A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials

The E-modulus of early age cement-based materials, and more importantly, its evolution in time, is one of the most critical material-to-structural design parameters affecting the likelihood of early-age concrete cracking. This paper addresses the problem by means of a multistep micromechanics approach that starts at the nanolevel of the C-S-H matrix, where two types of C-S-H develop in the course of hydration. For the purpose of homogenization, the volume fractions of the different phases are required, which are determined by means of an advanced kinetics model of the four main hydration reactions of ordinary portland cement (OPC). The proposed model predicts with high accuracy the aging elasticity of cement-based materials, with a minimum intrinsic material properties (same for all cement-based materials), and 11 mix-design specific model parameters that can be easily obtained from the cement and concrete suppliers. By way of application, it is shown that the model provides a quantitative means to determine (1) the solid percolation threshold from micromechanics theory, (2) the effect of inclusions on the elastic stiffening curve, and (3) the development of the Poisson's ratio at early ages. The model also suggests the existence of a critical water-to-cement ratio below which the solid phase percolates at the onset of hydration. The development of Poisson's ratio at early ages is found to be characterized by a water-dominated material response as long as the water phase is continuous, and then by a solid-dominated material response beyond the solid percolation threshold. These model-based results are consistent with experimental values for cement paste, mortar, and concrete found in the open literature.