Discrete element modelling of blast fragmentation of a mortar cylinder. Changping Yi Daniel Johansson

Transcription

1 Discrete element modelling of blast fragmentation of a mortar cylinder Changping Yi Daniel Johansson

2 Outline Introduction Background Particle Blast Method(PBM) for explosive modelling Bonded Particle Model(BPM) for solid modelling Blast modelling with PBM/BPM Results Concluding remarks

3 Introduction Background Numerical methods are becoming increasingly popular in rock blasting simulation. FEM Finite element method FDM Finite difference method DDA Discontinuous deformation analysis NMM Numerical manifold method DEM Discrete element method

4 Background Numerical modeling of rock blasting includes: (a)detonation and blast gas behavior, (b)fracturing and throwing of rock. Most existing researches focus on the rock fracture while ignore the detonation and the blast gas behavior. Some blasting models comprising blast gas were proposed but the blast gas behavior was oversimplified in these models.

5 Particle blast method(pbm) for explosive modelling Kinetic Molecular Theory (KMT) Accurately describe the properties of ideal gases The effect of transient gas dynamics and thermodynamics A particle represents a set of finite air or gas molecules Corpuscular particle method(cpm) Model airbag development The effect of co-volume Particle blast method (PBM) Simulate blast effects on structures

6 Particle blast method(pbm) for explosive modelling One particle represents ~ molecules Molecules Particles

7 Particle blast method(pbm) for explosive modelling Parameters to characterize explosive ρ Density E 0 Internal energy D Detonation velocity V Co-volume γ Ratio of heat capacities (Cp/Cv)

8 Particle blast method(pbm) for explosive modelling Simulation of a cylinder test (After Børvik et al, 2011 )

9 Particle blast method(pbm) for explosive modelling

10 Particle blast method(pbm) for explosive modelling Various of pressure in the plate

11 Bonded particle model(bpm) for solid modelling (After Karajan et al., 2013).

12 Bonded particle model(bpm) for solid modelling (After Karajan et al., 2013).

13 Bonded particle model(bpm) for solid modelling (After Karajan et al., 2013).

14 Blast modelling with PBM/BPM PBM

15 Blast modelling with PBM/BPM BPM

16 Blast modelling with PBM/BPM Four investigated cases Case Diameter of hole (mm) PETN strength (g/m) EDC (mm) Number of particles (D=3.6mm) Case Case Case Case

17 Blast modelling with PBM/BPM Four investigated cases Case Diameter of hole (mm) PETN strength (g/m) EDC (mm) Number of particles (D=3.6mm) Case Case Case Case

18 Blast modelling with PBM/BPM Four investigated cases Case Diameter of hole (mm) PETN strength (g/m) EDC (mm) Number of particles (D=3.6mm) Case Case Case Case

19 Blast modelling with PBM/BPM Four investigated cases Case Diameter of hole (mm) PETN strength (g/m) EDC (mm) Number of particles (D=3.6mm) Case Case Case Case

20 Results 1 Most particles of the explosive are restrained in the cylinder at the begining. 2 The cylinder is fragmented into small fragments. 3 The distance that particles of the explosive fly away is much larger than the distance that the particles of the cylinder fly away.

21 Results The mortar cylinder expansion process (a) T=2 ms (b) T=5 ms (c) T=20 ms

22 Results Particle distribution after blasting and a local enlargement

23 Results Fragment size distribution 1 Calculate the distance between the particles after blasting 2 Identify which particles form a fragment 3 Calculate the volume of the fragment 4 Calculate the fragment size Mass passing(%) Case 1 Case 2 Case 3 Case 4 10 Fragment size (mm)

24 Results Fragment size distribution 1 Calculate the distance between the particles after blasting 2 Identify which particles form a fragment 3 Calculate the volume of the fragment 4 Calculate the fragment size Mass passing(%) Case 1 Case 2 Case 3 Case 4 Case2 10 Fragment size (mm) Case3

25 Results Analysis of X 50 and X max 80 1 Large specific charge gives a small medium fragment size. 2 Large specific charge gives a small maximum fragment size. 3 The effect of coupling ratio on fragmentation is not notable. X50 and X max (mm) Numerical X 50 Experimental X 50 Numerical X max Experimental X max Specific charge q (kg/m 3 ) 2 4

26 Results Analysis of X 50 and X max 1 Large specific charge gives a small medium fragment size. 2 Large specific charge gives a small maximum fragment size. 3 The effect of coupling ratio on fragmentation is not notable. X50 and X max (mm) X 50 mm = e3.08 q Numerical X 50 Experimental X 50 Numerical X max Experimental X max Specific charge q (kg/m 3 ) 2 4

27 Results Analysis of X 50 and X max 1 Large specific charge gives a small medium fragment size. 2 Large specific charge gives a small maximum fragment size. 3 The effect of coupling ratio on fragmentation is not notable. X50 and X max (mm) X 50 mm = e3.08 q 0.88 X 50 mm = e2.91 q Numerical X 50 Experimental X 50 Numerical X max Experimental X max Specific charge q (kg/m 3 ) 2 4

28 Results X 50 and X max vs coupling ratio Case q (kg/m 3 ) Coupling ratio Numerical results Experimental results X 50 (mm) X max (mm) X 50 (mm) X max (mm) Case Case Case Case

29 Results X 50 and X max vs coupling ratio Case q (kg/m 3 ) Coupling ratio Numerical results Experimental results X 50 (mm) X max (mm) X 50 (mm) X max (mm) Case Case Case Case

30 Results X 50 and X max vs coupling ratio Case q (kg/m 3 ) Coupling ratio Numerical results Experimental results X 50 (mm) X max (mm) X 50 (mm) X max (mm) Case Case Case Case

31 Results X 50 and X max vs coupling ratio Case q (kg/m 3 ) Coupling ratio Numerical results Experimental results X 50 (mm) X max (mm) X 50 (mm) X max (mm) Case Case Case Case

32 Results Fragment size distribution for Case 2 1 The values of X 50 and X max from the numerical results are close to those of the experimental results Mass Passing (%) 100 Experimental result Numerical result 2 The shapes of curves are different Fragment size (mm)

33 Results Possible reasons for the differences : a) The fragment size in the numerical results is the cube root of the volume of the fragment b) The particles in the numerical model are not fine enough i.e. 3.6 mm is not sufficient

34 Concluding remarks 1)PBM can model detonation of explosive and blast gas behavior 2)BPM can take important physical features of solid materials and mimic the fracturing and throwing of rock 3) The combination of PBM and BPM could be suitable for rock blasting simulation

35 Acknowledegments Swebrec s stakeholders: AtlasCopco, Boliden, LKAB, LKAB Berg & Betong and Nordkalk Hailong Teng of Livemore Software Technology Corporation (LSTC)

36 Thank you!