A simple hydration model is used here by taking the composition of the cement and the initial water: cement ratio (w/c) into account explicitly. Its conceptual basis is a combination of the Avrami equation and Bentz's model based on simple spatial considerations. In this model, the Avrami equation determines the initial reaction, and Bentz's model describes the following hydration stage. The model favors engineers for it relies on one experimental parameter and has a reliable approximation in the practice.

Although elastic properties of hydrating cement paste are crucial in concrete engineering practice, there are only a few widely available models for engineers to predict the elastic behavior of hydrating cement paste. Therefore, in this paper, we derive an analytical model to efficiently predict the elastic properties (e.g., Young’s modulus) of hydrating cement paste. Notably, the proposed model provides the prediction of hydration, percolation, and homogenization of the cement paste, enabling the study of the early age elasticity evolution in cement paste. A hydration model considering the mineral composition and the initial w/c ratio was used, while the percolation threshold was calculated adopting a phenomenological semi-empirical method describing the effects of the solid volume fraction and the w/c ratio. An efficient mixing rule based on the degree of solid connectivity was then adopted to calculate the elastic properties of the hydrating cement paste. Moreover, for ordinary Portland cement, a simplified model was built using Powers’ hydration model. The obtained modeling results are following experimental data and other numerical results available in the literature.