Rémi Barbarulo

The Counteracting Effects of Capillary Porosity and of Unhydrated Clinker Grains on the Macroscopic Strength of Hydrating Cement Paste–A Multiscale Model

Strength of cement pastes increases overlinearly with decreasing capillary porosity, such as suggested by the gel-space ratio model of Freyssinet (1933). This model, however, cannot explain that strength of mature sub-stoichiometric cement pastes increases with decreasing w/c-ratio, such as observed by Fagerlund (1972). The latter observation might well stem from a strengthening effect of unhydrated clinker grains, but until very recently an etiological model for quantification of this effect was out of reach. This provides the motivation for the present study, where we envision that the strength of microscopic cement hydrates is the limiting factor for the load carrying capacity of macroscopic cement paste samples. In more detail, we envision a stress-based strength criterion for microscopic hydrate needles, whereby the involved hydrate strength constant is determined from the results of nanoindentation experiments on low-density C-S-H, performed by Constantinides and Ulm (2006). Strength upscaling is performed within the framework of continuum micromechanics (Pichler et al., 2008-2013). Modelpredicted macrostrength values of cement pastes (exhibiting different compositions and different maturities) agree very well with strength values measured at three different laboratories. The validated model confirms that strength of cement pastes is strongly influenced by capillary porosity, and that unhydrated clinker grains act as significantly strengthening reinforcements for mature substoichiometric pastes (Pichler et al. 2013).

Strength Evolution of Hydrating Cement Pastes: the Counteracting Effects of Capillary Porosity and Unhydrated Clinker Reinforcements

In the 1930s, Freyssinet presented a model describing that strength of cement paste decreases with increasing capillary porosity: he proposed that uniaxial compressive strength of cement pastes is proportional to a volume quotient which is nowadays referred to as “gel-space ratio”. In the 1970s, Fagerlund found out that capillary porosity is not the only governing factor, because he observed that the final strength of substoichiometric cement pastes increases with decreasing initial water-to-cement mass ratio. However, due to limited microstructural insight, he could only propose an empirical description of the observed effect. We here provide more insight into how microstructural properties of cement paste influence its macroscopic compressive strength, based on the experimentally confirmed elasto-brittle micromechanics model of Pichler and Hellmich [CemConRes, 41(5) 467-476, 2011]. Gel-space ratio is shown to be equal to the solid volume fraction of a “hydrate foam” which is defined at the scale of a few microns, and which exhibits a (quasi-)polycrystalline morphology of needle-shaped and isotropically oriented hydration products with capillary porosity filling the space in between. The model confirms that the material strength of cement pastes is not only determined by the capillary porosity, but unhydrated clinker grains (which are embedded, as inclusions, in the hydrate foam) act as reinforcements which increase the macroscopic strength; and that this is practically significant for substoichiometric mixes at