FLAC3D-PFC3D Coupled Simulation of Triaxial Hopkinson Bar sym… · Pneumatic-hydraulic Machines...
Transcript of FLAC3D-PFC3D Coupled Simulation of Triaxial Hopkinson Bar sym… · Pneumatic-hydraulic Machines...
FLAC3D-PFC3D Coupled Simulation
of Triaxial Hopkinson Bar
Wanrui Hu & Dr. Qianbing ZhangMonash University, Australia
Dr. David O. PotyondyItasca Consulting Group Inc., USA
FIFTH INTERNATIONAL ITASCA SYMPOSIUM ON APPLIED NUMERICAL MODELING IN GEOMECHANICS — 2020
Wanrui Hu is a PhD candidate in the Department of Civil Engineering,Monash University in Australia. He received both his Master and Bachelordegrees from Wuhan University in China. His research topic is dynamicfracturing and fragmentation of brittle materials. He is currently focusingon dynamic compression and shear behavior of rock under multiaxialloading using a coupled continuum-discrete modelling method.
OUTLINE• Introduction
– Dynamic loading resources– Experimental and numerical methods
• 3D Triaxial Hopkinson Bar• Numerical Modelling• Summary and Future Study
UndergroundSurface Lab scale In
tact
rock
Gra
nula
r mat
eria
lsNatural and Human-induced Hazards: Confinement and Impact
Impact velocity (v) Confinement (𝜎𝜎1 𝜎𝜎2 𝜎𝜎3) Different loading conditions
Fracturing(primary)
Fragmentation(secondary)
Compression
Liu PhD thesis
Tension
Liu PhD thesis
Single Shear
Liu PhD thesis
Double shear
Wu PhD thesis
Single particle impact Shan et al. 2018
Multi-particle impact Parab 2017
Particle chain impact Liu et al. 2016
Coal burst
Outburst of coal
Barringer Meteor Crater
Kenkmann et al. 2014
PressureProjectile
Austar Coal Mine, NSW, Australia
Rock fall
High-risk areaKalgoorlie Super Pit San Andreas fault at California
Earthquake fault
Rempe et al. 2013
1.2km
Dynamic Experimental Techniques
Pneumatic-hydraulic Machines Drop Weight Machines Split Hopkinson Bar Plate Impact Techniques
Zhang et al. 2019, AREPS
1D Split Hopkinson pressure bar (𝜎𝜎1 > 0,𝜎𝜎2 = 𝜎𝜎3 = 0)
Multiaxial loading boundary(𝜎𝜎1 > 𝜎𝜎2 > 𝜎𝜎3)
Monash University
Conventional confining boundary(𝜎𝜎1 > 𝜎𝜎2=𝜎𝜎3)
Nemat-Nasser et al. 2000
Monash University
Numerical Modelling Methods
Continuum-based methods RFPA, AUTODYN, LS-DYNA Incorporation of rate-dependent constitutive models Phenomenological representation of failure
Discontinuum-based methods UDEC, PFC, ESyS-Particle Explicitly modelling of fractures formed by microcracks Limited scale Insufficient strain rate effects
Hybrid Methods FDEM, FDM/DEM Computational efficiency Fracture and fragmentation Stress wave propagation
Discontinuum-based methods
Continuum-based methodsRFPA
Zhu et al. 2012 Saksala et al. 2017
LS-DYNA
Hao et al. 2013
AUTODYN
Gui et al. 2016
UDEC PFC
Li et al. 2018
ESyS-Particle
Du et al. 2018
Rougier et al. 2014
FDEM Hybrid Methods3D FDEM FDM/DEM
This study
2D FDEM
Mahabadi et al. 2010
OUTLINE• Introduction • 3D Triaxial Hopkinson Bar
– Components and Capabilities– High-Speed Imaging and Micro-CT Scan
• Numerical Modelling• Summary and Future Study
Dynamic Behaviours under Multiaxial Loading
Impact velocity up to 50 m/s Specimen size from 50 mm Triaxial quasi-static loads up to 100 MPa 3D Triaxial Hopkinson bar at Monash University
Liu et al. 2019, RMRE
Rock dynamic problems in underground engineering: multiaxial loading
