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