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

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, 1966 http://www.fhwa.dot.govhttp://www.fhwa.dot.gov

shotcreteagg

aggregates

Pichler and Hellmich, CemConRes 41 (5) 467-476, 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-homogeneousmaterial phases

Strain concentration from uniform strain boundary conditionsto average phase strains:

Stiffness homogenization

RVEs satisfy „separation of scales“

RVE size

length of stress- and strain- fluctuations in structurecontaining the RVE

phase strain con-centration tensorHill, JMPS, 11(5), 357-372, 1963

phase volume fractions phase elasticity tensors

Hill, JMPS, 11(5), 357-372, 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), 808-816, 2002

• polycrystalline composite Self-consistent scheme

Specification for: hydrate foam, cement paste, shotcrete

Eshelby, Proc.R.Soc.Lond.A. 241, 367-396,1957 Laws, Journal of Elasticity, 7(1), 91-97, 1977

Hill, JMPS, 11(5), 357-372, 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, 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

• 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 maturityPowers, Brownyard, Res.Lab.Port.Cem.Ass.Bull, 22 101-992, 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), 115-128, 1990 Dormieux, Molinari, Kondo, JMPS 50(10), 2203-2231, 2002

Pichler, Hellmich, Eberhardsteiner, Acta Mechanica, 203, 137-162, 2009Pichler, Hellmich, CemConRes , 41, 467-476, 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 predictions versusTaplin, Aus.J.Appl.Sci., 10(3), 329-345, 1959

independent experiments

Identification ofhydrate strength:

Model predictions agree well with experiments on 6 different compositions

Pichler and Hellmich, CemConRes 41 (5) 467-476, 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), 1727-1745, 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!

Bernhard.Pichler@tuwien.ac.at