Curing of Concrete
Spatial and Temporal Randomness Over
Multiple Length Scales
Jeffrey W. Bullard
National Institute of Standards and Technology
Gaithersburg, Maryland 20899
Inorganic Materials Group at NIST:
 Edward Garboczi, Group Leader
 composite theory, elasticity, finite element models
 Dale Bentz

microstructure models
 Clarissa Ferraris
 experimental rheology, durability
 Nicos Martys
 computational rheology, fluid dynamics
 Ken Snyder
 transport properties
 Paul Stutzman
 materials characterization, QXRD, SEM
Spatial Complexity of Concrete
Macro-scale
Courtesy Portland Cement Association
Microstructure Development in Cement Paste
t=0
t = 0.5 h
Ettringite
C3A
Gypsum
C2S
C3S
C-S-H Gel
Microstructure Development in Cement Paste
t=4h
t = 672 h
CH
Structural Complexity of Cement Paste
Micro-scale
250 µm
150 µm
75 µm
• 3-D solid-pore random composite
• Porosity forms 3-D percolating network
• Solids may begin as percolating (or not) “soft”
clusters; later form stiff percolating network
CMS of Cement & Concrete at NIST
Objective: Predict microstructure development and its
influence on properties (mechanical, transport,
rheological) and durability
20 µm
Principal:
Digitize
input µ-structure
model hydration
of µ-structure
predict properties
Each volume element has properties
of the phase at that location in space
compare w/ experiment
Building a Representative 3-D Microstructure
SEM/BSE Image…
Ca
Si
Al
K
K
… X-ray Element
Maps …
… are used to segment
image into phases
Building a Representative 3-D Microstructure
3-D image
of model
cement
paste
• 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
Cellular Automaton Model of Hydration
 Current Approach
– Each volume element is an independent agent
that can
• Dissolve
• Diffuse
• React
Pore solution
Stepwise random walk on lattice
Collisions between agents,
governed by reaction “rules”
Illustration of Model Cement Hydration
Image
courtesy
of Dale
Bentz,
NIST
initial/dissolution/diffusion/early/late
This example is in 2D, but all our modeling efforts
are on 3D microstructures
Heat of Hydration
Predicted Adiabatic Heat Signature
Prediction vs. Experiment
Calculated Elastic Properties
Status …
 Model quantitatively reproduces some phenomena
quite well
– Digital image format allows 3D spatial complexity
– CA algorithm allows rapid evolution of µ-structure and
tracking of properties (pixel counting)
But …
 Rules are incomplete or inaccurate model of
mechanisms
 Consequences:
– No intrinsic time scale (empirical mapping via fitting to
experimental data)
– Rules are customized to 1-µm length scale; no convergence
behavior; model breaks down at any other length scale
– Primarily interpolative--- works for those systems upon
which the rules were calibrated
Next Steps …
 Place the hydration model on firmer theoretical basis
 Implement diffusion, nucleation, growth, etc using CA
methods, but using rules with strict ties to diffusion
and transition state theories
Modeling the C-S-H Gel is Crucial
 For most of hydration, reactions are rate-controlled
by ionic diffusion through gel structure
 Need to know the transport factor for ionic species in
C-S-H gel
transport properties
C-S-H structure
& composition
hydration
conditions
Structural Complexity of C-S-H Gel
Nano-scale
“IP”
“OP”
Micrograph courtesy of I.G. Richardson,
University of Leeds
Porosity
50 nm
CaxSiO(2+x)·H2O
Structural Complexity of C-S-H Gel
Nano-scale
C3S Paste, 20°C, 8 yr
“IP”
“OP”
“IP”
Micrographs courtesy of I.G. Richardson,
University of Leeds
“OP”
C3S Paste, 80°C, 8 d
Critical Information Needed to Better Model
Hydration and Microstructure Development …
 Nanoscale understanding of C-S-H nucleation and
growth mechanisms, and structure under different
hydration conditions
– Function of temperature, aqueous composition
– Some exists in literature, needs to be synthesized
 Other information needed, too, but lower priority
– Composition ranges of hydration products (C-S-H, ettringite,
etc.)
– Growth morphologies of hydration products
How to Obtain?
 Enlightening experiments are very difficult to design
and control
 Molecular scale or multiscale models?
– Brownian dynamics used to study colloidal gel formation
– Molecular dynamics (gel structure, reaction mechanisms)
– Kinetic Monte Carlo (nano-scale film growth, etc.)
