ABSTRACT
Knowledge of the stresses in shotcrete tunnel shells is of great importance for assessing their safety against severe cracking or failure. Estimation of these stresses from optical measurements of 3D shell displacements requires shotcrete material models capable to deal with variations of the water-cement and the aggregate-cement ratio. This is the motivation for employing two representative volume elements within a continuum microme-chanics framework: One of them relates to cement paste (with a spherical material phase representing clinker, needle-shaped hydrate phases with isotropically distributed spatial orientations, a spherical water phase, and a spherical air phase, with all phases being in direct mutual interaction), whereas the second one relates to shotcrete (with a spherical aggregate phase, embedded into a matrix phase made up by cement paste). Elasticity homogenization follows self-consistent schemes (at the cement paste level) and Mori-Tanaka estimates (at the shotcrete level). Stress peaks in the hydrates related to quasi-brittle material failure are estimated by second-order stress averages over hydrates, derived from the elastic energy stored in the RVE. These higher-order stress averages permit 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 early-age (evolving) shotcrete elasticity and strength can be reasonably well predicted from mixture-and hydration-independent mechanical properties of aggregates, clinker, hydrates, water, and air, and from the strength properties of the hydrates. Notably, the model-predicted final strength (at completed hydration) almost perfectly follows the famous Feret formula. At the structural level, the micromechanics model, when combined with 3D displacement measurements of the tunnel
shell, allows for assessing the safety of the shotcrete tunnel shell as a function of the shotcrete mix (defined in terms of the water-cement ratio and of the aggregatecement ratio). Related micromechanics-based hybrid analyses of shotcrete tunnel shells predict that structural safety is rather sensitive to changes in the water-cement ratio, whereas standard-type variations in the aggregate-cement ratio, resulting from rebound during shotcreting, have virtually no influence on the overall structural safety.
