model set-up To test the hypothesis proposed by Rossmanith, a series of field tests have been performed at the Aitik open pit mine (Petropoulos et al., 2013b). The corresponding numerical modeling of the field tests is presented in this Chapter. A four-blasthole model was constructed to model the field tests. The model geometry and the sizes are shown in Fig 5.1 and the boundary conditions used in simulations are shown in Fig 5.2. The blasthole diameter is 310 mm. The green part in the model geometry was selected to be evaluated after blasting. The element size of the green part is 6 cm and the element size of the yellow part is 12 cm. The total number of elements is over 23 million. Four inter-hole delay cases were modeled in this section. The inter-hole delay times were 0 ms, 1 ms, 3 ms and 6 ms respectively. The 0 ms delay case will be used as a reference model. The initiation sequence is from right to left. The simulations of the 0 ms delay case and the 1 ms delay case were run to 15 ms. The simulation of the 3ms delay case was run to 18 ms and the simulation of the 6 ms delay case was run to 25 ms. The primer is located at the bottom of the blast holes.

As mentioned earlier, the exact same simulation approach as Schill (2012) was used for the simulation of the full-scale tests. The boundary between the rock and explosives are modeled with Eulerian elements to account for the large deformations in this interface. The Eulerian elements are merged to the Lagrangian elements. The radius of the interface between the Eulerian elements and the Lagrangian mesh is 0.5 m, see Fig.5.1.

Fig.5.1 Model size

26


Fig.5.2 Boundary conditions

5.2 Results

5.2.1 Evaluation method As mentioned before, the crack and fragmentation were simulated by removing the elements with the damage level above 0.6. The remained volumes of the evaluated region were compared for different delay cases after the elements with the damage level above 0.6 were removed. Then some cuts (cross-sections) were selected, see Fig.5.3, and the fragmentation of each cut was evaluated and the remaining area of the cuts were compared.

Fig.5.3 Vertical cuts used in the results presentation

5.2.2 Overall damage and crack pattern for each case The overall damage and crack pattern of different cases are shown in Fig.5.4, Fig.5.5, Fig.5.6 and Fig.5.7.

27


(a) Damage distribution for 0 ms delay time case at 15 ms

(b) Overall crack pattern for 0 ms delay time case at 15 ms Fig.5.4 Overall damage distribution and crack pattern for 0 ms delay time case

For the 0 ms delay time case, the results showed that the damage and crack distribution are roughly symmetric around the blastholes. The stress waves from different blastholes meet at the center line between the adjacent boreholes, see Fig.5.4. In Appendix A, the different vertical cuts are presented. The accumulated area distribution of each cut was fitted with the extended Swebrec function (Ouchterlony, 2005) and is shown in Fig.5.5. All fitting parameters of each section cut are presented in Appendix B. By observing the accumulated area plot in Fig.5.5, it can be concluded that the simulation results are similar for the cuts that have the same distance from the adjacent blast hole. i.e., the cuts of X11, X21 and X31 have similar fragment area distribution curves. The same results can be found for the cuts of X12, X22 and X32. Fig.5.5 also indicates that the fragmentation of cuts that are closer to the blast hole is finer than the cuts that are at the exact center between two adjacent blast holes.

28


Fig.5.5 Accumulated area plot for the 0 ms delay time

(a)Damage distribution for 1ms delay time at 15 ms

(b) Overall crack pattern for the 1 ms delay time case at 15 ms

Fig.5.6 Overall damage distribution and crack pattern for 1 ms delay time case

29


The overall damage distribution and crack pattern for the 1 ms delay time case is shown in Fig.5.6. The results show that the location of interacting stress waves is at the left side of blast holes, except the first blast hole, for which the location is found at the exact middle of two adjacent blastholes for the 0 ms delay time case. The crack pattern around the first blast hole is symmetric but the crack pattern around the other blast holes is shifted away from the first blast hole.

The fitting curves of the fragment area distribution of each cut with the five-parameter Swebrec function for the 1 ms delay time are shown in Fig.5.7. The result shows that these curves are quite similar, which indicates that all cuts have a similar fragmentation level.