Each voxel is a tri-linear finite element
Solve elastic state
by minimizing
  ij ij dV
V
E, G obtained by
sum over all voxels
4
Individual 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
Concrete Rheology Model:
Dissipative Particle Dynamics
Brownian Dynamics + Momentum Conserving Collision
Hydrodynamic Behavior
Model developed by N. Martys (NIST) based on
an algorithm by Hoogerbrugge and Koelman (1992)
Concrete flow: diam. 0.2
Coaxial Rheometer
What Is The
Virtual Cement and Concrete Testing
Laboratory?
 Internet-based and menu driven
 Predicts properties based on detailed
microstructure simulations of
well-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
CURING CONDITIONS
adiabatic, isothermal, T-programmed
sealed, saturated, saturated/sealed
variable evaporation rate
PREDICTED PROPERTIES
CEMENT
PSD
phase distribution
chemistry
alkali content
AGGREGATES
gradation
volume fraction
saturation
shape
VIRTUAL CEMENT
AND CONCRETE
TESTING
LABORATORY
(VCCTL)
http://vcctl.cbt.nist.gov
SUPPLEMENTARY CEMENTITIOUS
MATERIALS
PSD, composition
silica fume, fly ash
slag, kaolin,limestone
degree of hydration
chemical shrinkage
pore percolation
pore solution pH
ion concentrations
concrete diffusivity
set point
adiabatic heat signature
strength development
interfacial transition zone
rheology (yield stress, viscosity)
workability
elastic moduli
hydrated microstructures
MIXTURE PROPERTIES
w/cm ratio
fibers
chemical admixtures
air content
Industrial Participants
CEMEX, Dyckerhoff Zement GmbH, HOLCIM INC.,
International Center for Aggregate Research,
Master Builders Technologies, PORTLAND CEMENT ASSOCIATION
Verein Deutscher Zementwerke e.V., W.R. Grace & Co.- CT
VCCTL Web Interface
PREDICTED PROPERTIES
degree of hydration
chemical shrinkage
pore percolation
pore solution pH
ion concentrations
concrete diffusivity
set point
adiabatic heat signature
strength development
interfacial transition zone
rheology (yield stress, viscosity)
workability
elastic moduli
hydrated microstructures
ENVIRONMENT
temperature
relative humidity
carbon dioxide
sulfates
chlorides
alkalis
stress state
VCCTL Extension
to Durability
DEGRADATION MODELS
sulfate attack
chloride ingress (corrosion)
freeze/thaw damage
alkali-silica reaction
carbonation
leaching
transport
reactions
stress generation/ cracking
SERVICE LIFE
PREDICTION
and
LIFE CYCLE
COSTING
Final 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!
(R. Feynman)
NIST/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 Science?
K. Beardmore,
Loughboroug University, UK
J.D. Joannopoulos et al.
ab-initio.mit.edu
Techniques depend
on length and time
scales
J. Ramirez et al, U. Iowa
J. Guo and C. Beckermann,
U. Iowa
How Can We Construct 3-D Microstructures
from 2-D Images?
 Autocorrelation functions
– provide information on volume fraction and
surface area fraction of individual phases
f
-S
S
f2
r
– 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
Building a Representative 3-D Microstructure
X-ray Microprobe Analysis
RGB image: Ca, Si, Al
(courtesty of Paul Stutzman)
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 Microstructure
 Microstructure Information
–
–
–
–
Cement particle size distribution
Cement phase composition and statistical distribution
Gypsum content and form (hemihydrate, anhydrite)
Flocculation/Dispersion
 Individual Phase Properties
– Specific heat, heat of formation, elastic moduli, etc.
 Kinetic Information
– Model reaction mechanisms (nucleation,
– Activation energies (cement and mineral admixtures)
– Curing conditions (isothermal/adiabatic,
saturated/sealed)
Chemical Complexity of Cement Paste
c = 10 chemical species
(Ca, O, Si, Al, Fe, S, Mg,
K, Na, H)
Gibbs Phase Rule
• Maximum number of phases
that can coexist at equilibrium
is c + 2 = 12
• During curing, we often find
twice as many coexisting
phases. Many are amorphous
or poorly crystalline and finely
divided
75 µm
• A hydrating cement paste is a
complex chemical system far
from equilibrium