Evaluation of the elastic modulus of concrete based on indentation test and multi-scale homogenization method

This paper aims to quantitatively evaluate the elastic modulus of concrete through microscopic tests and a multi-scale mechanical homogenization method considering interface transition zone (ITZ). The mechanical properties tests were carried out for concrete samples with 0% or 10% silica fume. The elastic modulus and volume fraction of individual phases of hardened paste and elastic modulus and thickness of the ITZ around coarse aggregate were obtained by a series of microscopic tests and theoretical studies. The results showed that the incorporation of silica fume mainly increased the elastic modulus and volume proportion of the C–S–H gel, while results in the improvement on ITZ elastic modulus and reduction on its thickness. To further simulate macroscopic elastic modulus, the concrete was divided into four scales ranging from nano to macro and a model was established by homogenization scheme combining Mori-Tanaka (MT) and self-consistent (SC). The influence of bond-slip ITZ model or homogeneous ITZ model on the simulation results was discussed on the fourth scale. Moreover, the effects of the nanoscopic phases, microscopic phases and ITZ properties on the elastic modulus of concrete were analyzed to confirm the essential role of ITZ in the elastic deformation analysis.