Arch dams mainly rely on abutment to maintain stability. The heterogeneity of structural plane and the variability of the mechanical parameters in abutment rock mass bring great challenges to the accurate simulation of rock and the long-term stability evaluation of arch dam. Aiming at these challenges, The present work explores the construction method of fractal DFN (discrete fracture network) of fractured rock mass and carries out the research on its mechanical RVE (representative volume element). Firstly, the geometric characteristics of fractures are expressed by geometric parameters, and the distribution law of fractures is determined by the distribution function of geometric parameters. Subsequently, the LHS (Latin hypercube sampling) method is introduced to construct linear DFN. Considering its natural sawtooth characteristics, fractures with rough characteristics are generated by the IFS (Iterative function system) method, and the fractal DFN is constructed. On this basis, the finite element model of the fractal DFN is established, and the mechanical characteristics of fractures are simulated by the cohesive element model. As the inhomogeneity of fracture distribution, the variation coefficient is used to quantify the discreteness of parameters and determine the mechanical RVE of fractured rock mass. Finally, combined with the statistical data of exposed fractures in the left abutment of Jinping I arch dam, the fractal DFN is constructed, and the RVE size is determined to be 10 m. The construction of the fractal DFN and accurate determination of RVE lay a foundation for the analysis of geological engineering problems and study on long-term service of arch dams.