Porosity-based representative elementary volume for geomaterials and its fractal theory-based approximate criterion

The representative volume element (RVE) and/or the representative elementary volume (REV) and their existence and determination are a basic scientific issue in the research field of size effect. The similarities and differences between the RVE and REV are analyzed from the fields of composite micromechanics and geotechnical engineering. A three-level classification of the REV research on geomaterials is then proposed based on these fields, especially REV research in geotechnical engineering. The pore size distribution and the corresponding fractal dimension are introduced and selected as the constrained parameters for describing the complex pore structure of geomaterials. Accordingly, an approximate criterion is first presented via theoretical deduction and comparison with previous research results, through which the size of a P-REV of mesoscale porous geomaterials can be determined using their pore size distributions (i.e., the edge length of the cubic P-REV is approximately equal to five times of the maximum pore diameter). Finally, some statistical methods, such as low-order probability functions, are utilized to validate the performance of the proposed criterion. The verification results using two types of geomaterials, namely, sandstone and foamed concrete, reveal that both are in a reasonable agreement, indicating that the P-REV determined according to this approximate criterion can provide representative statistical results and find a balance between characterization accuracy and calculation efficiency.