Numerical and analytical effective elastic properties of degraded cement pastes

Cement pastes are heterogeneous materials composed of hydrates, anhydrous products and pores of various shapes. They are generally characterized by a high particle concentration and phase contrasts, in particular in the case of degraded materials which exhibit important porosity. This paper compares the performance of several classical effective medium approximation schemes (Mori–Tanaka, Zheng-Du, self-consistent) through their ability to estimate the mechanical parameters of cement paste samples obtained numerically. For this purpose, finite element simulations are performed on 3D structures to compute for each sample accurate values of these mechanical properties. For these simulations, the cement paste is considered as a matrix of C–S–H in which are embedded inclusions of anhydrous, hydration products, and pores. In order to evaluate the importance of the particle shape, two types of samples are generated, one with only spherical inclusions and the other containing both spherical and prismatic particles. Simulations with three perpendicular loading directions and both uniform and mixed boundary conditions are performed in order to verify that the dispersion in the computed elastic moduli is low, or equivalently that the generated structures are close to representative volume elements (RVEs). It is shown that the considered effective medium approximation schemes, except the self-consistent one, provide relatively good estimations of the overall mechanical parameters when compared to simulation results, including when both particle volume fraction and phase contrast are high. The analytical methods taking into account the particle shapes also give estimates close to the corresponding numerical simulations, the latter confirming the influence of the particle form.