Abstract
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.
Highlights
As a critical mechanical design parameter of concrete structures affecting their deformation and failure, the elastic modulus of cement pastes at early age constantly attracts engineering and scientific attention (Acker and Ulm, 2001; Bentur, 2002; Springenschmid, 2009)
The present paper proposes new methods for all three parts; i.e., an efficient hydration method is proposed to consider the composition of the cement and the initial w/c ratio explicitly, the percolation threshold is calculated using a semi-empirical formula considering the effects of the solid volume fraction and the w/c ratio; and, an efficient mixing rule based on the degree of solid connectivity is used as a homogenization method to estimate elastic properties
Based on the above analyses, we propose a semi-empirical formula considering the effects of the solid volume fraction and the w/c ratio to estimate the percolation threshold of a cement paste: αs
Summary
As a critical mechanical design parameter of concrete structures affecting their deformation and failure, the elastic modulus of cement pastes at early age constantly attracts engineering and scientific attention (Acker and Ulm, 2001; Bentur, 2002; Springenschmid, 2009). As the main evolving cement component at an early age, hydrating cement paste critically affects the elastic modulus of cement paste. On the one hand, during the cement paste hydration process, the elastic modulus of cement paste is subjected to changes in the physical environment due to the microstructural development of the cement paste. The chemical composition of hydrating cement paste varies over time, so these physical and chemical changes make the prediction of elastic properties of cement pastes very challenging. The literature on the experimental characterization of the elastic properties of cement-based materials during hardening is vast (Schutter and Taerwe, 1996; Boumiz et al, 1996; Princigallo et al, 2003; Constantinides and Ulm, 2004; Haecker et al, 2005; Voigt et al, 2005; Sun et al, 2005). Reinhardt and Grosse (2005) investigated cement-based samples during setting and hardening by adopting several testing methods based on the resonant frequency, ultra-sound wave propagation, impact echo, electric properties of concrete nuclear magnetic resonance, and acoustic emissions. Azenha et al (2010, 2011) measured the elastic modulus of cement pastes and mortars using a novel
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