Modeling of leaching-mechanicalcoupling in concrete

Dawei Hu, Fan Zhang, Hui Zhou, Jianfu SHAO

27 October 2011

Plan

• Background and problem• Mchanical model• Leaching• Coupling model• Conclusions and perspectives

Where is the studied concrete?• Structures;• Seal material;• Stock cell of nulear waste B.

Representation of stock cell of nuclearwaste B [ANDRA]

Representation of closed tunnel [ANDRA]

Background

Which is the concrete subjected? • Thermal load;• Mechanical evolution;• Chimical degradation.

Problem

Implemented models in COMSOL for concrete Mechanical Leaching Leaching-mechanical coupling

mechanic leaching

temperature

( )( , , ) , 0p pp ij m mf d q p d Ks g h a g= + - =

( ) ( )0 01

( , )= 1p

pm m m pd d

b

ga g a a a

g

é ùê ú- + -ê úê ú+ë û

• Plastic characterization

Mechanical model1) Plastic damage modeling

1 2 13

RcRt Rc

23

Rt RcKRt Rc

: Uniaxial compression strengthRc

: Tension strengthRt

Criteron of Drucker-Prager

• Damage characterization

Mechanical model1) Plastic damage modeling

21 exp pm mcd d b

( ) 01 : eij m ijkl kld Cs eé ù= -ê úë û

• Effective modulus

ppij

ij

fd de l

s

¶=

¶

• Associated plasticity

Mechanical model1) Plastic damage modeling Plane stress module for plastic damage modeling

subdomain settings

Mechanical model1) Plastic damage modeling Plane stress module for plastic damage damage

scalar expressions

05

1015202530354045

0 0.005 0.01 0.015 0.02 0.025 0.03

axial stress (MPa)

axial stain

012345678

0 0.0002 0.0004 0.0006 0.0008 0.001

axial stress (MPa)

axial stain

Mechanical model1) Plastic damage simulation

Simulation of uniaxial compression and tension

0

0.2

0.4

0.6

0.8

1

0 0.002 0.004 0.006 0.008

axial stain

,pmd

0

0.2

0.4

0.6

0.8

1

0 0.0002 0.0004 0.0006 0.0008 0.001

axial stain

,pmd

Evolution of plastic hardening and softening function

Mechanical model1) Plastic damage simulation

1 0 1cpt mt mt m

Mechanical model2) Creep characterization

1 0 1cpc mc mt m

First creep Second creep

• Creep strainin compression

In tension

• Total strainElastic + Plastic + Creep

e p cpij ij ij ij

Mechanical model2) Creep characterization PDE module for creep

• Mass balance equation

2

2 22

solidCa Ca D Ca CatCa

Leaching model

Hydric source of calcium ion

Diffusion coefficient of calcium ion

• Diffusion coefficient with ammonium nitrate

2 2 23 2 eD Ca NO D Ca Ca

Acceleration parameter Diffusion coefficient of calcium ion

1) Leaching characterization

Leaching model1) Leaching characterization Diffusion module for leaching

∂∂ 2 3 2

• Chemical damage

2+ 2+max 0

1 expc cd d Ca Ca

0

0

0

1

1

1

c

c c c

t t c

E E d

R R d

R R d

2) Leaching-plastic damage couplingLeaching model

• Chemical damage-mechanicalparameters

Test of micro indentation

2) Leaching-plastic damage simulationLeaching model

5 MPa

0 MPa

sound 18 months9 months

22 mol/m3

0 mol/m3

sound 9 months 18 months

2+Ca

Axial stress

Directe tension test after differentdegradation times (data after Camps 2008)

0

10

20

30

40

50

0 0.002 0.004 0.006 0.008

force (kN) CEM VF

displacement (mm)

sound

after 9 month leaching

after 18 month leaching

leaching surface

0

5

10

15

20

0 1 2 3 4 5

force (kN) CEM VF

flexility (mm)

sound

after 9 month leaching

after 18 month leaching

leaching surface

Flextion test after different degradation times (data after Camps 2008)

2) Leaching-plastic damage simulationLeaching model

1m e D mD d D d

1

1

1 compressive stress

1 tensive stress

cpc mc dc c

cpt mt dc c

mt d

mt d

1) Leaching-creep coupling characterizationCoupling Model

• Variation of diffusion coefficient with plastic damage

• Variation of creep strain rate with chemical damage

1) Leaching-creep coupling characterizationCoupling Model

Plane stress module

1) Leaching-creep coupling characterizationCoupling Model

PDE module for creep

1) Leaching-creep coupling characterizationCoupling Model

Diffusion module for leaching

5×10-3

8×10-5

22mol/m3

0 mol/m3

0

500

1000

1500

2000

2500

0 100 200 300 400 500 600 700

strain (10-6)

time (days)

CEM VF

with leaching

soundleaching surface

2) Leaching-creep simulationCoupling Model

2+Ca

Axial

strain

Creep compression test with degradation(data after Camps 2008)

l

Concentration of calcium ion

Longitudinale strain

Ca2+

22 mol/m3

0 mol/m3

1×10-3

-2.5×10-3

2) Leaching-creep simulationCoupling Model

Creep flexion test with degradation (data after Camps 2008)

00.010.020.030.040.050.060.070.08

0 100 200 300 400 500 600 700

flexility (mm)

time (days)

CEM VF

with leaching

sound

leaching surface

Creep flexion test with degradation(data after Camps 2008)

2) Leaching-creep simulationCoupling Model

Conclusions and perspectives

Conclusions• Elastoplastic damage model and creep model can

describe the mechanical behavior of concrete inshort and long term.

• The coupling of mechanical and leaching candescribe the mechanical behavior subjected tochimic degadation in long term .

Perspectives• Temperature-leaching-mechanical coupling

Thank you for your attention!