4. Empirical formula relating the decrease in the Young's modulus to the increase of the capillary porosity

Different empirical equations relating Young's modulus to porosity exist in the literature. However, the porosity considered depends on the experimental methods used to determine it. In this paper, we propose a new formula adapted for capillary porosity given by the CEMHYD3D model. A plot of the Young's modulus model values obtained from the different simulations, versus total capillary porosity, is provided in Fig. 7. The following equation relating Young's modulus to capillary porosity is fitted to the different model values.

(1)

where E = cement paste Young's modulus (GPa); p_cap = cement paste capillary porosity.

Figure 7. Numerical simulations results for the different cement pastes, leached and non-leached.

Based on Equation 1, the reduction of the Young's modulus due to leaching can be expressed as a function of unleached and leached cement paste capillary porosity as shown in Equation 2:

(2)

where E = leached cement paste Young's modulus (GPa); Eo = unleached cement paste Young's modulus (GPa); p_capo = unleached cement paste capillary porosity; p_cap = leached cement paste capillary porosity.