岩体裂隙网络等效渗透系数方向性的数值计算

采用渗流力学理论并结合Monte Carlo方法描述岩体裂隙的随机分布，研究渗流模型的尺寸效应并确定表征单元体积（REV），得到了3种开口度分布形式的等效渗透系数椭圆曲线，建立了等效渗透系数方向性的判别标准。离散裂隙网络（DFN）模型假定流体只在岩体裂隙内部流动，而不通过岩体本身渗流。基于二维离散元程序UDEC并进行二次开发，建立DFN模型，通过改变流体的流动方向，得到不同流动方向下岩体裂隙网络的等效渗透系数，并分析不同的开口度分布形式对岩体裂隙网络等效渗透系数方向性的影响。计算结果表明，表征单元体积存在的条件是等效渗透系数保持稳定且渗透椭圆比较光滑。等效渗透系数的方向性受开口度分布形式的影响很大：当开口度-长度关联分布时，等效渗透系数各向异性；当开口度对数正态分布时，等效渗透系数各向同性；当开口度恒定分布时，等效渗透系数的特性介于二者之间。变化系数（CV）是否大于5%是判定岩体裂隙网络渗透系数是否具有方向性的判别标准。

Numerical calculation of directivity of equivalent permeability of fractured rock masses network

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.