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

It is well known from experiments that the uniaxial compressive strength of cementitious materials depends linearly on the degree of hydration, once a critical hydration degree has been surpassed. It is less known about the microstructural material characteristics which drive this dependence, nor about the nature of the hydration degree–strength relationship before the aforementioned critical hydration degree is reached. In order to elucidate the latter issues, we here present a micromechanical explanation for the hydration degree–strength relationships of cement pastes and mortars covering a large range of compositions: Therefore, we envision, at a scale of fifteen to twenty microns, a hydrate foam (comprising spherical water and air phases, as well as needle-shaped hydrate phases oriented isotropically in all space directions), which, at a higher scale of several hundred microns, acts as a contiguous matrix in which cement grains are embedded as spherical clinker inclusions. Mortar is represented as a contiguous cement paste matrix with spherical sand grain inclusions. Failure of the most unfavorably stressed hydrate phase is associated with overall (quasi-brittle) failure of cement paste or mortar. After careful experimental validation, our modeling approach strongly suggests that it is the mixture- and hydration degree-dependent load transfer of overall, material sample-related, uniaxial compressive stress states down to deviatoric stress peaks within the hydrate phases triggering local failure, which determines the first nonlinear, and then linear dependence of quasi-brittle strength of cementitious materials on the degree of hydration.