1. 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

2. 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

3. CONCRETE By far the most important building material worldwide > 10 Billion tons/year produced worldwide > 700 Million tons/year produced in the US (2000)

4. Main Advantages  Mechanical Properties  Durability  Moldability  Adaptability  Fire Resistance  General Availability  Affordability  Engineered Material

5. 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

6. 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

7. Concrete Strength vs. Age (Mindess, Young, Darwin)

8. Shear Strength of Concrete

9. Concrete Creep Data – Theory vs. Experiment ( Sakata and Shimomura, J. Adv. Conc. Techn., 2004, p 134)

10. Frequency Distribution of 22 Mortar Bar ASR-Expansions

11. Expansion Error

12. Sources of Property Randomness Binder Aggregate Admixtures Mix Proportions Production Environmental Factors Testing Method/Protocol or Loading

13. Typical Composition of Ordinary Portland Cement Chemical Name Formula Shorthand =Weight % Tricalcium Silicate3CaO  SiO 2 C 3 S 55 Dicalcium Silicate2CaO  SiO 2 C 2 S 18 Tricalcium Aluminate3CaO  Al 2 O 3 C 3 A10 Tetracalcium Aluminoferrite4CaO  Al 2 O 3  Fe 2 O 3 C 4 AF 8 _ GypsumCaSO 4  2H 2 O CSH 2 6 (Role of impurities: Alite – impure C 3 S, Belite – impure C 2 S)

14. Typical Oxide Composition of Portland Cement Lime (C, CaO)63% Silica (S, SiO 2 )20% Alumina (A, Al 2 O 3 ) 6% Ferric Oxide (F, Fe 2 O 3 ) 3% Gypsum (SO 3, CaSO 4 ) 2% Magnesia (M, MgO)1.5% Alkalis (K 2 O, Na 2 O)1.0% Ignition Loss 2.0% Insoluble Residue 0.5% Balance 1.0%

15. 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 SiO 2 20 %22 %20 % Al 2 O 3 7 7.7 5.5 Fe 2 O 3 3 3.3 4.5 CaO 666366 Balance 4 4 4 Minerals C 3 S653373 C 2 S 838 2 C 3 A1415 7 C 4 AF 91014

16. Chemical Reactions of Hydration Tricalcium Silicate + Water  C-S-H + Calcium Hydroxide + Heat 2(3CaO  SiO 2 ) + 11H 2 O  3CaO  2SiO 2  8H 2 O + 3Ca(OH) 2 In shorthand, 2C 3 S + 11H  C 3 S 2 H 8 + 3CH Dicalcium silicate, 2C 2 S + 9H  C 3 S 2 H 8 + CH Tricalcium Aluminate + Gypsum + Water  Ettringite C 3 A + 3CSH 2 + 26H  C 6 AS 3 H 32 Later, after all gypsum has been consumed, 2C 3 A + C 6 AS 3 H 32 + 4H  3C 4 ASH 12 (Monosulfoaluminate) (Complex interactions)

17. Hydrated C 3 S Paste

18. Aggregate Natural vs. manufactured (crushed stone) Mineral composition (reactivity) Particle size distribution (grading curve) Mechanical properties

19. Mix Proportions Water/Cement Ratio Cement/Aggregate Ratio Air Content/Porosity Admixtures

20. Production (Quality Control) Impurities, Contaminants Mixing Conveyance, Transportation Placement Consolidation Finishing Curing (Age)

21. 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

22. 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)

23. 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

24. 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.