Schematic of 3D Triaxial Hopkinson bar
Dynamic Behaviours under Multiaxial LoadingPolycrystals Composites Porous media
Granite Concrete Sandstone
3D Triaxial Hopkinson bar
Uniaxial (UC) Biaxial (BC) Triaxial (TC)
Internal (X-ray CT)
• Microstructure • Failure mechanism
Micro scale (SEM)
• Fracture surface energy
256×256 pixels2
200,000 fps
Surface (3D DIC)
• kinetic energy of the flying fragments
Spherical surface
𝐸𝐸𝑘𝑘 =12𝑚𝑚𝑣𝑣
2 +12 𝐼𝐼𝑤𝑤
2
0.04
0.015
-0.01
Strain field8.0
0.0
-8.0
Velocity field m/s
Cube Sphere
80kev, 17.8µm
𝐸𝐸𝑠𝑠 = 𝑊𝑊𝐼𝐼𝐼𝐼. −𝑊𝑊𝑅𝑅𝑅𝑅. −𝑊𝑊𝑇𝑇𝑇𝑇. − 𝐸𝐸𝑘𝑘𝐺𝐺 = 𝐸𝐸𝑠𝑠/𝐴𝐴
Granite Marble Sandstone
Multiple contacts
OUTLINE• Introduction • 3D Triaxial Hopkinson Bar • Numerical Modelling
– A coupled continuum-discrete method– Flat-jointed model– Verification and comparison
• Summary and Future Study
A Coupled Continuum-discrete Model for 3D SHPB
Steel Bars: continuum20000 elements, size: 20×5×5 mm3
Rock: discontinuum20127 balls, radius: 0.8~1.2 mm
Mineral grains 3D Flat-jointed material
X1 Incident bar (2.0m) X2 Transmitted bar (2.0m) Rock Specimen
Coupling logic Model Components
Facets Nodes
Discrete particles Continuous zones
Contact forces acting on the facets
Node forces acting on the grid
Wall velocities Node velocities
A1 A2A3
X1
X3
X2
CP
Flat-joint contact
• 3D grain microstructure• Partial damage• Rotation resistance
Particle 1
Particle 2
Interface elements
𝑋𝑋(2)
𝑋𝑋(1)
𝑋𝑋𝑐𝑐
Reflected wave
Incident waveTransmitted wave
Lateral waves
Stress-time history
t=150µs
t=300µs
t=360µs
t=720µs
t=510µs
200
0
-200
-350
100
-100
Incident bar Transmitted bar Specimen
Incident wave
Incident wave
Transmitted wave
Transmitted wave
Reflected wave
Reflected wave
Unit: MPa
Wave propagation in X direction
Verification and Comparison
Comparison in X direction
Impact from multiple directions
Z1
Z2
Damage Pattern
Flat-jointed model (FJM)
Particle 1
Particle 2 Interface cement
Parallel-bonded model (PBM)
𝑋𝑋(2)
𝑋𝑋(1)𝑋𝑋𝑐𝑐
Full damage after breakage Particle 1
Particle 2
Interface elements𝑋𝑋(2)
𝑋𝑋(1)
𝑋𝑋𝑐𝑐
Partial damage is allowed
Damage ratio (%)
Triaxial
100
75
50
25
0
3.0
1.5
0.0
-1.5
-3.0
50
25
0.0
-25
-50
CT slice 3D fragments
Damage ratio = Broken contact elementsAll contact elements
×100%
Z displacement (mm) Z velocity (mm)
Double Impact on Rock Spheres
8 major fragments Powders
Surface fracture
Local crushing zone
Fragment slice
Meridian fracture
Internal fracture
Pulverized zone
𝜏𝜏𝜎𝜎𝐼𝐼𝜎𝜎𝑐𝑐
𝜎𝜎𝑐𝑐
CT slices characterizing fracture and damage High speed cameras and DIC techniques
Marble - impact velocity = 9.17m/s
Contact force chain
Fragments
Tensile/Shear Cracks
Numerical Modelling of Double Impact Test on SandstoneRock spheresIncident bar Transmitted bar
Different loading stages
Summary and Future Studies Summary
The coupled continuum-discrete method can be used to simulate the triaxial Hopkinson bar Consideration of rock microstructure represented by 3D FJM contributes to an enhanced dynamic strength Similar V-shaped and orange-slice failure pattern of cubic and spherical rock can be observed
Future Studies Dynamic constitutive relationship under true triaxial loading condition Dynamic fragmentation models considering rock heterogeneity Application in prediction of blasting and crushing during mining operations