The overall damage distribution and crack pattern for the 3 ms delay time case is shown in Fig.5.8. The damage distribution and crack pattern for the 3 ms delay time case is similar to the 1 ms delay time case. But the high level damage zone is located more to the left compared to the 1 ms delay time case. The same phenomenon can be found for the crack pattern.

30


(a) Damage distribution for the 3 ms delay time at 18 ms


Fig.5.8 Overall damage distribution and crack pattern for the 3 ms delay time case

The accumulated area plot for the 3 ms delay time is shown in Fig.5.9. The result shows that the finest fragmentation is found in cut x31 and the coarsest fragmentation is found in cut x11, which indicates that both the finest fragmentation and the coarsest fragmentation are found in the cuts that are closest to the blast holes.

The overall damage distribution and crack pattern for the 6 ms delay time case is shown in Fig.5.10. The damage distribution and crack pattern for the 6 ms delay time case becomes even more shifted to the left. Fig.5.10 (a) indicates that there is no effect from primary stress wave interaction.

31



(a)Damage distribution for the 6 ms delay time at 25 ms


Fig.5.10 Overall damage distribution and crack pattern for the 6 ms delay time case

32


The fragmentation is even more scattered between the cuts in the the 6 ms delay time case, see Fig.5.11.The finest fragmentation is found in cut X12 and the coarsest fragmentation is found in cut X11.The fragmentation of cut X21 is finer than that of cut x31 although they have the same distance from the adjacent blasthole. Cut X22 also shows finer fragmentation than cut X32.


5.3 Discussion The simulation results of full-scale tests show that the longer the delay time is, the more scattered the fragmentation is. The fragmentation of each cut with different delay times are compared in this section.

Fig.5.12 Accumulated area plot for cut X11

33


The fragmentation of cut X11 with different delay times is shown in Fig.5.12. The result shows that all cases have similar fragment area distribution curves, which indicates the delay time has little effect on the fragmentation in cut X11.

By studying the accumulated area plot of cut X12, see Fig.5.13, the results show that the delay time has a rather large effect on the fragmentation in this cut. The results also indicate that the longer the delay time is, the finer the fragmentation is.


The accumulated area plot for cut X21 is shown in Fig.5.14. The figure shows that 6 ms delay time yields the finest fragmentation in this cut. The 0 ms and 1 ms cases yield roughly the same level of fragmentation in this cut.


For cut X22, the finest fragmentation is again found in the simulation with 6 ms delay, see Fig.5.15. There is no interaction of stress waves when the delay time is 6

34


ms, which indicates that there are other factors rather than stress wave interaction that affect the fragmentation the most.


The accumulated area plot for cut x31 is shown in Fig.5.16. The figure shows that the 3 ms delay time yields the finest fragmentation in this cut and that the 6 ms delay time yields the second finest fragmentation.


35


The accumulated area plot for cut X32 is shown in Fig.5.17. The finest fragmentation is again found for the simulation with 3 ms delay time, and the 6 ms delay time yields the second finest fragmentation.


36


6 Discussion and conclusions

6.1 Discussion The fragmentation of rock under the action of blasting is complicated and a function of the initiation and propagation of cracks in the rock mass. The initiation and propagation of cracks in the rock mass can be modeled with several approaches in the LS-DYNA code. The approach in the report that removes the elements with the damage level above a certain value to simulate the fragmentation is one of them. This approach can provide a rough estimation of fragmentation. But the drawbacks of this approach are also obvious. First, it is hard to select a rational evaluation region because the blasted rock mass does not separate from the bench and no muck pile is formed. This is the possible reason why the largest fragment area of section cuts exceeds 20 m2 in numerical results, which is clearly unrealistic. As mentioned earlier, another drawback is that the size of crack and fragments depends on the size of the elements.

