Institutsname

Mikro- und Meso-Mechanische Simulationen

zum Verformungsverhalten von Tongesteinen

Heinz KonietzkyGeotechnical Institute, Chair for Rock MechanicsTU Bergakademie Freiberg, Germany

1

Content

1.General comments on

micro-mechanical modelling

2. Micro- and meso-mechanical

modelling of Opalinus Clay

2

Method of approach

Macro-mechanical view(scale: dm, m, km)

„Phenomenological“ concept

Micro-mechanical view(scale: nm, μm, mm)

„Physical“ concept

Micromechanical

simulation

approaches

4

Choice of simulation approach

deformablepolyhedra

more physics, more flexiblecomputer-intensivpotential of numerical instability

robust, fast, stablephysical less flexible

stiffspheres

Voronoi-bodies Spheres-Clusters-Clumps

5

Generation of models

Voro

noi B

odie

s

Sph

eres

–C

lum

ps -

Clu

ster

s

6

SandstoneM

odel

set

-up

base

d on

sph

eres

ac

cord

ing

to g

rain

siz

e di

strib

utio

n

She

ar fr

actu

re d

urin

g tri

axia

l tes

ting

Baumgarten & Konietzky 20137

Bruchbilder PFC-Modell

Longitudinal deformation and transverse deformationincluding hydrostatic pre-loading

Sandstone

Baumgarten & Konietzky 20138

9

Micromechanical simulation of concrete consideringgrain size, grain shape + grain and binder properties

9999999999999999999999999Groh, Konietzky, Walter & Herbst 20119

l

l

Micro fractures: red/black =t ensile-/shear fracture, dark =l ater

Roller force vs. steps

Fracture toughness test (Mode-I)

Groh, Konietzky, Walter & Herbst 2011

10

11

2a

2b

R=0.6 R=0.5 R=0.4 R=0.3 R=0.2

Elliptical pores with different aspect ratio

Micro-mechanical model of single pore of different shape

Tan & Konietzky 201311

12

n=0.33% n=2.56% n=4.54% n=6.81% n=8.36%

Random elliptical cracks (S=0.1)

0 2 4 6 8 10 12 140.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0 E1

E2

J=0.142 (R2=0.941) J=0.112 (R2=0.958)

E/E s

Porosity (%)0 2 4 6 8 10 12 14

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1

2

J=0.202 A=0.15 (R2=0.937) J=0.162 A=0.15 (R2=0.929)Bi

ot co

effic

ient

Porosity (%)Tan & Konietzky 2013

12

0 100 200 300 400 500 600 7000.00.51.01.52.02.53.03.54.04.55.05.5 VIVIVIIIIII

volumetrical strain

permeabilityA

FE

DCB

Perm

eabi

lity

(10-1

7 m2 )

Time (min)

stress

0.5

0.0

-0.5

-1.0

-1.5

-2.0

-2.5

-3.0

Volu

metr

ical s

train

(%)

A B C D E

Tan, Konietzky & Frühwirt 2014

13

A A1 B B1 C C1 D D1 D2 D3 D4 E E1 F0.0

0.2

0.4

0.6

0.8

1.0

Biot

's co

effic

ient

,

Marked points

test 1test 1test 2test 2

A A1 B B1 C C1 D D1 D2 D3 D4 E E1 F0.0

0.2

0.4

0.6

0.8

1.0

Biot

's co

effic

ient

Marked points

test 1test 2

Axial stress

Axial strain

Axial stress

Biot's coefficient

0

Volumetric strain

1

III

IVIII

VElastic region II

Crack closure I

Crack growth III

Unstable crack growth IV

Crack initiation

Unstable cracking

Peakstrength

cicdfcicd

Tan, Konietzky & Frühwirt 201414

151

200 pixels50 mm

200

pixe

ls50

mm

Mica

Feldspar

j

i

10 pixels

10 p

ixels

o

Quartz

a) Gray level image b) Aue granite sample

e) UDEC model

f) Voronoi blocks

c) Square region

d) Matrix of discrete function f (i, j)

