Elsevier

Cement and Concrete Research

Volume 45, March 2013, Pages 55-68
Cement and Concrete Research

Effect of gel–space ratio and microstructure on strength of hydrating cementitious materials: An engineering micromechanics approach

https://doi.org/10.1016/j.cemconres.2012.10.019Get rights and content

Abstract

Strengths of cement pastes with different mixture properties and maturities depend in a very similar overlinear fashion on the gel–space ratio, which is the ratio of the volume of hydration products over the volume of both hydration products and capillary pores. We here investigate the underlying microstructural effects by the experimentally validated micromechanics model of Pichler and Hellmich [CemConRes 41(5), 2011]. This model shows that the macrostrength of cement pastes are not only triggered by the capillary porosity, but also by a strengthening effect of unhydrated clinker “reinforcements” which are embedded as inclusions in the hydrate foam. The analysis is continued with quantifying the strength of the hydrates, in terms of an extended model validation activity. Satisfactory model performance is the motivation to present model predictions for the biaxial compressive failure envelopes of cement pastes, again as a function of gel–space ratio.

Introduction

Gel–space ratio is defined as the volume of gel divided by the sum of the volumes of gel and capillary pores [4], whereby “gel” is a synonym for hydration products which include the so-called gel pores of typically 0.5 nm to 2.5 nm characteristic length. Therefore, a relation between gel–space ratio, on the one hand, and initial water-to-cement mass ratio as well as hydration degree, on the other hand, is accessible through hydration models. The one of Powers and Acker [4], [5], for instance, provides expressions for the cement paste-related volume fractions of unhydrated clinker (fclin), hydration products (referred to herein as “hydrates”, fhyd), as well as water and air filling the capillary pores (fH2O and fair), as functions of the initial water-to-cement mass ratio w/c and of the hydration degree ξ:fclinw/c;ξ=1ξ1+ρclinρH2Ow/c=201ξ20+63w/c0,fhydw/c;ξ=1.42ρclinξρhyd1+ρclinρH2Ow/c=43.15ξ20+63w/c,fH2Ow/c;ξ=ρclinw/c0.42ξρH2O1+ρclinρH2Ow/c=63w/c0.42ξ20+63w/c0,fairw/c;ξ=1fclinfH2Ofhyd=3.31ξ20+63w/c.

In Eq. (1), ρclin = 3.15 kg/dm3 [6], ρH2O = 1 kg/dm3, and ρhyd = 2.073 kg/dm3 [7] are the mass densities of clinker, water, and hydrates, respectively. Hydration degree ξ is defined as the mass of currently formed hydrates over the mass of hydrates formed when – at least theoretically – all available clinker is consumed by the chemical hardening process. Formulating the definition of gel–space ratio γ in terms of the phase volume fractions (1) deliversγw/c;ξ=fhydfhyd+fH2O+fair=1.42ρclinξρhydξ+ρclinρH2Ow/c=43.15ξ20ξ+63w/c.

Strengths of cement pastes with different mixture properties and maturities depend in a very similar overlinear fashion on this gel–space ratio. This is typically explained through the capillary porosity playing, among all microstructural properties, the governing role for the strength of cement pastes [4]. However, the final strength of substoichiometric cement pastes (with water–cement ratio smaller than 0.42) increases with decreasing (initial) water-to-cement ratio, which Fagerlund [8] explained by an empirical relationship. Here, we wish to explain Fagerlund's observation from a micromechanical perspective, as to gain more detailed insight into the question on how microscopic properties and processes influence the macroscopic strength of cement paste. To this end, the present paper is structured as follows: Section 2 is devoted to the re-analysis of Taplin's landmark test results [9] in the framework of gel–space ratio. In Section 3 we apply a recently developed and validated elasto-brittle strength model [1] to Taplin's data, which sheds light on the strengthening effect of unhydrated clinker “reinforcements” on the macrostrength of cement pastes. Section 4 deals with identification of the microscopic strength of hydration products and with continued model validation, based on – in total – four different sets of strength data from uniaxial compressive testing on cement pastes and mortars. In Section 4, we evaluate the model for macroscopic biaxial compression in order to study failure envelopes (in the compression–compression quadrant of the biaxial stress plane) for cement pastes with different compositions as a function of gel–space ratio. In Section 5, we discuss several aspects of our model in light of other works from the published literature on the topic, before we conclude in Section 6.

Section snippets

Gel space ratio-dependent strength, derived for data of Taplin

Taplin [9] used a normal Portland cement for the production of cement pastes with water–cement ratios ranging from 15.7% to 80%. All samples were right rectangular prisms measuring 4 by 0.5 by 0.5 in. They were cured at 25 °C. At the time of testing, the prisms were broken into two halves, which resulted in two short bars with an axial length of 2 in. and a quadratic cross-section measuring by 0.5 by 0.5 in. Each bar was tested in uniaxial compression, perpendicular to its axis. Therefore,

Representative volume elements and separation of scales

During the last decade, micromechanics and homogenization theories have become a well-accepted tool for studying the mechanical properties of hydrating cement pastes and mortars [12], [6], [13], [14], [15], [16], [17], [18] and among these theories, continuum micromechanics plays an important role. In continuum micromechanics [19], [20], [21], [22], a material is considered as a macro-homogeneous, but micro-heterogeneous body occupying a representative volume element (RVE) with characteristic

Identification and validation of deviatoric hydrate strength, from independent test data sets

The value of the microscopic deviatoric hydrate strength σhydult,dev has been estimated on the order of magnitude of 50 MPa [1], but elaborate identification of this material property was not carried out so far. This is done next, based on data from macroscopic material testing on stoichiometric cement pastes samples, performed at the Vienna University of Technology (TU Wien). Subsequently, in Section 4.2, we will confront model predictions based on the identified hydrate strength with cement

Model-predicted biaxial compressive strength of cement paste

Motivated by the satisfactory validation results obtained in Section 4, we here evaluate the microelasto-brittle strength criterion (Eqs. (13), (14)) for macroscopic biaxial compressionΣcp=Σcp,1e¯1e¯1Σcp,2e¯2e¯2.

