Micromechanics Contribution to the Analysis of Diffusion Properties Evolution in Cement-Based Materials

Undergoing Carbonation Processes

Journées Scientifiques

du

Groupement MoMaS

CIRM Marseille, 23-25 novembre 2009

Eric Lemarchand(LMSGC – UR Navier – Univ. Paris Est)

Materials ability to avoid radioactive radionuclides migration

Groundwater

(Stora, 2006)

Microstructure evolution Transport properties evolution (diffusion here)

Industrial Issues – Storage of Radioactive Waste

Carbonation

Chemical reactions in Concrete

Leaching / decalcification processes

Precipitation (ettringite, calcite,…)

Atmospheric Carbonation / Steel rebar corrosion

CO

2 from ou

tside

rust formation

effective diameter

Expansion

C-S-H

Portlandite

Pore

CaCO3

Couplings

Transport (CO2, liquid water, ions)

Chemical Reactions (pores clogging)

Macroscopic loading effects

Project Outline

Hydration Model(curing conditions, microstructure morphology)

Transport Properties (Diffusion)

Carbonation (Portlandite, CSH,…)

Steel rebar corrosion

C-S-H

Portlandite

Pore

CaCO3

Damaging, Durability ?

Outline

Hydration process and microstructure definition

Multi-scale description for cement-based materials

application to diffusion coefficient estimates

Carbonation processes in cement-based materials Microstructure evolution

New estimates for diffusion coefficients

Conclusions

Hydration/Structuration of cement-based Materials

Anhydrous cement

+water

hydration

Heterogeneous microstructure

structuration

Mature cement materialApparent macro-homogeneity

hydration structuration

(liquid, viscoelastic solid) (porous medium)

• Solid Phase: anhydres, hydrates• Porosity: capillary, gel • Partial saturation: water, air

• Ions released• Dissolutions / Precipitations• Microstructure Organization

Cement Paste – Hydration (Powers model)

We aim to be able to propose estimates for te evolution of (macroscopic) cement paste diffusion coefficient undergoing carbonation processes at different (microscopic) scales, depending upon the initial water-to-cement ratio (w/c) (cement paste initial definition)

/

/

pg pg

pc pc

f = f (w c)

f = f (w c)

Cement Paste Hydration (Powers)

Initial water

Anhydrous grains

(C3S, C2S,C3A,C4AF)

w/c=0.5

Volume fraction

Hydration degree

0.21AFf

0.22innerCSHf

0.16CHf

0.32outerCSHf

0.06Wf

0.03Vf

Outer CSH

Inner CSH

PortlanditeWater

Aluminates

Voids, big capillary pores

62% 21% 9% 8%( C3S, C2S, C3A, C4AF)

« Outer CSH »

capillary pores (0.1-1 micron)

large capillary pores (>10 microns)

hydrated clinker

(=10 microns)

CHCH

CH

Portlandite (10-100 microns)

gel pores (5-50 nm)

« Inner CSH »

gel pores (< 5nm)

Cement Paste - A multiscale material

(Sanahuja & Dormieux, 2008)

Reinforced Concrete - Morphology

CH

CH

CH

Cement Paste

Mortar

Sand grains(0.1 – 1 mm)

homogenization

homogenization

Reinforced concrete

Aggregates(1 cm)

Steel rebar

Fick’s Diffusion – Homogenization procedure

0 γdiv j =

1

1

22

with

x

D xj = D x grad D x =

D x

1/20 on γj n =

γρ = H x sur

1 2. . . V E R =

1

2Ω

x

grad = A x H

Linear Problem

hom γ γ

Ω

D

J = j = D x A x H

Micro-Macro Diffusion Coefficient Estimates

feuillets Tobermorite MontmorilloniteD D D

CH

CH

CH

10 2 11.10 .fD = O m s

« outer » CSH

n

1ffeu ille tsD = D n n

CH

CH

CH

n

CH

Self-consistentScheme

nn

acDacD

+ + + …acD

1D = D

2 partD = D

Homogenized diffusion coefficient ? (« outer » CSH gel)

Micro-Macro Diffusion Coefficient Estimates

1H V

f part partpartD = D D n n + D n n

2 10H V part

part part part b

part

πD ,D X

0bb

b

cX =

a

, f part out bout outD = D D D , , ,X

"outer CSH" gel pores volume fraction( )out

CH

CH

CH

« outer » CSH gel + capillary pores

outoutD D

pcD =D

capillary pores volume fraction( )pc

Matrix/inclusion homogenization scheme (Mori-Tanaka)

