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Prediction of the early-age strength evolution of cement paste and shotcrete

Prediction of the early-age strength evolution of cement paste and shotcrete

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## Prediction of the early-age strength evolution of cement paste and shotcrete

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**Prediction of the early-age strength evolution of cement**paste and shotcrete Bernhard Pichler and Christian Hellmich Vienna University of Technology (TU Wien), Austria Institute for Mechanics of Materials and Structures**Motivation:**• Compressive strength of cementitious materials increases first overlinearly and the linearly with hydration degree Jan Byfors, PhD thesis, 1980 Challenge: • Identify microstructural characteristics driving this behavior**Hierarchical organization of shotcrete**Pichler and Hellmich, CemConRes 41 (5) 467-476, 2011 http://www.fhwa.dot.gov Chatterji and Jeffrey, Nature, 209, 1966 http://www.fhwa.dot.gov shotcrete agg aggregates**Elements of continuum micromechanics**• Representative volume elements consist of quasi-homogeneousmaterial phases • RVEs satisfy „separation of scales“ • length of stress- and strain- fluctuations in structurecontaining the RVE • heterogeneity • size • RVE size • Strain concentration from uniform strain boundary conditions to average phase strains: Hill, JMPS, 11(5), 357-372, 1963 • phase strain con-centration tensor • Stiffness homogenization Hill, JMPS, 11(5), 357-372, 1963 • phase elasticity tensors • phase volume fractions**Homogenized stiffness**Hill, JMPS, 11(5), 357-372, 1963 accessible via estimate of phase strain concentration tensors Zaoui, Lecture Notes, EcolePolytechnique, 1997 Zaoui, J.Eng.Mach (ASCE) 128(8), 808-816, 2002 Eshelby, Proc.R.Soc.Lond.A. 241, 367-396,1957 Laws, Journal of Elasticity, 7(1), 91-97, 1977 volume fraction Hill tensors (phase shape) aux. stiffness (phase interaction) elastic stiffness • matrix-inclusion composite Mori-Tanaka scheme • polycrystalline composite Self-consistent scheme Specification for: hydrate foam, cement paste, shotcrete**Elasticity of shotcrete phases**• Constant at all times (universal properties) • Accessible via ultrasonics and nanoindentation Acker, Proc.CONCREEP@MIT, 15-26, 2001 Bernard et al. CCR 33 (9) 1293-1309, 2003 Ulm et al. Mat. Struc. 37(1), 43-58, 2004 Pichler and Hellmich CCR 41 (5) 467-476, 2011 Liquid phases in drained conditions**Phase volume fractions depend on composition and maturity**Powers, Brownyard, Res.Lab.Port.Cem.Ass.Bull, 22 101-992, 1948 Acker et al. in Concrete at Early Ages, ACI, 33-48, 1986 shotcrete**Elasto-brittle strength of shotcrete**Cementitious materials behave linear elastic, as long as deviatoric stress peaks in all hydrates are smaller than a hydrate strength Pichler, Hellmich, Eberhardsteiner, ActaMechanica, 203, 137-162, 2009Pichler, Hellmich, CemConRes , 41, 467-476, 2011 • Elastic limit at microscale refers to macroscopic strength of RVE Access to stress peaks in hydrates via quadratic stress averages: Kreher, JMPS 38(1), 115-128, 1990 Dormieux, Molinari, Kondo, JMPS 50(10), 2203-2231, 2002**Validation of strength model for cement paste**independent experiments versus model predictions Taplin, Aus.J.Appl.Sci., 10(3), 329-345, 1959 Identification ofhydrate strength: Pichler and Hellmich, CemConRes 41 (5) 467-476, 2011 Model predictions agree well with experiments on 6 different compositions**Validation of strength model for shotcrete**model predictions versus independent experiments Ullah Pichler Scheiner Hellmich, I J Numer Anal MethGeomech, in print, 2011 Model predictions agree well with experiments from 2 labs on 2 compositions**From quasi-brittle hydrate strength to nanoindentation**hardness • von Mises strength • Pure shearstrength (cohesion) • Transition tohardness via yield design approach • Comparison with nanoindentation-derived C-S-H hardnesses Hydrate strength is consistent with nanoindentation hardness Ganneau, Constantinides, Ulm, IJSS, 43 (6), 1727-1745, 2006**Conclusions**• Strength of cement-based materials is governed by microstructure-dependent load transfer from the macroscale to micron-sized hydrates • One hydrate strength value allows for prediction of early-age strength evolutions of cement pastes and shotcretes with different compositions (no fitting parameters) • Identified hydrate strength is consistent with nanoindentation hardnesses**Thank you very much for your attention!**Bernhard.Pichler@tuwien.ac.at