Curing of ConcreteCuring of ConcreteSpatial and Temporal Randomness Spatial and Temporal Randomness

Over Multiple Length ScalesOver Multiple Length Scales

Jeffrey W. BullardNational Institute of Standards and Technology

Gaithersburg, Maryland 20899

Inorganic Materials Group at NIST:Inorganic Materials Group at NIST:

Edward Garboczi, Group LeaderEdward Garboczi, Group Leader composite theory, elasticity, finite element models

Dale BentzDale Bentz microstructure models

Clarissa FerrarisClarissa Ferraris experimental rheology, durability

Nicos MartysNicos Martys computational rheology, fluid dynamics

Ken SnyderKen Snyder transport properties

Paul StutzmanPaul Stutzman materials characterization, QXRD, SEM

Spatial Complexity of Spatial Complexity of ConcreteConcrete

Macro-scaleMacro-scale

Courtesy Portland Cement Association

C3S

Gypsum

C2S

C3A

t = 0

Ettringite

C-S-H Gel

t = 0.5 h

Microstructure Development in Microstructure Development in Cement PasteCement Paste

CH

t = 4 h t = 672 h

C-S

-H

C-S

-H

C-S

-H

C-S-H

Microstructure Development in Microstructure Development in Cement PasteCement Paste

Structural Complexity of Structural Complexity of Cement Cement PastePaste

Micro-scaleMicro-scale

250 µm

150 µm

75 µm

• 3-D solid-pore random composite3-D solid-pore random composite• Porosity forms 3-D percolating networkPorosity forms 3-D percolating network• Solids may begin as percolating (or not) Solids may begin as percolating (or not)

“soft” clusters; later form stiff percolating “soft” clusters; later form stiff percolating networknetwork

CMS of Cement & Concrete at NISTCMS of Cement & Concrete at NIST

ObjectiveObjective: Predict microstructure development and its influence on properties (mechanical, transport, rheological) and durability

Principal:Principal:

input µ-structureinput µ-structure

model hydrationmodel hydrationof µ-structureof µ-structure

predict propertiespredict properties

compare w/ compare w/ experimentexperiment

Each volume element has propertiesof the phase at that location in space

DigitizDigitizee

20 µm20 µm

Ca

Si

K

Al

K

… X-ray Element Maps …

… are used to segment image into phases

SEM/BSE Image…

Building a Representative 3-D Building a Representative 3-D MicrostructureMicrostructure

3-D image of model cementpaste

3-D image of model cementpaste

• 2D Segmented image is analyzed by constructing autocorrelation functions on the majority phases

• Autocorrelation functions are used to distribute these phases statistically in a 3D digitized microstructure

Building a Representative 3-D Building a Representative 3-D MicrostructureMicrostructure

Cellular Automaton Model of Cellular Automaton Model of HydrationHydration

Current ApproachCurrent Approach– Each volume element is an independent agent that

can

• DissolveDissolve

• DiffuseDiffuse

• ReactReact

Pore solution

Stepwise random walk on lattice

Collisions between agents,governed by reaction “rules”

Illustration of Model Cement HydrationIllustration of Model Cement Hydration

initial/dissolution/diffusion/early/late

This example is in 2D, but all our This example is in 2D, but all our modeling efforts are on 3D modeling efforts are on 3D

microstructuresmicrostructures

Image courtesy of Dale Bentz,NIST

Heat of HydrationHeat of Hydration

Predicted Adiabatic Heat SignaturePredicted Adiabatic Heat Signature

Prediction vs. ExperimentPrediction vs. Experiment

Calculated Elastic PropertiesCalculated Elastic Properties

Status …Status … Model quantitatively reproduces some Model quantitatively reproduces some

phenomena quite wellphenomena quite well– Digital image format allows 3D spatial complexityDigital image format allows 3D spatial complexity– CA algorithm allows rapid evolution of µ-structure CA algorithm allows rapid evolution of µ-structure

and tracking of properties (pixel counting)and tracking of properties (pixel counting)

But …But … Rules are incomplete or inaccurate model of mechanismsRules are incomplete or inaccurate model of mechanisms Consequences:Consequences:

– No intrinsic time scale (empirical mapping via fitting to No intrinsic time scale (empirical mapping via fitting to experimental data)experimental data)

– Rules are customized to 1-µm length scale; no convergence Rules are customized to 1-µm length scale; no convergence behavior; model breaks down at any other length scalebehavior; model breaks down at any other length scale

– Primarily interpolative--- works for those systems upon which the Primarily interpolative--- works for those systems upon which the rules were calibratedrules were calibrated

Next Steps …Next Steps … Place the hydration model on firmer Place the hydration model on firmer

theoretical basistheoretical basis Implement diffusion, nucleation, growth, etc Implement diffusion, nucleation, growth, etc

using CA methods, but using rules with strict using CA methods, but using rules with strict ties to diffusion and transition state theoriesties to diffusion and transition state theories

