Determining The Representative Elementary Volume For Fracture Rock Mass Using The Equivalent Permeability Tensor

The equivalent porous medium model plays an important role in the study and engineering application of fracture rock flow. The key of its application lies in designing a correct fracture rock mass model, which means a representative element volum (REV).According to the standard of rock fracture classification established by ISRM in 1978, the paper discusses the sizes of REV depending on different fracture rock masses using a DFN software and propses a general method which determines the existence of REV.The code FractureToKarst, which is a main analysis tool in this paper and developed by Prof. YU, is a DFN (Discrete Fracture Network) software. Various 2-D DFN models are generated by it using the Monte Carlo simulation of the fracture system based on the data obtained from the design. And then it can filter disconnected fractures in the study region and remember all necessary information for next step automatically, In the end the equivalent permeability is obtained depending on water balance method.The ISRM divides the fracture into five classes according to their tractility and seven classes according to their mean distances. Based on the classification, DFN models with two groups of orthometric fracture are built. Survey regions with varying sizes of from 1.0m x 0.5m to 100m x 50m and fixed length-width ratio 2 and fixed hydraulic gradient 1 are also rotated in 10°intervals to calculate the equivalent permeability. And then 36 equivalent permeabilities in different orientations will be got in each region in order to evaluate a size whether or not can be considered approximately as a homogeneous area in each model. Next, whether or not the 36 permeablities can be ploted as a smoolth ellipse in polar coordinates and whether or not the medium can be describe by a second order symmetric conductivity tensor is discussed and determined. Based on the existing study of the fracture rock flow, the major results are as follows:1. The REV does not exist in all kinds of fracture rock mass, and they can be obtained from the rock mass under certain condition.2. In the rock mass which fracture length are less than 1 meter, only when their average spacing is less than 0.2 m, the REV exists.3. In the rock mass which fractures length are between 1 m and 3m, when their average spacing is more than 0.2 m and less than 0.6m, the REV can be obtained.4. In the rock mass which fractures length are between 10m and 20m, the REV can be obtained from rock mass which fracture average spacing is less than 4m.