# Microstructure-Based Prediction of the Elastic Behaviour of Hydrating Cement Pastes
## 3 Microstructure of the Cement Paste  
In the present study the latest version of HYMOSTRUC3D computer software [10], developed in the Materials & Environment Department at Delft University, is used for the construction of the cement paste microstructure during hydration. This simulation is implemented in a cubic REV volume of the cement paste where the cement particles are modelled as spheres randomly distributed. The initial number and diameter of the particles are built in accordance with the PSD--see Figure 1. The main cement hydration products are the Calcium-Silicate-Hydrate (C-S-H) and the Calcium Hydroxide (CH). C-S-H is formed as two layers of inner and outer products, which are the result of the inward and outward radial growing of the cement spheres, as shown in Figure 2a. Figure 2b presents the interaction between the cement particles during the hydration process in the REV. Examples of the simulated microstructure of the cement paste after 1 h and 156 h of hydration are depicted in Figure 3.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Cement**} & \multicolumn{2}{c}{**[PERSON] et al. (2001) [18]**} & \multicolumn{2}{c}{**[PERSON] et al. (2009) [19]**} & \multicolumn{4}{c}{**Present Study**} & \multicolumn{4}{c}{**[PERSON]**} \\ \cline{2-13}  & \(E\) & \(G\) & \(\upsilon\) & \(E\) & \(G\) & \(\upsilon\) & \(E\) & \(G\) & \(\upsilon\) & \(E\) & \(G\) & \(\upsilon\) \\  & (GPa) & (GPa) & - & (GPa) & (GPa) & - & (GPa) & (GPa) & - & (GPa) & (GPa) & - \\ \hline Alite (C\({}_{3}\)S) & 135 & 51.9 & 0.3 & 138.9 & 54.5 & 0.28 & 137 & 53 & 0.30 & & & & \\ Belite (C\({}_{2}\)S) & 130 & 50.0 & 0.3 & 137.9 & 53.1 & 0.3 & 134 & 52 & 0.30 & & & \\ C\({}_{3}\)A & 145 & 55.8 & 0.3 & - & - & - & 145 & 56 & 0.30 & & 137 & 53 & 0.3 \\ C\({}_{4}\)AF & 125 & 48.1 & 0.3 & - & - & - & 125 & 48 & 0.30 & & & & \\ \hline \hline \end{tabular} \(E\): Elastic modulus; \(G\): Shear modulus; \(\upsilon\): Poisson’s ratio.  
\end{table}
Table 2: Elastic properties of cement clinker constituents.  
Figure 3: Microstructure formation of the cement paste in a 2D view: (**a**) after 1 h of hydration; (**b**) after 170 h of hydration (grey: unreacted cement grain; red: Inner C-S-H; yellow: Outer C-S-H; green: CH grain; blue: water or void).  
Figure 2: (**a**) Cement hydration products in HYMOSTRUC3D, (**b**) Overlapping of the product layers in particle contacts.  
The important parameters to be defined in HYMOSTRUC3D for modelling cement hydration are summarised in Table 3. For further details on fundamental aspects of the model parameters, the reader is addressed to the studies published by [PERSON] and by [PERSON] [10; 20]. The hydration parameters shown in Table 3 were calibrated using the degree of hydration measured through isothermal calorimetry, performed on the same cement for different \(w/c\) ratios [17]. The experimental and numerical results are plotted and compared in Figure 4. By giving a relevant set of hydration parameters to the model, a good estimation is obtained regarding the degree of reaction for the three cement paste mixtures under study.