Abstract
The development of the elastic properties of a hardening cement paste results from the microstructural evolution due to cement hydration. The elastic behaviour of cement paste can be predicted by a combination of the hydration model and micromechanical analysis, which originates from a microstructural representative volume where the elastic behaviour of different hydrating cement products can be recognised. In this paper, the formation of the microstructural volume is simulated with the computational code HYMOSTRUC3D for cement hydration. The obtained microstructure is an input for a micromechanical modelling. A 3D regular lattice model is proposed to predict the elastic modulus of the microstructure, considering a water-to-cement (w/c) ratio within the range [0.30–0.50]. In addition, the Finite Element Method (FEM) is used to compare and validate the results from the lattice model. Predictions from these two modelling approaches are then compared to the experimental results provided by the EMM-ARM (Elasticity Modulus Measurement through Ambient Response Method) testing technique, the latter allowing measurement of the elastic modulus of hydrating cement pastes. Finally, the above-referred numerical models are used to evaluate the influence of the following features: the particle size distribution of the cement grains, the microstructure discretisation refinement and the elastic modulus of the C-S-H cement hydration product.
Highlights
Most existing modelling practices for analysis of cement-based materials are based on continuum descriptions of their responses to external driving forces, namely stresses due to deformation gradients, heat fluxes due to temperature differences, diffusion due to concentration gradients, etc.These continuum approaches basically relate responses to the driving forces, considering the governing differential equations and the appropriate boundary conditions, which are usually solved with numerical methods such as the Finite Element Method (FEM)
The basic idea of the present work is to derive the macroscopic constitutive laws of cement-based materials by modelling the physical processes at a small length scale, so that the constitutive laws may be looked as micromechanics-based, rather than being phenomenologically approximated. This aids scientists and engineers to bridge the gap between knowledge of microscopic mechanisms and the macroscopic responses, while they are still using continuum approaches with an acceptable accuracy for modelling complex phenomena. This modelling strategy is the genesis of continuum micromechanics approaches [1,2], in which a cement-based material is looked as a macro-homogeneous body, yet micro-heterogeneous, filling a Representative Elementary Volume (REV) with a prescribed characteristic length
The previous lattice model adopted by the authors in [12] significantly underestimated the experimental results, and the results obtained from the FEM model
Summary
Most existing modelling practices for analysis of cement-based materials are based on continuum descriptions of their responses to external driving forces, namely stresses due to deformation gradients, heat fluxes due to temperature differences, diffusion due to concentration gradients, etc. The basic idea of the present work is to derive the macroscopic constitutive laws of cement-based materials by modelling the physical processes at a small length scale, so that the constitutive laws may be looked as micromechanics-based, rather than being phenomenologically approximated This aids scientists and engineers to bridge the gap between knowledge of microscopic mechanisms and the macroscopic responses, while they are still using continuum approaches with an acceptable accuracy for modelling complex phenomena. This modelling strategy is the genesis of continuum micromechanics approaches [1,2], in which a cement-based material is looked as a macro-homogeneous body, yet micro-heterogeneous, filling a Representative Elementary Volume (REV) with a prescribed characteristic length. Towards evaluating the influence of some involved microstructural parameters on the predictions of the macroscopic elastic moduli of the cement pastes
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