Acta Mech 203, 137–162 (2009)
DOI 10.1007/s00707-008-0007-9
Bernhard Pichler · Christian Hellmich · Josef Eberhardsteiner
Spherical and acicular representation of hydrates
in a micromechanical model for cement paste:
prediction of early-age elasticity and strength
Received: 25 September 2007 / Revised: 9 January 2008 / Published online: 20 June 2008
© Springer-Verlag 2008
Abstract Early-age stiffness and strength evolution of cement paste is studied in the framework of con
micromechanics. Based on the self-consistent scheme, elastic and strength properties are upscaled f
scale of several micrometers up to the scale of several hundreds or thousands of micrometers. Four
phases are considered: clinker, hydration products, water and air. We assign a spherical geometry to
grains and pores, while we investigate both spherical and acicular (needle-type) shapes as geometric
resentation of the micrometer-sized hydration products. As regards macroscopic poromechanical boundary
conditions, two extreme cases are considered: drained conditions and sealed conditions, respectively
choices allow for studying the influence of (i) the morphological representation of hydrates, and of (i
bulk stiffness of water, on the micromechanical prediction of early-age behavior of cement paste, inc
setting and the hydration-dependent evolutions of both elastic stiffness and uniaxial compressive str
newly proposed strength model is based on a von Mises-type elastic limit criterion for individual hyd
Corresponding deviatoric stress peaks within hydrates are estimated through quadratic stress avera
way, the micromechanical strength criterion is formulated in terms of macroscopic loading (stresses
respectively). Model-predicted elasticity and strength evolutions are compared with data from exper
testing of cement pastes with water–cement ratios ranging from 0.35 to 0.60. Satisfactory agreemen
model predictions and experiments allows for two conclusions: the morphology of hydrates significan
ences micromechanics-based elastic stiffness estimates of cement paste particularly at very early ag
elastic properties of mature cement paste can be estimated reliably on the basis of both spherical or
shaped hydrates. The development of a reliable strength model, however, requires consideration of h
as non-spherical particles, no matter what age of cement paste is considered.
List of symbols and abbreviations
C
2
S abbreviation for dicalcium silicate: 2CaO · SiO
2
C
3
A abbreviation for tricalcium aluminate: 3CaO · Al
2
O
3
C
4
F A abbreviation for calcium aluminoferrite: 4CaO · Al
2
O
3
· Fe
2
O
3
C
3
S abbreviation for tricalcium silicate: 3CaO · SiO
2
C-S-H abbreviation for calcium silicate hydrates
B. Pichler ( B) · C. Hellmich · J. Eberhardsteiner
Institute for Mechanics of Materials and Structures, Vienna University of Technology (TU Wien),
Karlsplatz 13/202, 1040 Vienna, Austria
E-mail: Bernhard.Pichler@tuwien.ac.at
C. Hellmich
E-mail: Christian.Hellmich@tuwien.ac.at
J. Eberhardsteiner
E-mail: Josef.Eberhardsteiner@tuwien.ac.at