Representative elementary volume assessment of three-dimensional x-ray microtomography images of heterogeneous materials: Application to limestones

Over the last 15 years, x-ray microtomography has become a useful technique to obtain morphological, structural, and topological information on materials. Moreover, these three-dimensional (3D) images can be used as input data to assess certain properties (e.g., permeability) or to simulate phenomena (e.g., transfer properties). In order to capture all the features of interest, high spatial resolution is required. This involves imaging small samples, raising the question of the representativity of the data sets. In this article, we (i) present a methodology to analyze the microstructural properties of complex porous media from 3D images, (ii) assess statistical representative elementary volumes (REVs) for such materials; and (iii) establish criteria to delimit these REVs. In the context of cultural heritage conservation, a statistical study was done on 30 quarry samples for three sorts of stones. We first present the principles of x-ray microtomography experiments and emphasize the care that must be taken in the 3D image segmentation steps. Results show that statistical REVs exist for these media and are reached for the image sizes studied (1300 x 1300 x 1000 voxels) for two characteristics: porosity and chord length distributions. Furthermore, the estimators used (porosity, autocorrelation function, and chord length distributions) are sufficiently sensitive to quantitatively distinguish these three porous media from each other. Lastly, this study puts forward criteria based on the above-mentioned estimators to evaluate the REVs. These criteria avoid having to repeat the statistical study for each new material studied. This is particularly relevant to quantitatively monitor the modifications in materials (weathering, deformation...) or to determine the smallest 3D volume for simulation in order to reduce computing time.