Addition of water to cementitious minerals triggers the hydration reaction which results in the formation of an interconnected network of complex microstructures constituted by calcium silicate hydrate (C-S-H). C-S-H thus formed is of heterogeneous nature differentiated by its chemical configuration, mechanical properties and relative crystallinity or amorphicity. A variety of microstructures are observed in the hydrating cement matrix as a result of C-S-H nucleation on the parent grain surface. These microstructures are predominantly needle like and they intertwine at the interface with similar needles from the adjacent grains. Although there have been many attempts to model hydration, microstructure development and the resultant evolution of mechanical properties, these unique needle-like features have seldom been considered. However, they constitute the basis for inter-grain connectivity in a hydrating cement matrix and the subsequent binding property of cement paste. Thus, in this work, we propose a multiscale mechanical modelling approach which considers the grain-grain interface as the basic unit of strength. The model incorporates the needle-like geometry of outer product C-S-H into a finite element (FE) model derived from the SEM images at micro-scale. To this FE model, the mechanical properties of constituent phases, determined at nanoscale, were distributed. This 2D finite element model was then subjected to tension and shear and the respective stiffnesses were estimated. The estimated stiffnesses were then translated into a 3D discrete lattice spring model to derive the bulk mechanical properties such as Youngs modulus of the matrix. The proposed approach was tested and validated with different cementitious systems namely (i) Pure tricalcium silicate (C3S), (ii) nano-silica doped C3S and (iii) C3S-C2S (dicalcium silicate) mix.

A unique attempt is made in this work to model the evolution of strength in a hydrating cement matrix from the fundamental length scale of C-S-H needle geometry. The difference in the needle geometry of C-S-H under different conditions such as (i) state of hydration, (ii) presence of SNP and (iii) under varying pore water ionic concentration as in the case of different C3S-C2S blends, have been investigated in detail in this work. The incorporation of these features into a multi-scale mechanical model is an addition to the existing knowledge paradigm of cement science. The proposed model reliably predicts the evolution of mechanical strength of various cementitious systems over time. It analyses the relative contribution of microstructure and mechanical properties of different forms of C-S-H towards this evolution of modulus. The approach, albeit having certain limitations, accomplish this objective and provides scope for further refinement and fine tuning of the methodology. The approach can be further extended to different directions such as (i) evaluate the viscoelastic behaviour of cement paste, by extending the elastic spring at the lattice-spring scale to a spring and dash pot combination or (ii) evaluating the effect of C3A on the resultant needle microstructure and the subsequent change in bilk mechanical properties.