159 152 149 168 198 193 165 170 209 223151 156 161 181 185 167 157 184 245 244163 133 104 161 198 201 214 216 249 25585 40 3 90 232 253 255 235 242 25313 0 0 22 187 255 255 252 252 25513 0 0 0 133 255 255 255 255 25513 0 0 23 179 227 251 255 255 25514 26 40 147 235 182 211 255 254 25398 176 205 226 216 195 207 229 220 200

215 213 242 249 239 216 208 225 204 183

i

jo

Gra

yle

veli

mag

ete

chni

que

todu

plic

ate

mic

rost

ruct

ure

15

16

Micro-structural model of gneiss disc

0° 45° 90°16

17

Schist

shear cracks

tensile cracks 60°

tensile cracks90°

17

18

Schist

0 15 30 45 60 75 900

2

4

6

8

10

12

14

16

18

20

Orietation angle (o)

0

2

4

6

8

10

12

14

16

18

20

Tens

ile st

reng

th (M

Pa)

Numerical modelLab results (average)

Lab results range

18

19A B C D E

SchistCohesion

Cohesion

19

Spatial acoustic emission (AE) locations and experimental failure of red sandstone at a confining pressure of 35 MPa (Yang et al. 2012)

Acoustic emission (AE) locations and final macroscopic fracture pattern in the three-point bending test (a) Berea sandstone; (b) Sioux quartzite; (c) Charcoal granite; (d) Rockville granite (Zietlow and Labuz 1998)

Lab test results

20

Stress intensity factor approach

Subcritical crack growth theory

Charles equation

Crack propagation schemes

Theories and approaches utilized

Linear elastic fracture mechanics

Elasto-plastic stress redistribution

21

Subcritical crack growth simulationusing Charles equation and celluarautomate

Konietzky, Heftenberger & Feige 200922

uniaxialtension

uniaxialcompression

Typical damage development during uniaxial loadingKonietzky, Heftenberger & Feige 2009

23

Compressive load

Tensile load

Same load magnitude !!

Com

paris

on: d

amag

e de

velo

pmen

t un

der u

niax

ial c

ompr

essi

on a

nd te

nsio

n

24

57.7 MPa12 MPa

30º 45º 60º

9.6e10 years 9.0e10 years 6.8e12 years

Zone size: 0.04 m;Initial crack lengths: normal distribution;(Mean: 0.013 m, STD: 0.0001 m)Initial crack orientations: uniform distribution

Hwangdeung granite (Lee and Jeon 2011)

Li & Konietzky 201325

Practical Application: Pillar

Li & Konietzky 201326

Practical Application: Tunnel , Drift

Li & Konietzky 201327

Model concepts

for

Opalinus clay

28

(Nagra, 2003) 29

2 concepts

„Phenomenological“concept

„Physical“ concept

„Physical“ concept

at the micro-scale

31

Numerical modelwith clay plates, free water and bounded water (Lennard-Jones-Potential)

te Kamp & Konietzky 200232

Model set-up

Initialstate

Finalstate

Compaction ofsaturated clay packageunder loading

33

45

90

135

180

225

270

315

12

45

90

135

180

225

270

315

12

45

90

135

180

225

270

315

12

45

90

135

180

225

270

315

10

45

90

135

180

225

270

315

12

45

90

135

180

225

270

315

12

10 20 30 40

0.8

1.2

1.4

1.6

1.8

10

20

30

40

10 20 30 40-70-60-50-40-30-20-10

Re-orientation of clay plates during compaction process

te Kamp & Konietzky 2002

Porosityapp. 50%

Clay plate model without explicit consideration of water

te Kamp & Konietzky 2002 35

I: accumulated cracks

II: new cracks per phase

Stress strain behaviourand fracture patternof numerical clay stone model

te Kamp & Konietzky 2002

36

0 0.4 0.8 1.2 1.6 2Normalized axial strain

(with respect to the reference model)

