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

Abstract

The upscaling of mechanical properties of fractured media requires the definition of an appropriate size for the Representative Elementary Volume (REV). Because of the stochastic nature of the fracture networks, the REV size is not deterministic and should be defined based on the variability of the equivalent properties. This work presents a new general methodology to define the size of the REV for the geometrical and elastic moduli of fractured media. Following previous works on heterogeneous materials, the decision criterion is based on the precision error that arises from the statistical theory of samples. The proposed methodology also relies on the use of the Central Limit Theorem (CLT) to assess the REV of fractured rocks. The CLT is shown to theoretically apply to both the geometrical and the elastic equivalent properties. From that observation, a general equation is drawn to predict the variance of an equivalent property for any REV candidate size, provided that the variance for one size only is known. These concepts are tested using numerous finite element simulations to obtain the distribution of the equivalent elastic moduli of two-dimensional samples containing two fracture networks previously studied for their elastic properties. These properties are confirmed to tend to a normal distribution, as stated by the CLT. Also, the standard deviations associated to the tested REV sizes were predicted with accuracy from the standard

Size effect of parallel-joint spacing on uniaxial compressive strength of rock

“…For example, Ying et al [ 14 ] proposed a method for estimating rock-mass REV based on the volumetric fracture strength ( P 32 ) and statistical tests. Loyola et al [ 15 ] evaluated the REV of fractured rock by using the central limit theorem. Scholars have obtained the characteristic size of rocks based on field data, theoretical models, and probability statistics.…”

A precise modeling method of three‐dimensional discrete fracture network based on rectangular joint model

“…There are two types of REV in the research of jointed rock mass, namely geometrical REV and mechanical REV. 57,58 The geometrical REV is usually determined based on the joint number in each sampled volume and the volumetric joint intensity of the samples, while the mechanical REV is often estimated according to the permeability, uniaxial compressive strength, and elastic modulus of the samples. Due to the limitation on article length, only the geometrical REV is discussed here.…”

The Influence of the Number of Joints on the Size Effect of Shear Strength and Characteristic Strength

“…(4) e shear characteristic strength of structural plane is related to the number of joints, and its particular form (obtained by simulation) is τ w � 50.118 − 0.464n. (18)…”

“…Scholars use different methods to evaluate the size of rock REV. For example, Loyola et al [18] proposed to use the central limit theorem to evaluate the REV size of fractured rocks. Yuan et al [19] studied the REV of fractured rocks based on a dual-pore model.…”