Numerical Study On Equivalent Permeability Of Fractured Rock Masses By Using Stochastic Discrete Fracture Networks And Fractal Dimension Method

In recent years, more and more large-scale rock engineering projects such as dam foundations, underground storage caverns, submarine tunnels and waste disposal facilities are under design and construction. The flow characteristics of rock fractures in rock mass is one of the crucial issues in the safety assessment of these projects. In the investigation of hydraulic behavior of fracture networks using numerical approaches, model size effect and equivalent permeability are two of the essential problems that need to be answered. For the first problem, the representative elementary volume (REV), when it does exist, can be used to define the minimum volume of a sampling domain of a fracture network beyond which the permeability of sampling domain remains essentially constant. For the second problem, when orientations of fluid flow are changed, the equivalent permeability tensor has directivity with maximum and minimum permeability values. The purpose of this paper is to establish a stochastic discrete fracture network (DFN) model by using the Monte Carlo method. And then, the equivalent permeability of rock fracture networks is calculated with varying model sizes and rotation angles, resulting in a reasonable REV size. Finally, the fractal dimension is utilized to describe the fractal characteristics and to investigate the relationship between statistical, fractal parameters of fracture network geometry and equivalent permeability.A large number of realizations of stochastic discrete fracture network models (DFNs) are generated, based on realistic fracture system information and the two-dimensional distinct element code, UDEC. Then, the existence of representative element volume (REV) and the possibility of equivalent permeability tensor of the fracture rock mass, are determined by simulating fluid flow through a large number of stochastic discrete fracture network models with varying sizes and varying hydraulic conditions. The results show that as the increase of DFN side length, fluctuates of equivalent permeability tend to be stable. The equivalent permeability kxx and kyy became stable after the side lengths of DFN models become larger than40m. Therefore, a DFN model size of40m can be approximated as a REV for practical uses. Permeability tensor is another way to describe the distribution of fracture network in the rock masses. From the principal axis of ellipse, percolation principal value and percolation directivity have been obtained. What’ more, according to the represent in the figure of percolation ellipse, mainly percolation direction which can be used to describe the percolation directivity also have been determined directly. Finally, in this study, fractal dimensions of fracture networks are calculated to quantitatively evaluate the geometrical distribution characteristics by using the box-counting method. During the calculations, the geometrical distributions (such as fracture density, trace length, et. al) are taken as the variations. In the end, a linear regression is obtained to describe the relations between fractal dimension and equivalent permeability.