Modeling the C-S-H Gel is CrucialModeling the C-S-H Gel is Crucial For most of hydration, reactions are rate-For most of hydration, reactions are rate-

controlled by ionic diffusion through gel controlled by ionic diffusion through gel structurestructure

Need to know the transport factor for ionic Need to know the transport factor for ionic species in C-S-H gelspecies in C-S-H gel

transport properties

C-S-H structure& composition

hydrationconditions

Structural Complexity of Structural Complexity of C-S-H GelC-S-H Gel

Nano-scaleNano-scale

50 nmCaxSiO(2+x)·H2O

PorosityPorosity

““IP”IP”

““OP”OP”

Micrograph courtesy of I.G. Richardson,University of Leeds

Structural Complexity of Structural Complexity of C-S-H GelC-S-H Gel

Nano-scaleNano-scale

CC33S Paste, 20S Paste, 20°°C, 8 yr C, 8 yr

CC33S Paste, 80S Paste, 80°°C, 8 d C, 8 d

““IP”IP”

““OP”OP”

““IP”IP”

““OP”OP”

Micrographs courtesy of I.G. Richardson,University of Leeds

Critical Information Needed to Better Critical Information Needed to Better Model Hydration and Microstructure Model Hydration and Microstructure

Development …Development … Nanoscale understanding of C-S-H nucleation and growth Nanoscale understanding of C-S-H nucleation and growth mechanisms, and structure under different hydration conditionsmechanisms, and structure under different hydration conditions– Function of temperature, aqueous compositionFunction of temperature, aqueous composition– Some exists in literature, needs to be synthesizedSome exists in literature, needs to be synthesized

Other information needed, too, but lower priorityOther information needed, too, but lower priority– Composition ranges of hydration products (C-S-H, ettringite, etc.)Composition ranges of hydration products (C-S-H, ettringite, etc.)– Growth morphologies of hydration productsGrowth morphologies of hydration products

How to Obtain?How to Obtain? Enlightening experiments are very difficult to design Enlightening experiments are very difficult to design

and controland control Molecular scale or multiscale models?Molecular scale or multiscale models?

– Brownian dynamics used to study colloidal gel formationBrownian dynamics used to study colloidal gel formation– Molecular dynamics (gel structure, reaction mechanisms)Molecular dynamics (gel structure, reaction mechanisms)– Kinetic Monte Carlo (nano-scale film growth, etc.)Kinetic Monte Carlo (nano-scale film growth, etc.)

Each voxel is a tri-linear finite elementEach voxel is a tri-linear finite element

E, G obtained bysum over all voxelsE, G obtained bysum over all voxels

4

Solve elastic stateby minimizing

Solve elastic stateby minimizing

Vij

V

ij d

Individual phase moduliIndividual phase moduli

Some cement minerals in the geology literature, or have been measured (Lafarge) or being worked on

Nanoindentation gives EC-S-H 25-30 GPa

Good ultrasonic data for C3S seems to overestimate E slightly

Good ultrasonic data for CH and ettringite

Do C-S-H moduli change with age? Probably yes, but no evidence for how much, so neglect for now

Brownian Dynamics + Momentum Conserving Collision Hydrodynamic Behavior

Concrete Rheology Model: Concrete Rheology Model: Dissipative Particle DynamicsDissipative Particle Dynamics

Model developed by N. Martys (NIST) based on an algorithm by Hoogerbrugge and Koelman (1992)

Concrete flow: diam. Concrete flow: diam. 0.20.2

Coaxial RheometerCoaxial Rheometer

What Is TheWhat Is TheVirtual Cement and Concrete Testing Virtual Cement and Concrete Testing

Laboratory?Laboratory?

Internet-based and menu driven Predicts properties based on detailed

microstructure simulations of well-characterizedwell-characterized starting materials

Goal is to reduce number of physical concrete tests, thus expediting the R&D process and enabling optimization in the material design process

PREDICTED PROPERTIESdegree of hydrationchemical shrinkage

pore percolationpore solution pH

ion concentrationsconcrete diffusivity

set pointadiabatic heat signaturestrength development

interfacial transition zonerheology (yield stress, viscosity)

workabilityelastic moduli

hydrated microstructures

VIRTUAL CEMENT AND CONCRETE

TESTING LABORATORY

(VCCTL)http://vcctl.cbt.nist.gov

CURING CONDITIONSadiabatic, isothermal, T-programmedsealed, saturated, saturated/sealed

variable evaporation rate

SUPPLEMENTARY CEMENTITIOUSMATERIALS

PSD, compositionsilica fume, fly ash

slag, kaolin,limestone

AGGREGATESgradation

volume fractionsaturation

shape

MIXTURE PROPERTIESw/cm ratio

fiberschemical admixtures

air content

CEMENTPSD

phase distributionchemistry

alkali content

Industrial ParticipantsCEMEX, Dyckerhoff Zement GmbH, HOLCIM INC.,International Center for Aggregate Research,

