Influence of Representative Volume Element Size on Inferred Properties of Random Heterogeneous Materials from X-Ray Microtomography

In the present work, an insight into the identification of an appropriate representative volume element (RVE) size for random heterogeneous materials is carried out because it is not straightforward and no standard methods can be found in the literature. The influence of RVE size on the properties of a heterogeneous material characterized by random double porosity microstructure [i.e., lightweight cemented soils (LWCS)] is studied using X-ray microtomography. LWCS are prepared by mixing air foam with soil, water, and cement, and are characterized by a large pore system induced by foam in a cemented porous matrix. Data derived from scans of LWCS samples prepared at two different foam percentages (i.e., 20% and 40%) are used to evaluate foam-induced porosity and its dependency on the RVE size. The influence of RVE size on the homogenized elastic stiffness of LWCS is evaluated through a numerical model based on 3D scans of the samples. RVE size selection is validated by comparing LWCS elastic stiffness derived from computational homogenization with available experimental results and with results from mean field homogenization methods. The results show that, regardless of foam content and curing time, a proper RVE size can be set equal to 80% of the sample volume, both considering porosity analysis and numerical simulation on LWCS homogenized elastic stiffness.