# Microstructure-Based Prediction of the Elastic Behaviour of Hydrating Cement Pastes
## 6 Results and Discussion
### Experimental vs. Numerical Results  
The effective [PERSON]'s modulus predicted by the lattice and FEM models are compared in Figure 13 with the experimental measurements from the EMM-ARM testing technique for the cement pastes with \(w/c\) ratios of 0.32, 0.40 and 0.48, at different hydration ages. For the \(w/c\) ratios of 0.32 and 0.40, there is an acceptable predictive performance from the two numerical models, though the results at very early ages (\(\sim\)5 h) are highly overestimated. At very early ages, the cement paste changes from a liquid to a solid phase, being rather difficult and complex to capture such solidification transition with the available mechanical models. The packing density of C-S-H is low at very early ages, so considering constant values for the elastic moduli of C-S-H phases during this hydration stage may be unrealistic. In Section 6.3.3, the dependency of the effective elastic modulus of the cement paste on [PERSON]'s modulus of C-S-H will be discussed. On the other hand, the ratio of the volume of connected solid phases to the total volume of the solid phase (the so-called \"solid percolation threshold\" [33]) plays an important role to estimate the elastic modulus of the cement paste correctly. The percolation threshold is influenced by the resolution of the mechanical model as concluded by [PERSON] et al. [34]. In Section 6.3.2, the influence of voxel size on the predictions of the effective elastic modulus at early ages of cement pastes will be analysed. Moreover, [PERSON]'s modulus may be influenced by cohesion between solid particles, and not only by their contact as it was reported by [PERSON] and [PERSON] [35]. This effect, which was named as \"mechanical percolation threshold\" [35], was not included in the mechanical FEM model. In the case of the lattice model, an averaged property of two connected solid phases was defined for the interface beams, which may not represent the real cohesion formed between the solid particles. The predictive performance of both numerical models decreases for the \(w/c\) = 0.48, leading to an underestimation of the experimental results (Figure 13). The performance of the numerical models depends on many involved parameters. Among them, the accuracy of HYMOSTRUC3D to predict the pore size distribution is possibly the most important one, since it has a direct link to the morphology of the microstructure, and consequently to the solid phase con  
Figure 13: [PERSON]’s modulus of the cement paste: experimental vs. numerical results. microstructure [36]. By increasing the \(w/c\), this effect is more significant since the number of capillary porosity increases. In the recent study by [PERSON] et al. [37], a good agreement was reported between the pore size distribution (both capillary and gel pores) predicted by HYMOSTRUC3D and those obtained by SEM and MIP testing methods, for a Portland cement paste at ages ranging from 1 to 28 days. However, the porosity provided by HYMOSTRUC3D contradicts the results obtained from the \({}^{1}\)H-NMR testing technique [17] for the materials under testing. It is also criticised that \({}^{1}\)H-NMR does not measure all the volume of capillary pores since only pores filled by capillary water are measured for a sealed cement paste sample. Further analysis is thus still required for validation of mechanical properties on the same paste evaluated at different \(w/c\) values, and tested by SEM, MIP and possibly \({}^{1}\)H-NMR. Regardless of the deficiency that was observed for the cement paste with \(w/c=0.48\), the overall predictive performance of both the lattice and FEM models can be acceptable. To evaluate the influence of several parameters on the effective [PERSON]'s modulus of cement pastes, a parametric study is carried out in the following sections.