Some researchers have tried to model the fragmentation of rock with other methods. For example, the Hybrid Stress Blasting Model (HSBM) can be used to model the fragmentation process of rock, which uses a unique combination of continuous and discontinuous numerical methods to represent the key processes occurring in non-ideal detonation, rock fracturing and muck pile formation (Hustrulid, et al., 2009). However, there are some weaknesses associated with this model (Hansson, 2009). The combined finite-discrete element method (FEM/DEM) has also been employed to model the fragmentation of the rock mass (Munjiza et al., 2000). Discontinuous Deformation Analysis (DDA) method was also used to model the breakage of rock (Ning et al., 2009).

Despite a lot of work has been done in the past to study the physics of fracture and fragmentation patterns, a break-through numerical technology in the failure simulation is still missing. The main difficulty emanates from the inherent multi-scale nature of failure process. For example, the crack initiation and propagation are affected by the presence of flaws at the micro-scale and multiple cracks occur through a complex communication process of stress-wave interactions between them (Guo and Wu, 2010(a)). The new fracture simulation methods, Element-Free Galerkin (EFG) method and Extended Finite Element Method (XFEM), in LS-DYNA (Guo and Wu, 2010(b)) are being improved and they could be suitable to model the fragmentation of rock mass in the future. A new code named IMPETUS Afea Solver seems to be able to model fragmentation because of blasting too. It can simulate large deformations with higher order elements and supports the GPU acceleration, which improves calculation speeds (http://www.impetus-afea.com).

37


6.2 Conclusions

Based on the simulations of the small-scale tests and the full-scale tests, the following may be concluded:

Small-scale tests

1) The fragmentation for simultaneous initiation is always coarser compared with initiation with delay times.

2) The delay time has a clear effect on the rock fragmentation. Although a short delay time can improve the fragmentation compared to simultaneous initiation, the finest fragmentation was found for relatively long delay times implying that stress wave superposition may not be the primary factor governing fragmentation.

3) The simulation results showed that the optimal delay time may be in the interval between 73 to 86 μs for row#1 shot in the small scale tests, i.e. the optimal delay time may be in the interval between 1.04 ms/m of burden to 1.23 ms/m of burden. .

4) The initial damage from row#1 shots has a significant effect on the rock fragmentation of row#2 shots, which makes the fragmentation finer in the small-scale tests.

Full-scale tests

1) The 6 ms delay time yields the finest fragmentation at the cuts of X11, X12, X21and X22, while 3 ms delay time yields the finest fragmentation at the cuts of X31 and X32.

2) The simulation results indicate that the case of no interacting stress waves (6 ms delay) yields the finer fragmentation for most of the intepretation section cuts compared to the cases with interacting stress waves (0, 1 and 3 ms delay times).

In general, the simulation results of both small and full-scale tests indicate that a delayed initiation can improve fragmentation compared to simultaneous initiation. However, the results do not support the hypothesis that the quite short delay time can improve blasting effect due to the stress wave interaction.

38


7 Recommendations Due to the lack of information about the parameters of the rock in Aitik mine, the parameters of Westerly granite (Schill, 2012) were used in the simulation of full-scale bench blasting. It may be beneficial to retrieve the rock characteristics and model the blasting effects using the real parameters. In that case the comparison of numerical simulations results with the field tests may lead to clearer conslusions. 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. The conclusion of field tests is different from the conclusion from numerical simulation. The field test results indicate that the bench with inter-hole delay time of 3 ms gave the finest fragmentation among all trials (Petropoulos, et al., 2013b). The field test results also indicate that although the x80 and xmax values are significantly smaller, the improvement of the mean fragment size is negligible. The results from field trials and numerical simulations showed the need for further investigation of the short delay times, with more detailed data acquisition. Compared to the simulation of row#2 shot in small-scale tests, the initial damage induced by last blasting operation in the bench to be blasted was not taken into account in simulations of full-scale tests. A larger model (more than one row) is worth to be simulated to investigate the influence of initial cracks on the fragmentation for the full scale tests.