,γout pcmatrix matrix

D = D D , D

Micro-Macro Diffusion Coefficient Estimates

CH

CH

,f ininner innerD = D D ,D

CH

Self-consistentScheme

nn

acDacD

+ + + …acD

1D = D

2 feuilletsD = D

Homogenized diffusion coefficient ? (« inner » CSH)

n 1ffeuilletsD = D n n

= inner CSH intrinsic porosity ( 0.3)in

Micro-Macro Diffusion Coefficient Estimates

CHCH

CH

Incomplete hydration

Inclusion/matrix model (Mori-Tanaka, 1973)

matrix of « homogenized » outer CSH

Morphology Representative Pattern (Hervé & Zaoui, 1993)

Complete hydration (inner CSH phase)

CH Assume spherical Portlandite phase

Micro-Macro Diffusion Coefficient Estimates

0CHD( )

0anD( )

2 1[ . ]m s

Total porosity [-]

Mac

rosc

op

ic d

iffu

sio

n c

oef

fici

ent

Model predictionExperimental measurements (Richet et al, 1997)

9 2 12 210Model Validation D m s( . )

Carbonation of hydrated products

Carbonation of (small amount of) alkaline species

Carbonation of great amount of Portlandite

Carbonation of CSH (+ formation of silica gel)

2 23 03CaCO ( ) 22x y z Si HxC S H OH CO H Ox y t x t z

2 3CaCO2 2Ca(O CO HH) O

(Calcium carbonates precipitation + release of free water)

Mercury Porosimeter Results (Thiery,2009)

Microstructure evolution evidences

very large

capillary pores

Capillary

pores

Outer

CSH

gel

pores

Inner

CSH W/C=0.5

Portlandite CarbonationCSH Carbonation

(Thiery, 2009)

Portlandite Carbonation - Observations

Calcite grains

precipitation

Initial

Portlandite Crystal

Complete Calcite precipitation

(Fully-Carbonated Portlandite Crystal)

1 m

Carbonatation de la Portlandite

0 0 0,

1.121.12 1.5

1CH CH CH

calcite s CH calcite CH calcite CHCHcalcite

V V V V f f

( 0.24 for w/c=0.5)

Non porous phase Porous phase

Portlandite Carbonation

0.26CHcalcite (maximum packing density of spheres)

(characteristic size of pores (0.05 0.5 ))O m

3 2 (Differential sc e h me)CHcalcite wD D /

Volume increase (stochiometry arguments):

Equivalent diffusion coefficient (new calcite phase):

Carbonation shrinkage

50 nm

5-30nm

Calcium Silicate Hydrates (CSH) Carbonation

80-100 nm

<20nm

Calcium Silicate Hydrates Carbonation

Calcite crystals precipitation yields gel pores and capillary pores clogging !

Effects of Carbonation on Diffusion (Model estimates)

2 1[ . ]m s

Total porosity [-]

Mac

rosc

op

ic d

iffu

sio

n c

oef

fici

ent

Non-carbonated Cement

(model)

Carbonated Cement

(model)

Non-carbonated Cement (Experiments, Richet et al 1997)

The key role of the diffusion within calcite aggregates

3 2CH

calciteCarbonated cement (D D )/

7 2CH

calciteCarbonated cement (D D )/

Mac

rosc

op

ic d

iffu

sio

n c

oef

fici

ent

Total porosity [-]

Effect of w/c on Diffusion coefficient (model)

cementcarbonated

cementnon carbonated

D

D

w c/7 2CH

calciteCarbonated cement (D D )/

3 2CH

calciteCarbonated cement (D D )/

Diffusion properties of calcite

need better understanding !

Project Conclusions and Coming Issues

Objectives: A Multi-scale and multi-physics model for diffusion processes in cement-based materials accounting for chemical kinetics and possible couplings with mechanical loadings – application to carbonation processes

Behavior analysis in absence of chemo-mechanical couplings

Behavior (poroelasticity, creep) [Sanahuja,2008]

Diffusive transport in saturated conditions (better informations required)

Diffusive transport in unsaturated conditions

Microstructure evolution: the kinetics point of view

Dissolution/precipitation uncoupled laws (known by chemo-physicists)

Mechanical couplings in local dissolution/precipitation laws (already identified)

Portlandite Carbonatation – Kinetics Aspects

2 3 2Ca(OH) CO CaCO H O 2

Dissolution kinetics of Ca(OH)2

h : kinetics prameters, Ri : geometrical variables

D : diffusion coefficient

o

P Pξ =-κ A

Project Conclusions and Coming Issues

Objectives: A Multi-scale and multi-physics model for diffusion processes in cement-based materials accounting for chemical kinetics and possible couplings with mechanical loadings – application to carbonation processes

Behavior analysis in absence of chemo-mechanical couplings

Behavior (poroelasticity, creep) [Sanahuja,2008]

Diffusive transport in saturated conditions (better informations required)

Diffusive transport in unsaturated conditions

Microstructure evolution: the kinetics point of view

Dissolution/precipitation uncoupled laws (chemo-physics)

Mechanical couplings in local dissolution/precipitation laws (already identified)

Extension to steel rebar corrosion processes

Damage analysis – Crack propagation …

Thank you for your attention !