Development of various rock engineering projects demands more knowledge about deformability and strength properties of fractured rocks. Among different direct and indirect methods for determining mechanical parameters of rock mass, Discrete Fracture Network-Distinct Element Method (DFN-DEM) approach has comparatively prominence for considering discrete systems and interactions between intact rock matrix and fractures. Attempts have been conducted to measure aforementioned parameters in two dimensional media in the literature which may be overestimated compared to a three dimensional approximation. In this study, we use a numerical systematic method to determine fractured rock mass with irregular and stochastic fracture system, equivalent elastic parameters and strength in 3D. For this purpose, different DFN realizations were generated with Monte Carlo simulation based on geometric parameters and then compliance tensor and Representative Elementary Volume (REV) for rock mass deformability and strength in 3D were determined. The numerical modelling results show an anisotropy in deformability parameters in different directions. The rock mass equivalent deformability modulus compared to Young modulus of intact rock was decreased in vertical and horizontal directions about 48 and 62 percent respectively, which shows anisotropy behavior in two different directions. The approximated REV for rock mass deformability and strength properties was 1 m in three-dimensions where it was evaluated to be 5 m when 2D numerical analysis had been performed. The rock mass peak strength reduced drastically compared to unconfined strength of intact rock. Comparison of fitting a few two-dimensional and three-dimensional failure criteria shows that, failure criteria which estimates rock mass strength merely with empirical relations do not well match with numerical results. 3D failure criteria that consider the influence of mean principle stress, estimate different values for strength parameters compared to 2D shear failure criteria. Moreover, rock mass failure phenomena shows intensive dependency to the loading path.
