Multiscale strength modeling of low-carbon cement pastes: the roles of the stiffness of binder constituents and surrogate modeling

The production of ordinary Portland cement (OPC) results in some 8% of the world green house gas emissions. Partially replacing OPC with supplementary cementitious materials such as limestone and calcined clay is a promising approach for developing more sustainable alternatives. In this study, we model the compressive strength development of pastes made with limestone Portland cement (LPC) and limestone calcined clay cement (LC3) binders. We investigate whether or not the stiffness of microscopic binder constituents play a crucial role in the strength predictions, and we give polynomial formulae for approximating the tensorial strength model. To this end, three binders are investigated: one type each of OPC, LPC, and LC3. For the blended binders, the cement replacement ratio amounts to 30%. The limestone-to-calcined clay ratio is set to 1.0. The water is dosed at an initial water-to-binder mass ratio of 0.45. Strength modeling is performed using a multiscale strength model which is based on methods of continuum micromechanics. The model is extended to account for inert limestone and calcined clay inclusions. Volume fractions are calculated using Powers’ hydration model. Elastic phase constants are taken from the literature. Qualitative input for the multiscale model is visualized using material organograms: spherical residual binder particles are embedded in a continuous matrix of hydrate foam, which itself consists of isotropically oriented hydrate gel needles in direct interaction with spherical capillary pores. A sensitivity analysis regarding the stiffness of binder particles is carried out. It is found that the strength predictions are virtually independent of the stiffness differences within the binder powder. This provides the motivation for developing a surrogate model which approximates the tensorial strength predictions by polynomial equations, based solely on the strength of the hydrate gel needles, the hydrate foam-related volume fractions of the capillary pores, and the cement paste-related volume fraction of the binder constituents.