Institute for Mechanics of Materials and Structures Vienna University of Technology Prediction of the early-age strength evolution of cement paste and shotcrete 1 / 13 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

Vienna University of Technology Prediction of the early-age strength evolution of cement paste and shotcrete 2 / 13 Motivation: Compressive strength of cementitious materials increases first overlinearly and the linearly with hydration degree Challenge: Jan Byfors, PhD thesis, 1980 Identify microstructural characteristics driving this behavior

Institute for Mechanics of Materials and Structures Vienna University of Technology Prediction of the early-age strength evolution of cement paste and shotcrete 3 / 13 Hierarchical organization of shotcrete Chatterji and Jeffrey, Nature, 209, shotcrete agg aggregates Pichler and Hellmich, CemConRes 41 (5) , 2011

Institute for Mechanics of Materials and Structures Vienna University of Technology Prediction of the early-age strength evolution of cement paste and shotcrete 4 / 13 heterogeneity size Elements of continuum micromechanics  Representative volume elements consist of quasi-homogeneous material phases  Strain concentration from uniform strain boundary conditions to average phase strains:  Stiffness homogenization  RVEs satisfy „separation of scales“ RVE size length of stress- and strain- fluctuations in structure containing the RVE phase strain con- centration tensor Hill, JMPS, 11(5), , 1963 phase volume fractions phase elasticity tensors Hill, JMPS, 11(5), , 1963

Institute for Mechanics of Materials and Structures Vienna University of Technology Prediction of the early-age strength evolution of cement paste and shotcrete 5 / 13 Homogenized stiffness volume fraction elastic stiffness Hill tensors (phase shape) aux. stiffness (phase interaction) matrix-inclusion composite Mori-Tanaka scheme accessible via estimate of phase strain concentration tensors Zaoui, Lecture Notes, Ecole Polytechnique, 1997 Zaoui, J.Eng.Mach (ASCE) 128(8), , 2002 polycrystalline composite Self-consistent scheme Specification for: hydrate foam, cement paste, shotcrete Eshelby, Proc.R.Soc.Lond.A. 241, ,1957 Laws, Journal of Elasticity, 7(1), 91-97, 1977 Hill, JMPS, 11(5), , 1963

Institute for Mechanics of Materials and Structures Vienna University of Technology Prediction of the early-age strength evolution of cement paste and shotcrete 6 / 13 Elasticity of shotcrete phases Acker, 15-26, 2001 Bernard et al. CCR 33 (9) , 2003 Ulm et al. Mat. Struc. 37(1), 43-58, 2004 Pichler and Hellmich CCR 41 (5) , 2011 Liquid phases in drained conditions Constant at all times (universal properties) Accessible via ultrasonics and nanoindentation

Institute for Mechanics of Materials and Structures Vienna University of Technology Prediction of the early-age strength evolution of cement paste and shotcrete 7 / 13 Phase volume fractions depend on composition and maturity Powers, Brownyard, Res.Lab.Port.Cem.Ass.Bull, , 1948 Acker et al. in Concrete at Early Ages, ACI, 33-48, 1986 shotcrete

Institute for Mechanics of Materials and Structures Vienna University of Technology Prediction of the early-age strength evolution of cement paste and shotcrete 8 / 13 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 Access to stress peaks in hydrates via quadratic stress averages: Kreher, JMPS 38(1), , 1990 Dormieux, Molinari, Kondo, JMPS 50(10), , 2002 Pichler, Hellmich, Eberhardsteiner, Acta Mechanica, 203, , 2009 Pichler, Hellmich, CemConRes, 41, , 2011  Elastic limit at microscale refers to macroscopic strength of RVE

Institute for Mechanics of Materials and Structures Vienna University of Technology Prediction of the early-age strength evolution of cement paste and shotcrete 9 / 13 Validation of strength model for cement paste model predictionsversus Taplin, Aus.J.Appl.Sci., 10(3), , 1959 independent experiments Identification of hydrate strength: Model predictions agree well with experiments on 6 different compositions Pichler and Hellmich, CemConRes 41 (5) , 2011

Institute for Mechanics of Materials and Structures Vienna University of Technology Prediction of the early-age strength evolution of cement paste and shotcrete 10 / 13 Validation of strength model for shotcrete model predictions versus independent experiments Model predictions agree well with experiments from 2 labs on 2 compositions Ullah Pichler Scheiner Hellmich, I J Numer Anal Meth Geomech, in print, 2011

Institute for Mechanics of Materials and Structures Vienna University of Technology Prediction of the early-age strength evolution of cement paste and shotcrete 11 / 13 From quasi-brittle hydrate strength to nanoindentation hardness von Mises strength Pure shear strength (cohesion) Transition to hardness via yield design approach Ganneau, Constantinides, Ulm, IJSS, 43 (6), , 2006 Comparison with nanoindentation- derived C-S-H hardnesses Hydrate strength is consistent with nanoindentation hardness

Institute for Mechanics of Materials and Structures Vienna University of Technology Prediction of the early-age strength evolution of cement paste and shotcrete 12 / 13 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 Conclusions

Institute for Mechanics of Materials and Structures Vienna University of Technology Prediction of the early-age strength evolution of cement paste and shotcrete 13 / 13 Thank you very much for your attention!