Wedge shaped blocks (WSB) are attracting increasing attention as protection against overtopping for earth and rock-fill dams. However, there are limited examples of application and some aspects of the technology merit additional research and improvement. One key issue is the design of drainage and supporting layer for WSB protections. During overtopping, part of the overflow leaks through the joints between blocks, hence circulating through the granular material. The permeability and thickness of the supporting layer must be sufficient to prevent the flow from generating pressure on the bottom side of the blocks, which contributes to its destabilization. However, it must also be structurally stable to avoid undesirable deformations on the downstream face. Both the material permeability and the layer thickness determine the hydraulic behavior of this element. These, together with the weight of the blocks and the slope of the downstream face, directly influence mass and block stability. These aspects should be taken into account for the numerical modeling of seepage through the supporting layer. To this end, an application of the open source software Kratos Multi-physics was employed. A parametric study was conducted to quantify the influence of each design variable in the safety factor against mass sliding of the supporting and drainage layer.