Upscaling quasi-brittle strength of cement paste and mortar: A multi-scale engineering mechanics model

Uncertainty propagation of a multiscale poromechanics-hydration model for poroelastic properties of cement paste at early-age

“…In particular, Sanahuja et al [15] considered LD C-S-H particles as platelets (oblates) with an aspect ratio varying in function of the water-to-cement ratio. On the other hand, Pichler et al [39,51] represented C-S-H as needle-like particles independently of the water-tocement ratio. Although both of these approaches were successfully applied, they were adapted to specific representations of the microstructure that differ from the ones adopted by Bernard et al [6] and presented on Fig.…”

“…The self consistent scheme is well-suited to capture the solid percolation threshold of the REV drawn at level II [6]. However, as it was pointed out by different authors for low water-to-cement ratios, additional precautions must be taken into account to ensure the accuracy of the prediction of the solid percolation threshold [6,14,15,51]. In particular, Sanahuja et al [15] considered LD C-S-H particles as platelets (oblates) with an aspect ratio varying in function of the water-to-cement ratio.…”

“…However, the steady value reached after the hydration of 50% of the cement suffers less from discrepancy with observations than the shape of the predicted relation ν u (t). We remind here that none of the studies conducted by Bernard et al [6], Sanahuja et al [15] and Pichler et al [39,51] The multiscale poromechanics-hydration model is validated for its capaciy to predict the evolution at early-age of the elastic properties of cement pastes with water-to-cement ratios between 0.35 and 0.70. The upper-limit value of w/c is imposed by the validity domain of the kinetic parameters calibrated by Berliner et al [64] and the lower value is prescribed by the limitation of the self-consistent homogenization scheme adopted at level II (see Section 3.2.2) to model percolation.…”

Self-Consistent Channel Approach for Upscaling Chloride Diffusivity in Cement Pastes

“…We may also mention that our approach is fully consistent with the current state of the art in the mathematical modeling of concrete: In fact, our microheterogeneous formulation rests on the famous hydration model of Powers and Brownyard (1948) and Acker (2001), which has not only provided the basis for numerous, experimentally validated, micromechanical descriptions Sanahuja et al 2007;Pichler et al 2009b;Scheiner and Hellmich 2009), but has also been kind of corroborated by very recent statistical physics approaches (Ioannidou et al 2016). In the aforementioned micromechanics approaches, an RVE of cement paste is either composed of water pores, air pores, hydrates, and unhydrated cement (clinker) grains Pichler et al 2009b;Scheiner and Hellmich 2009), or of clinker grains embedded into a hydrate foam matrix, whereby the latter is, at a smaller scale, resolved into hydrates, water pores, and air pores; i.e., a hierarchical system of two RVEs is used to represent cement paste (Pichler and Hellmich 2011; Pichler et al (2009b) and Scheiner and Hellmich (2009), involving only one RVE representing the composite material cement paste. Actually, we additionally merge, on the one hand, the water and air pore phases into one phase called "capillary porosity" (this merging results from the experimental conditions realized in standard diffusion tests), and on the other hand, the hydrate and clinker phases are merged as well, into one "solid phase" (given their non-diffusible nature as compared to that of the pores).…”

“…Explicit consideration of the latter has allowed for substantial improvements of microstructural models for the mechanics of cement paste and concrete (Sanahuja et al 2007;Pichler et al 2009a;Pichler and Hellmich 2011). The same is true for a micromechanical model of gypsum which considers the physically active (solid) parts of the microstructure as infinitely many non-spherical phases (Sanahuja et al 2010), while the physically non-active (fluid) parts were considered, for simplicity, as spheres.…”