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

Abstract

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(Pichler et al., -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).

Characterizing Strength and Failure of Calcium Silicate Hydrate Aggregates in Cement Paste under Micropillar Compression

“…In the framework of continuum micromechanics, Hellmich (2011) andPichler et al (2013a) calculated deviatoric strength of microscopic hydrates to be 69.9 MPa based on an elasto-brittle multiscale model for cementitious materials. Using Mohr-Coulomb parameters from finite-element reanalysis of nanoindentation results, the corresponding model predicted uniaxial compressive strength of low-density C-S-H of 123.5 MPa, which is slightly lower than, but in the same order of magnitude as, the experimental results presented here (Pichler et al 2013b;Sarris and Constantinides 2013). Furthermore, in modeling hydrate foam in the first step of homogenization, Pichler et al (2013a) used a representative volume element (RVE) of 20 μm, which is considerably larger than the average diameter of the tested micropillars in the present study.…”

Unloading‐Based Stiffness Characterisation of Cement Pastes During the Second, Third and Fourth Day After Production

“…Notably, strength evolutions have turned out to be overlinear at very early ages, see Figure of , such that straight line extrapolations to very early ages are expected to yield upper bounds for hydration degree thresholds, see Figure of . Given that similar over‐linearities of stiffness histories were observed for cement paste at very early age , reminiscent of the situation encountered with concretes , it is recommended to interpret the thresholds listed in Table as upper bounds.…”

Strength of a cement-based dental material: Early age testing and first micromechanical modeling at mature age

“…Biodentine, in turn, consists of LDCR hydrates and HDCR hydrates ( Dohnalík et al, 2021 ). The microstructure of construction “cement pastes” typically consists of two times more low-density than high-density C-S-H ( Constantinides and Ulm, 2004 ), and the strength properties of low-density C-S-H ( Sarris and Constantinides, 2013 ) can be upscaled to explain the macroscopic strength of construction “cement pastes” ( Pichler and Hellmich, 2011 ; Pichler et al, 2013b ) and of related concretes ( Königsberger et al, 2018 ). The microstructure of Biodentine, in turn, consists of six times more HDCR than LDCR hydrates ( Dohnalík et al, 2021 ), and the macroscopic strength of Biodentine is significantly larger than that of construction “cement pastes”.…”

“…Cementitious hydration products resulting from the dissolution of dicalcium and tricalcium silicate and from precipitation of solids out of the oversaturated porewater solution, are known to exhibit pressure-sensitive shear failure ( Constantinides et al, 2006 ; Pichler et al, 2013b ; Sarris and Constantinides, 2013 ; Königsberger et al, 2018 ). The corresponding Mohr-Coulomb failure criterion reads as ( Königsberger et al, 2018 ): where σ I denotes the largest principal normal stress, σ III the smallest principal normal stress, c the cohesion, and φ the angle of internal friction.…”