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

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 self-consistent schemes (at the cement paste level) and Mori–Tanaka 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.