Directivity of permeability of fractured rock masses is investigated through numerical models with varying flow directions and 3 kinds of aperture distributions. Besides constant aperture distribution and distribution of apertures correlated with trace length of fractures

a log-normal distribution of apertures

which is verified through experiments and is closer to reality due to its allowance of aperture deviations to some extents

is further introduced into numerical models to evaluate their influences on the directivities of permeability. The basic assumptions are that fluid flow only take place in fractures

and that the intact rock is impermeable and linearly elastic. A large number of stochastic discrete fracture network (DFN) models of varying sizes and varying fracture properties are established to examine the existence of representative elementary volume (REV) and to determine the directivities of equivalent permeability

using a discrete element method (DEM)

which provides intact rock masses as an assemblage of discrete blocks and the discontinuities/fractures as interfaces between blocks. These numerical simulation results show that REV exists if the equivalent permeability holds steady and the deviations of coefficient of variance (CV) are less than 10%. The distributions of fracture apertures can influence the directivities of equivalent permeability greatly. The directivity of equivalent permeability is remarkable when apertures are correlated with trace lengths

however

the equivalent permeability seems to be isotropic when apertures are log-normally distributed. The reasons may be that when fracture apertures are correlated with trace lengths

the apertures could vary significantly along different fracture sets with different trace lengths

causing differential permeability values in different directions. The inclined angle of maximum permeability and minimum permeability is about 90° when the curves of directional permeability are smooth. The ‘CV’ value is a crucial factor for identifying the directivities of permeability. When the ‘CV’ value is less than 5%

for example with log-normally distributed fracture apertures

the equivalent permeability in different directions is coincident with the mean permeability

which means the rock masses are hydraulically isotropic and can be treated as a continuum. When the ‘CV’ value varies from 5% to 10%

for example with a constant aperture distribution

the permeability trends to be directional for different rotation models. If the ‘CV’ value exceeds 10%

for example with length correlated apertures

the directivities of permeability become remarkable

resulting in heterogeneous characteristics of rock masses. The coefficient of variance (CV) with the value of varying from 5% to 10%

is the critical condition to identify the directivity of permeability of a fracture network.