0

0.2

0.4

0.6

0.8

1

Nor

mal

ized

axia

lstre

ss(w

ithre

spec

tto

the

peak

valu

eof

the

refe

renc

em

odel

)

90% of peak

60% of peak

30%of peak

0 0.5 1 1.5 2 2.5Normalized axial strain

(with respect to the reference model)

0

-0.2

-0.4

-0.6

-0.8

-1

Nor

mal

ized

axia

lstre

ss(w

ithre

spec

tto

the

peak

valu

eof

the

refe

renc

em

odel

)

Compaction under constant load levels(note: irreversible plastic deformations)

te Kamp & Konietzky 2002 37

„Physical“ concept

at the meso-scale

38

microscopic DLVO andnon-DLVO forces

clay particles formingaggregates

silt particle

inter-crystalline porefilled with liquid

bedding planematrix plane

microscopiclevel

mesoscopiclevel

bedding plane

matrix plane

P-sample

S-sample

Z-sample

Anisotropic model for Opalinus Clay

39

Stress – strain behaviour and fracture pattern: uniaxial compression test(S-Sample)

40

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00% 0.01% 0.02% 0.03% 0.04% 0.05% 0.06% 0.07% 0.08%

Axial strain

Tens

ile s

tress

[MP

a]

P-sample

S-sample

Z-sample

Uniaxial tensile testing: stress-straincurves and fracture pattern

41

Uniaxialcompression:

fracture patternlab vs. model

P-Sample

Z-Sample

S-Sample

42

nach 15 dEDZ: fracture pattern as function of time

nach 150 d

Permeability and flow area development in EDZ vs. time

VVKP

XPKaQ 3

0

00

FFFaa

EDZ-study: Mt. Terri, tunnel radius = 1.8 m

Numerical model set-up andIlustration of HM-coupling scheme

te Kamp, Konietzky & Blümling 1999Konietzky, te Kamp & Blümling 2001

45

1 day

1 month

MPa

MPa

Pp,ini=2 MPa

Por

e pr

essu

re d

istri

butio

n ar

ound

ope

ning

te Kamp, Konietzky & Blümling 1999Konietzky, te Kamp & Blümling 2001

46

0 30 60 90 120 150 180Time (days)

0

1

2

3Po

rePr

essu

re(M

Pa)

Wet_1: 0°0.20 m0.45 m0.70 m0.95 m1.20 m1.45 m1.70 m1.95 m2.20 m

Development of pore pressureinside individual pores vs. time

te Kamp, Konietzky & Blümling 1999Konietzky, te Kamp & Blümling 2001

47

dry wet

Red: shear cracksBlack: tensile cracks

Final StaticSolution

After6 Months

Number of cracks

Comparison: damage state under dry and wet conditionste Kamp, Konietzky & Blümling 1999Konietzky, te Kamp & Blümling 2001

48

Simulation potential

at the meso/macro-scale

based on DEM technique

49

Emplacement of

backfill

Bimodalesize

distribution

Fullerdistribution

screw

Placement of bentonite pelletsInside drift with waste canister

50

Correct micro- and meso-mechanical simulation demands the explicitconsideration of:

Grain shapesGrain size distributionInitial damageIntragranular and intergranular

fracturingPorosity (shape, size, distribution)Mineral components / phasesCritical and subcritical crack growthSimulation of granular flow and

compaction

Korrekte mikro- und meso-mechanische Simulationen erfordern die explizitethe Berücksichtigung von:

KornformKorngrößenverteilungInitiale SchädigungIntragranulare und intergranul.

BruchprozessePorosität (Form, Größe,

Verteilung)MineralbestandKritisches und subkritisches

RisswachstumSimulation of Partikelströmen

und Kompaktion

Verständnis mikromech. Prozesse = Voraussetzung für fundierte Prognose

Knowledge micromech. Processes = Prerequisit for reliable Prediction

51

Thanks for your kind attention

Following co-workers have contributed to the presented results:Dr. Li, Dr. te Kamp, Dr. Gröger, Dr. Tan, Mr. Baumgarten, Dr. Herbst, Dr. Groh

52