From micron-sized needle-shaped hydrates to meter-sized shotcrete tunnel shells: micromechanical upscaling of stiffness and strength of hydrating shotcrete

Abstract

Knowledge on the stresses in shotcrete tunnel shells is of great importance, as to assess their safety against severe cracking or failure. Estimation of these stresses from 3D optical displacement measurements requires shotcrete material models, which may preferentially consider variations in the water-cement and aggregate-cement ratios. Therefore, we employ two representative volume elements within a continuum micromechanics framework: the first one relates to cement paste (with a spherical material phase representing cement clinker grains, needle-shaped hydrate phases with isotropically distributed spatial orientations, a spherical water phase, and a spherical air phase; all being in mutual contact), and the second one relates to shotcrete (with phases representing cement paste and aggregates, whereby aggregate inclusions are embedded into a matrix made up by cement paste). Elasticity homogenization follows selfconsistent schemes (at the cement paste level) and MoriTanaka estimates (at the shotcrete level), and stress peaks in the hydrates related to quasi-brittle material failure are estimated by second-order phase averages derived from the RVE-related elastic energy. The latter permits upscaling from the hydrate strength to the shotcrete strength. Experimental data from resonant frequency tests, ultrasonics tests, adiabatic tests, uniaxial compression tests, and nanoindentation tests suggest that shotcrete elasticity and strength can be reasonably predicted from mixture-and hydration-independent elastic properties of aggregates, clinker, hydrates, water, and air, and from strength properties of hydrates. At the structural level, the micromechanics model, when combined with 3D displacement measurements, predicts that a decrease of the water-cement ratio increases the safety of the shotcrete tunnel shell.

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).…”

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

“…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.…”

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

“…Calcium-silicatehydrates are present as a sole homogeneous aging phase. At this scale, C-S-H particles can either be considered as needles [38,39] or as spherical inclusions [6,7]. This is a long-standing and still open scientific debate.…”