# Determination of Geometrical REVs Based on Volumetric Fracture Intensity and Statistical Tests
## 1 Introduction  
There are many discontinuities in fractured rock masses, and the structural characteristics (such as joint orientation, spacing, spatial distribution, and combination condition) control the mechanical properties, the deformation, and the failure behavior of rock masses. Discontinuities are also the source of the anisotropy and inhomogeneity of rock masses. The size effects of the mechanical and geometrical properties of a rock mass are prominent; the parameters of a rock mass will change gradually as the research scope changes. When the rock mass size is larger than or equal to a certain value, the fluctuation of rock properties significantly decreases; the continuum method can be used to perform a numerical analysis; and the equivalent continuum parameters can represent the properties of the rock masses. Accordingly, this critical cube size is defined as the representative element volume (REV) [1]. Thus, it is important to accurately determine the equivalent hydraulic, mechanical and geometrical parameters when analyzing the properties of rock masses. The concept of REV was presented in the study of porous media seepage [2]. Subsequently, research on REVs has been carried out in various fields. [PERSON] et al. [3] generated a 2D fracture system to study the equivalent permeability of fractured rock masses. [PERSON] and [PERSON] [4] and [PERSON] et al. [5] used the permeability coefficient and the equivalent permeability tensor to evaluate the REV size in the field of rock seepage. The REV size of porous media has been estimated based on X-ray micro computed tomography (micro-CT) [6; 7; 8]. [PERSON] and [PERSON] [9] estimated the REV size of the fractured rock mass based on fracture network modeling tools (REPSIM code) and geometrical parameters (such as the fractal dimension of the fracture midpoints, length exponent, and relative dip) and analyzed the relationship between the size of percolation clusters and REVs at a study site in the Pannonian Basin. In the field of rock mechanics, [PERSON] [10] and [PERSON] and [PERSON] [11] adopted an in situ test method to obtain the REV size of rock masses, but this method was limited by site conditions and high costs. Subsequently, the finite element method was developed to study the size effect of a rock mass and to explore the REV size of a jointed rock mass [12; 13]. By considering numerical homogenization (NH) and the geometrical approach, the mechanical REV was discussed by [PERSON] and [PERSON] [14]. [PERSON] et al. [15] used the displacement discontinuity method to discuss the scale effects of rock masses. With the innovation of research technology, the distinct element method was developed to discuss REV size and to study the size effect of REVs based on the equivalent elastic compliance tensor, fracture length, fracture aperture, deformation modulus, and Poisson's ratio of fractured rock masses [16; 17; 18]. Recently, the REV was also studied in the field of damage mechanics. By considering joint aperture and roughness, [PERSON] et al. [19] used the damage coefficient to determine the REV size. [PERSON] and [PERSON] [20] established a mesoscopic constitutive law of REV based on a statistical meso-damage mechanical method (SMDMM) to simulate the rock failure process. In addition to numerical methods, statistical methods are also widely applied to study the REV size. [PERSON] et al. [21] determined REV size by using a fractal geometry method based on the evaluation of the statistical homogeneity of the structure of a rock mass. [PERSON] et al. [22] introduced a method using Particle Flow Code to explore REV size based on a 3D fracture network model. [PERSON] et al. [23] determined a geometrical REV and mechanical REV using the T test and the F test; the mechanical REV size was larger than the geometrical REV size. [PERSON] et al. [24] analyzed REV size by considering the blocky structure of a fractured rock mass using the GeneralBlock program. The relationship between REV size and average joint trace length was discussed by various scholars.