Wedge-shaped block spillways are an innovative typology that allows overflowing over the body of earth and rockfill dams in a safe and economic way, in front of the usual solutions of side concrete spillways. However, this solution has hardly been applied due to some uncertainties, related with the saturation process of the granular support layer and the stability effects induced on the blocks, as well as the lack of technical design procedures. In this thesis a complete procedure has been proposed to design wedge-shaped block spillways. The procedure has been automated through the development of a computer code. The development of the design procedure was based on several numerical campaigns, supported by physical validation tests. In such way the behavior of the drainage layer and its saturation conditions were characterized, a method for numerical-experimental fitting of parabolic head loss laws in porous media was developed, as well as a formulation to obtain a safety factor against mass sliding for partially saturated drainage layers. A specific numerical method was also calibrated and validated in order to reproduce the infiltration between blocks. Finally, the stability of wedge-shaped blocks was characterized against vandalism and hydraulic actions. According to these results a specific procedure was proposed to define the appropriate spillway geometry, to ensure the stability of the dam body, the drainage layer and the blocks.