Baltimore

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

 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 Formula Shorthand =Weight %



Tricalcium

Silicate 3CaOSiO2 C 3S 55

Dicalcium

Silicate 2CaOSiO2 C 2S 18

Tricalcium

Aluminate 3CaOAl2O3 C 3A 10

Tetracalcium

Aluminoferrite 4CaOAl2O3Fe2O3 C4AF 8

_

Gypsum CaSO42H2O CSH2 6

(Role of impurities: Alite – impure C3S, Belite – impure C2S)

Typical Oxide Composition of Portland Cement



Lime (C, CaO) 63%

Silica (S, SiO2) 20%

Alumina (A, Al2O3) 6%

Ferric Oxide (F, Fe2O3) 3%

Gypsum (SO3, CaSO4) 2%

Magnesia (M, MgO) 1.5%

Alkalis (K2O, Na2O) 1.0%

Ignition Loss 2.0%

Insoluble Residue 0.5%

Balance 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 Cement No. 1 Cement No. 2 Cement No. 3

SiO2 20 % 22 % 20 %

Al2O3 7 7.7 5.5

Fe2O3 3 3.3 4.5

CaO 66 63 66

Balance 4 4 4



Minerals

C3S 65 33 73

C2S 8 38 2

C3A 14 15 7

C4AF 9 10 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.