The fragment area indentifaction routine provides a way to evaluate the blasting fragmentation, which can reflect the blasting effect to some extent. The accumulated fragment area plot greatly depends on the location of the evaluated cut. How to calculate the volume of the fragment and then get its characteristic size is needed to be further studied. Calculating the characteristic size of the framents is convenient to compare the results of numerical simulation and the field trials. According to the idea of stress wave interaction, it is interest to investigate using the superposition of stress wave from different boreholes to reduce the blasting-incduced vibration in the field where is far from the blasting area. The far field can be taken as an elastic area compared to the blasting area. If the positive phase of stress wave from one borehole and the negative phase of stress wave from the adjacent borehole overlap in the far field, the blasting-induced vibration is reduced.

39


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42


Appendix A: Section cuts of full-scale test simulation

0 ms delay 1 ms delay


X11 section

43




X12 section

44




X21 section

45




X22 section

46




X31 section

47




X32 section

48

Impr

oved

bla

stin

g re

sult

s w

ith p

reci

se in

itia

tion

Sw

ebre

c R

epor

t 201

3:2

App

endi

x B

: Fitt

ing

para

met

ers o

f ful

l-sca

le te

st si

mul

atio

n w

ith th

e ex

tend

ed S

web

rec

func

tion

Del

ay

[ms]

X11

D

elay

[ms]

X12

X

max

[m2 ]

X50

[m2 ]

a[-]

b[

-]

c[-]

r2 [-

] X

max

[m2 ]

X50

[m2 ]

a[-]

b[

-]

c[-]

r2 [-

]

0 22

.00

4.10

0.

913

1.21

5 0.

928

0.99

8 0

18.0

0 3.

06

0.30

3 0.

544

0.78

6 0.

998

1 24

.00

2.86

0.

211

0.31

9 0.

681

0.99

9 1

22.0

0 2.

34

0.19

2 0.

261

0.69

5 0.

999

3 14

.00

3.97

0.

059

1.65

9 0.

495

0.99

5 3

12.0

0 1.

47

0.34

0 3.

530

0.48

1 0.

998

6 12

.00

3.38

0.

028

2.24

4 0.

470

0.99

6 6

9.00

0.

92

0.53

1 3.

741

0.29

8 0.

999

Del

ay

[ms]

X21

D

elay

[ms]

X22

X

max

[m2 ]

X50

[m2 ]

a[-]

b[

-]

c[-]

r2 [-

] X

max

[m2 ]

X50

[m2 ]

a[-]

b[

-]

c[-]

r2 [-

]

0 19

.00

3.58

0.

535

1.04

5 0.

637

0.99

6 0

18.0

1 2.

43

0.08

0 4.

743

0.55

7 0.

999

1 21

.00

3.36

0.

420

0.41

0 0.

683

0.99

6 1

24.0

0 3.

47

0.64

8 0.

997

0.78

0 0.

997

3 7.

00

2.14

0.

012

3.24

9 0.

467

0.99

5 3

9.06

1.

60

0.18

6 1.

843

0.68

2 0.

999

6 9.

00

1.51

0.

353

3.08

5 0.

343

0.99

3 6

14.0

0 1.

36

0.09

7 2.

244

0.70

4 0.

998

Del

ay

[ms]

X31

D

elay

[ms]

X32

X

max

[m2 ]

X50

[m2 ]

a[-]

b[

-]

c[-]

r2 [-

] X

max

[m2 ]

X50

[m2 ]

a[-]

b[

-]

c[-]

r2 [-

]

0 19

.00

3.24

0.

079

1.27

3 0.

542

0.99

5 0

18.0

9 2.

97

0.07

2 1.

273

0.72

7 0.

998

1 22

.00

3.73

0.

005

4.30

0 0.

516

0.99

6 1

24.0

0 2.

82

0.28

0 0.

457

0.73

3 0.

997

3 8.

00

1.38

0.

032

3.00

2 0.

598

0.99

9 3

13.0

0 1.

66

0.06

0 4.

945

0.52

0 0.

999

6 15

.00

2.53

0.

078

2.92

8 0.

546

0.99

2 6

13.0

0 2.

22

0.25

1 3.

283

0.42

7 0.

996

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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