Abstract: A simplified numerical testing method is developed to estimate the three-dimensional (3D) elastic compliance tensor and study the mechanical representative element volume (REV) of fractured rock mass, on the basis of the numerical test for two-dimensional (2D) elastic compliance tensor. Firstly, 3D stochastic discrete fracture networks are randomly generated using the Monte Carlo method, according to the statistical parameters and the probability distribution functions. Then rock samples are collected in varied directions and the 2D elastic compliance tensors of the examples are further calculated using the 2D numerical test. Thus the 3D elastic compliance tensors are obtained, regarding to the topological relationship between the 2D and 3D elastic compliance tensors. For rock samples with three sets of orthogonal and continuous fractures, it is found that the maximum relative error of the main diagonal components of the elastic compliance tensor is less than 5%, comparing the results of the numerical test with analytical solutions. Therefore, the reliability and effectiveness of the numerical tests are verified. Finally, this method is applied to determine mechanical properties of Xiaowan Hydropower Station and the REV is approximately estimated as REV≈11×11×11m3.

Key words: three-dimensional elastic compliance tensor, mechanical representative elementary volume, stochastic fracture network, Monte Carlo method, composite element method.