General Statistics-Based Methodology for the Determination of the Geometrical and Mechanical Representative Elementary Volumes of Fractured Media

The upscaling of mechanical properties fractured media requires the definition an appropriate size for Representative Elementary Volume (REV). Because stochastic nature fracture networks, REV is not deterministic and should be defined based on variability equivalent properties. This work presents a new general methodology to define geometrical elastic moduli media. Following previous works heterogeneous materials, decision criterion precision error that arises from statistical theory samples. proposed also relies use Central Limit Theorem (CLT) assess rocks. CLT shown theoretically apply both From observation, equation drawn predict variance property any candidate size, provided one only known. These concepts are tested using numerous finite element simulations obtain distribution two-dimensional samples containing two networks previously studied their confirmed tend normal distribution, as stated by CLT. Also, standard deviations associated with sizes were predicted accuracy deviation obtained in numerical proper reference volume. was compared REV, which first invariant tensor. In addition, reduce computational costs, procedure number volume proposed. A preliminary verification applicability non-elastic problems made. Proper predictions compression strength calculated studies considered, altogether, three-dimensional samples, well plastic damage models.