For the computation of model-predicted failure surfaces, we set ∑ cp,2 equal to κ  cp,1, and we consider biaxial stress ratios κ in the interval ranging from − 0.1 to 1.0. The intensity of the macrostress component ∑ cp,1 yielding to an equality in the described strength criterion,

Discussion

We here discuss several aspects of our engineering mechanics approach in light of other works from the published literature. This includes maximum hydration degrees typically reached in real applications, potentially occurring cracks in the pre-failure regime, the possibility of clinker failure prior to hydrate failure, the typical shape of real hydration products and the motivation to model hydrates as needles, the reliability of bound water content-based determination of hydration degrees, as

Conclusions

The maturity parameter “gel–space ratio” is equal to the solid volume fraction of a hydrate foam consisting of hydration products and capillary pores. The used micromechanics model [1] envisions cement paste to be a matrix-inclusion composite, with a matrix made up of this hydrate foam and inclusions in form of unhydrated clinker grains which act as reinforcements. The key quantity governing all outputs of the presented micromechanics model is the deviatoric hydrate strength, which we

Acknowledgment

The fourth author gratefully acknowledges the “Erasmus Student Mobility Grant for Training” from the Education and Culture Department of the European Commission within the “Lifelong Learning Program”, rendering his stay at Vienna University of Technology possible.

References (69)

  • W.R. Drugan et al.

    A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites

    J. Mech. Physics Solids

    (1996)
  • A. Fritsch et al.

    Universal microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: micromechanics-based prediction of anisotropic elasticity

    J. Theor. Biol.

    (2007)
  • R. Hill

    A self-consistent mechanics of composite materials

    J. Mech. Physics Solids

    (1965)
  • B. Budiansky

    On the elastic moduli of some heterogeneous materials

    J. Mech. Physics Solids

    (1965)
  • T. Mori et al.

    Average stress in matrix and average elastic energy of materials with misfitting inclusions

    Acta Metall.

    (1973)
  • Y. Benveniste

    A new approach to the application of Mori-Tanaka's theory in composite materials

    Mech. Mater.

    (1987)
  • T.D. Ciach et al.

    Microstructure of calcium silicate hydrates

    Cem. Concr. Res.

    (1971)
  • R.B. Williamson

    Solidification of Portland cement

    Prog. Mater. Sci.

    (1972)
  • X.F. Gao et al.

    Analysis of the infrared spectrum and microstructure of hardened cement paste

    Cem. Concr. Res.

    (1999)
  • J. Tritthart et al.

    Pore solution analysis of cement pastes and nanostructural investigations of hydrated C3S

    Cem. Concr. Res.

    (2003)
  • K.L. Scrivener

    Backscattered electron imaging of cementitious microstructures: understanding and quantification

    Cem. Concr. Compos.

    (2004)
  • R. Berliner et al.

    Quasielastic neutron scattering study of the effect of water-to-cement ratio on the hydration kinetics of tricalcium silicate

    Cem. Concr. Res.

    (1998)
  • L. Dormieux et al.

    Micromechanical approach to the behavior of poroelastic materials

    J. Mech. Phys. Solids

    (2002)
  • W. Kreher et al.

    Residual stresses in polycrystals as influenced by grain shape and texture

    J. Mech. Physics Solids

    (1993)
  • P. Termkhajornkit et al.

    Modeling the coupled effects of temperature and fineness of Portland cement on the hydration kinetics in cement paste

    Cem. Concr. Res.

    (2012)
  • F. Lin et al.

    Hydration kinetics modeling of Portland cement considering the effects of curing temperature and applied pressure

    Cem. Concr. Res.

    (2009)
  • K. Velez et al.

    Determination by nanoindentation of elastic modulus and hardness of pure constituents of Portland cement clinker

    Cem. Concr. Res.

    (2001)
  • G. Constantinides et al.

    The nanogranular nature of C–S–H

    J. Mech. Physics Solids

    (2007)
  • I.G. Richardson

    Tobermorite/jennite- and tobermorite/calcium hydroxide-based models for the structure of C–S–H: applicability to hardened pastes of tricalcium silicate, β -dicalcium silicate, Portland cement, and blends of Portland cement with blast-furnace slag, metakaolin, or silica fume

    Cem. Concr. Res.

    (2004)
  • L.J. Parrott et al.

    Monitoring Portland cement hydration: comparison of methods

    Cem. Concr. Res.

    (1990)
  • J.I. Escalante-Garcia

    Nonevaporable water from neat OPC and replacement materials in composite cements hydrated at different temperatures

    Cem. Concr. Res.

    (2003)
  • K.L. Scrivener et al.

    Quantitative study of Portland cement hydration by X-ray diffraction/Rietveld analysis and independent methods

    Cem. Concr. Res.

    (2004)
  • F.P. Ganneau et al.

    Dual-indentation technique for the assessment of strength properties of cohesive-frictional materials

    Int. J. Solids Struct.

    (2006)
  • P. Catharin

    Hydratationswärme und Festigkeitsentwicklung [Hydration heat and strength development]

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    From 10/2010 to 03/2011 on leave from Centre for Material Research, Brno University of Technology, Purkyňova 118, CZ-61200 Brno, Czech Republic.

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