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Whether the hydraulic conductivity representative elementary volume (KREV) exists is a fundamental question for understanding the hydraulic behavior of fractured rock masses. The fracture density and size of rocks vary greatly, and are the two most important parameters affecting the existence of a KREV. The International Society for Rock Mechanics (ISRM) presented quantitative descriptions of fracture persistence and density, dividing the persistence into 5 rates and the density into 7 rates, defining 35 basic types of isotropic fractured rock masses with different persistence and densities. Based on ISRM classification suggestions, we construct an additional 40 anisotropic fractured rocks and conduct a systematic investigation of the KREVs of all 75 rock types. The 3D DFNs of the 75 rocks are established with the Monte Carlo method; the water flow in the DFNs is simulated with the finite difference method; the equivalent conductivities of each rock are calculated in 10 domain sizes and 21 different flow directions; and the optimum conductivity ellipsoid and the fitting errors of the equivalent directional conductivity vectors are analyzed to determine the existence and size of the KREVs. A KREV is more likely to exist in rock masses with a high fracture density and persistence. The effect of fracture density and persistence can be comprehensively represented by blockiness, defined as the ratio of the volume of isolated blocks formed by fractures to the total rock volume. A strong correlation is found between the blockiness and the existence of a KREV. A KREV always exists when the blockiness is higher than 0.5%, and its size is between 2 and 18 times the fracture spacing. A KREV may or may not exist in the range of 0.1% < B < 0.5%. When B < 0.1%, a KREV does not exist. [ABSTRACT FROM AUTHOR]