Concrete’s Challenges to Material Modeling
Christian Meyer
Department of Civil Engineering and Engineering Mechanics
Columbia University, New York, NY
Probability and Materials: From Nano- to Macroscale
NSF Workshop, Baltimore, MD, January 5-7, 2005
Definition
“Concrete is a composite material that consists of a binding
medium embedded with fine aggregate (typically sand) and
coarse aggregate (typically gravel)”
B. Mather and C. Ozyildirim, ACI Concrete Primer
CONCRETE
By far the most important building material worldwide
> 10 Billion tons/year produced worldwide
> 700 Million tons/year produced in the US (2000)
Main Advantages
 Mechanical Properties
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Durability
Moldability
Adaptability
Fire Resistance
General Availability
Affordability
Engineered Material
From Macro- to Nano-Scale
Macro:
cement composite (RVE)
Meso:
aggregate particles and cement matrix,
pores
Micro:
calcium-silicate-hydrate gel (C-S-H), CH
crystals, unhydrated cement particles,
micropores
Nano:
C-S-H particles, gel pores, molecules
Compressive Strength, f‘c
A true random property
Subject to a large number of influence factors, only
some of which can be controlled
Definition: Compressive strength of a 28-day old
standard cylinder, produced, cured, and tested
according to precisely defined ASTM standards
Concrete Strength vs. Age
(Mindess, Young, Darwin)
Shear Strength of Concrete
Concrete Creep Data – Theory vs. Experiment
(Sakata and Shimomura, J. Adv. Conc. Techn., 2004, p 134)
Frequency Distribution of 22 Mortar Bar ASR-Expansions
Expansion Error
Sources of Property Randomness
Binder
Aggregate
Admixtures
Mix Proportions
Production
Environmental Factors
Testing Method/Protocol or Loading
Typical Composition of Ordinary Portland Cement
Chemical Name
Tricalcium
Silicate
Dicalcium
Silicate
Tricalcium
Aluminate
Tetracalcium
Aluminoferrite
Gypsum
Shorthand
=Weight %
3CaOSiO2
C 3S
55
2CaOSiO2
C 2S
18
3CaOAl2O3
C 3A
10
4CaOAl2O3Fe2O3
C4AF
_
CSH2
8
Formula
CaSO42H2O
(Role of impurities: Alite – impure C3S, Belite – impure C2S)
6
Typical Oxide Composition of Portland Cement
Lime (C, CaO)
Silica (S, SiO2)
Alumina (A, Al2O3)
Ferric Oxide (F, Fe2O3)
Gypsum (SO3, CaSO4)
Magnesia (M, MgO)
Alkalis (K2O, Na2O)
Ignition Loss
Insoluble Residue
Balance
63%
20%
6%
3%
2%
1.5%
1.0%
2.0%
0.5%
1.0%
All minerals have different rates of hydration, strength development, and heat
evolution. By changing the chemical composition, one can design a cement with
certain properties (e.g., high early strength or low heat development). Example:
Oxide
SiO2
Al2O3
Fe2O3
CaO
Cement No. 1
20 %
7
Cement No. 2
22 %
7.7
Cement No. 3
20 %
5.5
3
66
3.3
63
4.5
66
Balance
4
4
4
Minerals
C3S
C2S
C3A
C4AF
65
8
14
9
33
38
15
10
73
2
7
14
Chemical Reactions of Hydration
Tricalcium Silicate + Water  C-S-H + Calcium Hydroxide +
Heat
2(3CaO  SiO2) + 11H2O  3CaO  2SiO2  8H2O + 3Ca(OH)2
In shorthand,
2C3S + 11H  C3S2H8 + 3CH
Dicalcium silicate,
2C2S + 9H  C3S2H8 + CH
Tricalcium Aluminate + Gypsum + Water  Ettringite
C3A + 3CSH2 + 26H  C6AS3H32
Later, after all gypsum has been consumed,
2C3A + C6AS3H32 + 4H  3C4ASH12 (Monosulfoaluminate)
(Complex interactions)
Hydrated C3S Paste
Aggregate
Natural vs. manufactured (crushed stone)
Mineral composition (reactivity)
Particle size distribution (grading curve)
Mechanical properties
Mix Proportions
Water/Cement Ratio
Cement/Aggregate Ratio
Air Content/Porosity
Admixtures
Production (Quality Control)
Impurities, Contaminants
Mixing
Conveyance, Transportation
Placement
Consolidation
Finishing
Curing (Age)
Environmental Factors
Temperature
Humidity, moisture content
Mechanical damage (cracking, abrasion)
Chemical attack (chlorides, sulfates, acid rain, etc)
Carbonation, Alkali-Silica-Reaction (ASR)
Delayed Ettringite Formation (DEF)
Self-healing
Loading or Testing Method
Loading rate
Number of load applications (damage, fatigue)
In-situ vs. lab produced specimen
Specimen size and shape
Loading direction vs. casting direction
Stiffness of testing machine (post-peak response)
Concrete Reinforcement
• Discrete steel reinforcing bars (reinforced concrete)
• Randomly distributed and oriented short fibers to modify the
mechanical properties of the cement matrix (fiber reinforced
concrete)
• Continuous fiber mesh or textiles with fibers (rovings) in at least
two directions (textile reinforced concrete)
Properties of reinforcement display much less statistical scatter
than those of concrete, so do the properties of the composite
Conclusions
• The mechanical and other properties of concrete are subject to
many variables, only some of which can be controlled to reduce
statistical scatter.
• Concrete is often modeled as a simplified two-phase composite
(aggregate and cement paste), using the representative volume
element (RVE).
• Since the properties of reinforcement have less statistical scatter
than those of concrete, the properties of Reinforced Concrete (a
three-phase composite) are likewise subject to lower uncertainty.