Master Builders Technologies, PORTLAND CEMENT ASSOCIATIONVerein Deutscher Zementwerke e.V., W.R. Grace & Co.- CT

VCCTL Web InterfaceVCCTL Web Interface

VCCTL ExtensionVCCTL Extensionto Durabilityto Durability

PREDICTED PROPERTIESdegree of hydrationchemical shrinkage

pore percolationpore solution pH

ion concentrationsconcrete diffusivity

set pointadiabatic heat signaturestrength development

interfacial transition zonerheology (yield stress, viscosity)

workabilityelastic moduli

hydrated microstructures

ENVIRONMENTtemperature

relative humiditycarbon dioxide

sulfateschlorides

alkalisstress state

DEGRADATION MODELSsulfate attack

chloride ingress (corrosion)freeze/thaw damagealkali-silica reaction

carbonationleaching

SERVICE LIFEPREDICTION

and LIFE CYCLE

COSTING

transportreactions

stress generation/ cracking

Final RemarksFinal Remarks

VCCTL is based on years of computational and experimental materials science research

VCCTL is being “made ready for prime time” with the help of companies and industrial groups

These partners cover all the generic materials that make up concrete

The field of cement and concrete materials needs to be, and will be, revolutionized

VCCTL is leading the way

THERE’S ALWAYS ROOM AT THE BOTTOM!THERE’S ALWAYS ROOM AT THE BOTTOM!

(R. Feynman)

NIST/ACBM Modeling WorkshopNIST/ACBM Modeling Workshop

Annual 5-day summer workshop hosted by NIST

Covers key concepts relevant to many areas of computational materials science– Composite/Effective Medium Theory– Percolation Theory– Microstructure modeling– Finite element/Finite Difference methods– And more

Ideal for grad students and/or faculty who are new to computer modeling of composites

Visit http://ciks.cbt.nist.gov/~garbocz/let02.html

What is Computational Materials What is Computational Materials Science?Science?

J. Ramirez et al, U. Iowa J. Guo and C. Beckermann,U. Iowa

J.D. Joannopoulos et al.ab-initio.mit.edu

K. Beardmore,Loughboroug University, UK

Techniques dependTechniques dependon length and timeon length and time

scalesscales

How Can We Construct 3-D MicrostructuresHow Can We Construct 3-D Microstructuresfrom 2-D Images?from 2-D Images?

Autocorrelation functions– provide information on volume fraction and

surface area fraction of individual phases

– are identical in 2-D and 3-D! Measure autocorrelation fns. on 2-D images for each

clinker phase Use them to build a 3-D microstructure that is

consistent with these functions

S

r

RGB image: Ca, Si, Al(courtesty of Paul Stutzman)

RGB image: Ca, Si, Al(courtesty of Paul Stutzman)

Building a Representative 3-D Building a Representative 3-D MicrostructureMicrostructure

X-ray Microprobe AnalysisX-ray Microprobe Analysis

Model Output …Model Output …

Degree of hydration of all phases– phase fractions vs. time

Heat release– adiabatic heat signature

Chemical shrinkage Phase percolation properties (set point and

capillary porosity) Elastic moduli (by coupling to FE calculation) Compressive strength (via Power’s gel-space

ratio or differential EMT on a mortar or concrete) Transport factor (relative diffusivity) Pore solution pH, ionic concentrations, and

conductivity

Building a Meaningful 3-D Building a Meaningful 3-D MicrostructureMicrostructure

Microstructure InformationMicrostructure Information– Cement particle size distribution– Cement phase composition and statistical

distribution– Gypsum content and form (hemihydrate, anhydrite)– Flocculation/Dispersion

Individual Phase PropertiesIndividual Phase Properties– Specific heat, heat of formation, elastic moduli, etc.

Kinetic InformationKinetic Information– Model reaction mechanisms (nucleation,– Activation energies (cement and mineral

admixtures)– Curing conditions (isothermal/adiabatic,

saturated/sealed)

Chemical Complexity of Chemical Complexity of Cement Cement PastePaste

75 µm

c = c = 10 chemical species10 chemical species(Ca, O, Si, Al, Fe, S, Mg,(Ca, O, Si, Al, Fe, S, Mg,K, Na, H)K, Na, H)

Gibbs Phase RuleGibbs Phase Rule

•Maximum number of phases that can coexist at equilibrium is c + 2 =c + 2 = 1212

•During curing, we often find twice as many coexisting phases. Many are amorphous or poorly crystalline and finely divided

•A hydrating cement paste is a complex chemical system far from equilibrium